TSTP Solution File: DAT073_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT073_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:05:55 EDT 2024
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 118
% Syntax : Number of formulae : 340 ( 38 unt; 12 typ; 0 def)
% Number of atoms : 1132 ( 207 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1358 ( 554 ~; 646 |; 49 &)
% ( 86 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 1471 ( 444 atm; 253 fun; 243 num; 531 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 25 ( 11 >; 14 *; 0 +; 0 <<)
% Number of predicates : 92 ( 86 usr; 84 prp; 0-3 aty)
% Number of functors : 14 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 676 ( 666 !; 10 ?; 676 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
array: $tType ).
tff(func_def_0,type,
read: ( array * $int ) > $int ).
tff(func_def_1,type,
write: ( array * $int * $int ) > array ).
tff(func_def_2,type,
init: $int > array ).
tff(func_def_3,type,
max: ( array * $int ) > $int ).
tff(func_def_5,type,
rev: ( array * $int ) > array ).
tff(func_def_10,type,
sK0: ( array * array ) > $int ).
tff(func_def_11,type,
sK1: ( array * $int * $int ) > $int ).
tff(func_def_12,type,
sK2: ( array * array * $int ) > $int ).
tff(pred_def_4,type,
sorted: ( array * $int ) > $o ).
tff(pred_def_6,type,
inRange: ( array * $int * $int ) > $o ).
tff(pred_def_7,type,
distinct: ( array * $int ) > $o ).
tff(f1785,plain,
$false,
inference(avatar_sat_refutation,[],[f73,f77,f81,f85,f89,f93,f97,f101,f105,f109,f119,f123,f135,f139,f143,f168,f190,f196,f205,f214,f228,f232,f249,f253,f262,f271,f285,f296,f300,f304,f349,f353,f372,f376,f380,f384,f406,f448,f452,f456,f460,f464,f629,f633,f637,f641,f645,f714,f722,f726,f730,f734,f823,f827,f831,f835,f839,f996,f1000,f1026,f1030,f1036,f1040,f1091,f1095,f1101,f1105,f1111,f1115,f1119,f1123,f1127,f1139,f1143,f1162,f1166,f1180,f1195,f1199,f1225,f1229,f1238,f1733,f1784]) ).
tff(f1784,plain,
( ~ spl3_5
| ~ spl3_83 ),
inference(avatar_contradiction_clause,[],[f1783]) ).
tff(f1783,plain,
( $false
| ~ spl3_5
| ~ spl3_83 ),
inference(evaluation,[],[f1776]) ).
tff(f1776,plain,
( $less(0,0)
| $less($uminus(-1),0)
| ~ spl3_5
| ~ spl3_83 ),
inference(superposition,[],[f1732,f88]) ).
tff(f88,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f87]) ).
tff(f87,plain,
( spl3_5
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
tff(f1732,plain,
( ! [X0: $int] :
( $less($sum(-1,X0),0)
| $less(X0,0) )
| ~ spl3_83 ),
inference(avatar_component_clause,[],[f1731]) ).
tff(f1731,plain,
( spl3_83
<=> ! [X0: $int] :
( $less(X0,0)
| $less($sum(-1,X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_83])]) ).
tff(f1733,plain,
( spl3_83
| ~ spl3_37
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f1082,f994,f404,f1731]) ).
tff(f404,plain,
( spl3_37
<=> ! [X0: $int] : $less($sum(-1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
tff(f994,plain,
( spl3_59
<=> ! [X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,0)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).
tff(f1082,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($sum(-1,X0),0) )
| ~ spl3_37
| ~ spl3_59 ),
inference(resolution,[],[f995,f405]) ).
tff(f405,plain,
( ! [X0: $int] : $less($sum(-1,X0),X0)
| ~ spl3_37 ),
inference(avatar_component_clause,[],[f404]) ).
tff(f995,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X1,0)
| $less(X0,0) )
| ~ spl3_59 ),
inference(avatar_component_clause,[],[f994]) ).
tff(f1238,plain,
( ~ spl3_37
| ~ spl3_58 ),
inference(avatar_contradiction_clause,[],[f1234]) ).
tff(f1234,plain,
( $false
| ~ spl3_37
| ~ spl3_58 ),
inference(resolution,[],[f992,f405]) ).
tff(f992,plain,
( ! [X2: $int] : ~ $less(X2,0)
| ~ spl3_58 ),
inference(avatar_component_clause,[],[f991]) ).
tff(f991,plain,
( spl3_58
<=> ! [X2: $int] : ~ $less(X2,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).
tff(f1229,plain,
( spl3_82
| ~ spl3_6
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f290,f283,f91,f1227]) ).
tff(f1227,plain,
( spl3_82
<=> ! [X2: array,X0: $int,X1: $int] :
( ( read(X2,sK2(init(X0),X2,X1)) != X0 )
| ( rev(init(X0),X1) = X2 )
| ~ $less(sK2(init(X0),X2,X1),X1)
| $less(sK2(init(X0),X2,X1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_82])]) ).
tff(f91,plain,
( spl3_6
<=> ! [X0: $int,X1: $int] : ( read(init(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
tff(f283,plain,
( spl3_27
<=> ! [X2: $int,X0: array,X1: array] :
( ( read(X1,sK2(X0,X1,X2)) != read(X0,$sum(X2,$uminus($sum(1,sK2(X0,X1,X2))))) )
| ( rev(X0,X2) = X1 )
| ~ $less(sK2(X0,X1,X2),X2)
| $less(sK2(X0,X1,X2),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
tff(f290,plain,
( ! [X2: array,X0: $int,X1: $int] :
( ( read(X2,sK2(init(X0),X2,X1)) != X0 )
| ( rev(init(X0),X1) = X2 )
| ~ $less(sK2(init(X0),X2,X1),X1)
| $less(sK2(init(X0),X2,X1),0) )
| ~ spl3_6
| ~ spl3_27 ),
inference(superposition,[],[f284,f92]) ).
tff(f92,plain,
( ! [X0: $int,X1: $int] : ( read(init(X0),X1) = X0 )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f91]) ).
tff(f284,plain,
( ! [X2: $int,X0: array,X1: array] :
( ( read(X1,sK2(X0,X1,X2)) != read(X0,$sum(X2,$uminus($sum(1,sK2(X0,X1,X2))))) )
| ( rev(X0,X2) = X1 )
| ~ $less(sK2(X0,X1,X2),X2)
| $less(sK2(X0,X1,X2),0) )
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f283]) ).
tff(f1225,plain,
( spl3_81
| ~ spl3_12
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f233,f226,f121,f1223]) ).
tff(f1223,plain,
( spl3_81
<=> ! [X2: array,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ( read(X2,X0) = max(X2,X1) )
| $less(0,sK1(X2,X1,read(X2,X0)))
| ( 0 = sK1(X2,X1,read(X2,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_81])]) ).
tff(f121,plain,
( spl3_12
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
tff(f226,plain,
( spl3_21
<=> ! [X0: array,X1: $int,X3: $int] :
( ( read(X0,X3) = max(X0,X1) )
| $less(X3,0)
| ~ $less(X3,X1)
| ~ $less(sK1(X0,X1,read(X0,X3)),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
tff(f233,plain,
( ! [X2: array,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ( read(X2,X0) = max(X2,X1) )
| $less(0,sK1(X2,X1,read(X2,X0)))
| ( 0 = sK1(X2,X1,read(X2,X0)) ) )
| ~ spl3_12
| ~ spl3_21 ),
inference(resolution,[],[f227,f122]) ).
tff(f122,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f227,plain,
( ! [X3: $int,X0: array,X1: $int] :
( ~ $less(sK1(X0,X1,read(X0,X3)),0)
| $less(X3,0)
| ~ $less(X3,X1)
| ( read(X0,X3) = max(X0,X1) ) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f226]) ).
tff(f1199,plain,
( spl3_80
| ~ spl3_10
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f275,f269,f107,f1197]) ).
tff(f1197,plain,
( spl3_80
<=> ! [X0: array,X3: $int,X2: $int,X1: $int] :
( $less(X2,read(write(X0,X1,X2),sK1(write(X0,X1,X2),X3,X2)))
| $less(X1,0)
| ~ $less(X1,X3)
| ( max(write(X0,X1,X2),X3) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_80])]) ).
tff(f107,plain,
( spl3_10
<=> ! [X2: $int,X0: array,X1: $int] : ( read(write(X0,X1,X2),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
tff(f269,plain,
( spl3_26
<=> ! [X0: array,X1: $int,X3: $int] :
( ( read(X0,X3) = max(X0,X1) )
| $less(X3,0)
| ~ $less(X3,X1)
| $less(read(X0,X3),read(X0,sK1(X0,X1,read(X0,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
tff(f275,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int] :
( $less(X2,read(write(X0,X1,X2),sK1(write(X0,X1,X2),X3,X2)))
| $less(X1,0)
| ~ $less(X1,X3)
| ( max(write(X0,X1,X2),X3) = X2 ) )
| ~ spl3_10
| ~ spl3_26 ),
inference(superposition,[],[f270,f108]) ).
tff(f108,plain,
( ! [X2: $int,X0: array,X1: $int] : ( read(write(X0,X1,X2),X1) = X2 )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f107]) ).
tff(f270,plain,
( ! [X3: $int,X0: array,X1: $int] :
( $less(read(X0,X3),read(X0,sK1(X0,X1,read(X0,X3))))
| $less(X3,0)
| ~ $less(X3,X1)
| ( read(X0,X3) = max(X0,X1) ) )
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f269]) ).
tff(f1195,plain,
( spl3_79
| ~ spl3_11
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f273,f269,f117,f1193]) ).
tff(f1193,plain,
( spl3_79
<=> ! [X0: $int,X3: $int,X2: array,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ( read(X2,X0) = max(X2,X1) )
| ~ $less(X3,read(X2,X0))
| $less(X3,read(X2,sK1(X2,X1,read(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_79])]) ).
tff(f117,plain,
( spl3_11
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
tff(f273,plain,
( ! [X2: array,X3: $int,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ( read(X2,X0) = max(X2,X1) )
| ~ $less(X3,read(X2,X0))
| $less(X3,read(X2,sK1(X2,X1,read(X2,X0)))) )
| ~ spl3_11
| ~ spl3_26 ),
inference(resolution,[],[f270,f118]) ).
tff(f118,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f1180,plain,
( spl3_78
| ~ spl3_9
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f241,f230,f103,f1178]) ).
tff(f1178,plain,
( spl3_78
<=> ! [X2: array,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,$sum(X1,1))
| ( read(X2,X0) = max(X2,$sum(X1,1)) )
| ~ $less(X1,sK1(X2,$sum(X1,1),read(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_78])]) ).
tff(f103,plain,
( spl3_9
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
tff(f230,plain,
( spl3_22
<=> ! [X0: array,X1: $int,X3: $int] :
( ( read(X0,X3) = max(X0,X1) )
| $less(X3,0)
| ~ $less(X3,X1)
| $less(sK1(X0,X1,read(X0,X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
tff(f241,plain,
( ! [X2: array,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,$sum(X1,1))
| ( read(X2,X0) = max(X2,$sum(X1,1)) )
| ~ $less(X1,sK1(X2,$sum(X1,1),read(X2,X0))) )
| ~ spl3_9
| ~ spl3_22 ),
inference(resolution,[],[f231,f104]) ).
tff(f104,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f103]) ).
tff(f231,plain,
( ! [X3: $int,X0: array,X1: $int] :
( $less(sK1(X0,X1,read(X0,X3)),X1)
| $less(X3,0)
| ~ $less(X3,X1)
| ( read(X0,X3) = max(X0,X1) ) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f230]) ).
tff(f1166,plain,
( spl3_77
| ~ spl3_11
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f239,f230,f117,f1164]) ).
tff(f1164,plain,
( spl3_77
<=> ! [X0: $int,X3: $int,X2: array,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ( read(X2,X0) = max(X2,X1) )
| ~ $less(X3,sK1(X2,X1,read(X2,X0)))
| $less(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_77])]) ).
tff(f239,plain,
( ! [X2: array,X3: $int,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ( read(X2,X0) = max(X2,X1) )
| ~ $less(X3,sK1(X2,X1,read(X2,X0)))
| $less(X3,X1) )
| ~ spl3_11
| ~ spl3_22 ),
inference(resolution,[],[f231,f118]) ).
tff(f1162,plain,
( spl3_76
| ~ spl3_14
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f1068,f994,f137,f1160]) ).
tff(f1160,plain,
( spl3_76
<=> ! [X0: $int] :
( $less($sum(X0,1),0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_76])]) ).
tff(f137,plain,
( spl3_14
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
tff(f1068,plain,
( ! [X0: $int] :
( $less($sum(X0,1),0)
| $less(X0,0) )
| ~ spl3_14
| ~ spl3_59 ),
inference(resolution,[],[f995,f138]) ).
tff(f138,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f137]) ).
tff(f1143,plain,
( spl3_75
| ~ spl3_10
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f243,f230,f107,f1141]) ).
tff(f1141,plain,
( spl3_75
<=> ! [X0: array,X3: $int,X2: $int,X1: $int] :
( $less(sK1(write(X0,X1,X2),X3,X2),X3)
| $less(X1,0)
| ~ $less(X1,X3)
| ( max(write(X0,X1,X2),X3) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_75])]) ).
tff(f243,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int] :
( $less(sK1(write(X0,X1,X2),X3,X2),X3)
| $less(X1,0)
| ~ $less(X1,X3)
| ( max(write(X0,X1,X2),X3) = X2 ) )
| ~ spl3_10
| ~ spl3_22 ),
inference(superposition,[],[f231,f108]) ).
tff(f1139,plain,
( spl3_74
| ~ spl3_10
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f236,f226,f107,f1137]) ).
tff(f1137,plain,
( spl3_74
<=> ! [X0: array,X3: $int,X2: $int,X1: $int] :
( ~ $less(sK1(write(X0,X1,X2),X3,X2),0)
| $less(X1,0)
| ~ $less(X1,X3)
| ( max(write(X0,X1,X2),X3) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_74])]) ).
tff(f236,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int] :
( ~ $less(sK1(write(X0,X1,X2),X3,X2),0)
| $less(X1,0)
| ~ $less(X1,X3)
| ( max(write(X0,X1,X2),X3) = X2 ) )
| ~ spl3_10
| ~ spl3_21 ),
inference(superposition,[],[f227,f108]) ).
tff(f1127,plain,
( spl3_73
| ~ spl3_6
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f265,f251,f91,f1125]) ).
tff(f1125,plain,
( spl3_73
<=> ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(X1,init(X0),X2)) != X0 )
| ( init(X0) = rev(X1,X2) )
| $less(sK2(X1,init(X0),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_73])]) ).
tff(f251,plain,
( spl3_24
<=> ! [X2: $int,X0: array,X1: array] :
( ( rev(X0,X2) = X1 )
| ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| $less(sK2(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
tff(f265,plain,
( ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(X1,init(X0),X2)) != X0 )
| ( init(X0) = rev(X1,X2) )
| $less(sK2(X1,init(X0),X2),X2) )
| ~ spl3_6
| ~ spl3_24 ),
inference(superposition,[],[f252,f92]) ).
tff(f252,plain,
( ! [X2: $int,X0: array,X1: array] :
( ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| ( rev(X0,X2) = X1 )
| $less(sK2(X0,X1,X2),X2) )
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f251]) ).
tff(f1123,plain,
( spl3_72
| ~ spl3_6
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f263,f251,f91,f1121]) ).
tff(f1121,plain,
( spl3_72
<=> ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(init(X0),X1,X2)) != X0 )
| ( rev(init(X0),X2) = X1 )
| $less(sK2(init(X0),X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_72])]) ).
tff(f263,plain,
( ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(init(X0),X1,X2)) != X0 )
| ( rev(init(X0),X2) = X1 )
| $less(sK2(init(X0),X1,X2),X2) )
| ~ spl3_6
| ~ spl3_24 ),
inference(superposition,[],[f252,f92]) ).
tff(f1119,plain,
( spl3_71
| ~ spl3_25
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f1065,f994,f260,f1117]) ).
tff(f1117,plain,
( spl3_71
<=> ! [X0: $int] :
( $less($sum(1,X0),0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_71])]) ).
tff(f260,plain,
( spl3_25
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
tff(f1065,plain,
( ! [X0: $int] :
( $less($sum(1,X0),0)
| $less(X0,0) )
| ~ spl3_25
| ~ spl3_59 ),
inference(resolution,[],[f995,f261]) ).
tff(f261,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f260]) ).
tff(f1115,plain,
( spl3_70
| ~ spl3_6
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f256,f247,f91,f1113]) ).
tff(f1113,plain,
( spl3_70
<=> ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(X1,init(X0),X2)) != X0 )
| ( init(X0) = rev(X1,X2) )
| ~ $less(sK2(X1,init(X0),X2),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_70])]) ).
tff(f247,plain,
( spl3_23
<=> ! [X2: $int,X0: array,X1: array] :
( ( rev(X0,X2) = X1 )
| ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| ~ $less(sK2(X0,X1,X2),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
tff(f256,plain,
( ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(X1,init(X0),X2)) != X0 )
| ( init(X0) = rev(X1,X2) )
| ~ $less(sK2(X1,init(X0),X2),0) )
| ~ spl3_6
| ~ spl3_23 ),
inference(superposition,[],[f248,f92]) ).
tff(f248,plain,
( ! [X2: $int,X0: array,X1: array] :
( ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| ( rev(X0,X2) = X1 )
| ~ $less(sK2(X0,X1,X2),0) )
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f247]) ).
tff(f1111,plain,
( spl3_69
| ~ spl3_6
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f254,f247,f91,f1109]) ).
tff(f1109,plain,
( spl3_69
<=> ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(init(X0),X1,X2)) != X0 )
| ( rev(init(X0),X2) = X1 )
| ~ $less(sK2(init(X0),X1,X2),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).
tff(f254,plain,
( ! [X2: $int,X0: $int,X1: array] :
( ( read(X1,sK2(init(X0),X1,X2)) != X0 )
| ( rev(init(X0),X2) = X1 )
| ~ $less(sK2(init(X0),X1,X2),0) )
| ~ spl3_6
| ~ spl3_23 ),
inference(superposition,[],[f248,f92]) ).
tff(f1105,plain,
( spl3_68
| ~ spl3_17
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f224,f212,f188,f1103]) ).
tff(f1103,plain,
( spl3_68
<=> ! [X2: $int,X4: $int,X0: array,X5: $int,X3: $int,X1: $int] :
( ~ $less(read(X0,X3),0)
| $less(X3,0)
| ~ $less(X3,X4)
| ~ inRange(write(X0,X1,X2),X5,X4)
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).
tff(f188,plain,
( spl3_17
<=> ! [X0: array,X3: $int,X2: $int,X1: $int] :
( ( read(X0,X2) = read(write(X0,X1,X3),X2) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
tff(f212,plain,
( spl3_20
<=> ! [X0: array,X3: $int,X2: $int,X1: $int] :
( ~ $less(read(X0,X3),0)
| $less(X3,0)
| ~ $less(X3,X2)
| ~ inRange(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
tff(f224,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int,X4: $int,X5: $int] :
( ~ $less(read(X0,X3),0)
| $less(X3,0)
| ~ $less(X3,X4)
| ~ inRange(write(X0,X1,X2),X5,X4)
| ( X1 = X3 ) )
| ~ spl3_17
| ~ spl3_20 ),
inference(superposition,[],[f213,f189]) ).
tff(f189,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int] :
( ( read(X0,X2) = read(write(X0,X1,X3),X2) )
| ( X1 = X2 ) )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f213,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int] :
( ~ $less(read(X0,X3),0)
| $less(X3,0)
| ~ $less(X3,X2)
| ~ inRange(X0,X1,X2) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f212]) ).
tff(f1101,plain,
( spl3_67
| ~ spl3_17
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f219,f203,f188,f1099]) ).
tff(f1099,plain,
( spl3_67
<=> ! [X2: $int,X4: $int,X0: array,X5: $int,X3: $int,X1: $int] :
( ~ $less(X4,read(X0,X3))
| $less(X3,0)
| ~ $less(X3,X5)
| ~ inRange(write(X0,X1,X2),X4,X5)
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_67])]) ).
tff(f203,plain,
( spl3_19
<=> ! [X0: array,X3: $int,X2: $int,X1: $int] :
( ~ $less(X1,read(X0,X3))
| $less(X3,0)
| ~ $less(X3,X2)
| ~ inRange(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
tff(f219,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int,X4: $int,X5: $int] :
( ~ $less(X4,read(X0,X3))
| $less(X3,0)
| ~ $less(X3,X5)
| ~ inRange(write(X0,X1,X2),X4,X5)
| ( X1 = X3 ) )
| ~ spl3_17
| ~ spl3_19 ),
inference(superposition,[],[f204,f189]) ).
tff(f204,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int] :
( ~ $less(X1,read(X0,X3))
| $less(X3,0)
| ~ $less(X3,X2)
| ~ inRange(X0,X1,X2) )
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f203]) ).
tff(f1095,plain,
( spl3_66
| ~ spl3_12
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f220,f212,f121,f1093]) ).
tff(f1093,plain,
( spl3_66
<=> ! [X0: $int,X3: $int,X2: array,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ~ inRange(X2,X3,X1)
| $less(0,read(X2,X0))
| ( 0 = read(X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_66])]) ).
tff(f220,plain,
( ! [X2: array,X3: $int,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ~ inRange(X2,X3,X1)
| $less(0,read(X2,X0))
| ( 0 = read(X2,X0) ) )
| ~ spl3_12
| ~ spl3_20 ),
inference(resolution,[],[f213,f122]) ).
tff(f1091,plain,
( spl3_65
| ~ spl3_12
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f215,f203,f121,f1089]) ).
tff(f1089,plain,
( spl3_65
<=> ! [X0: $int,X3: $int,X2: array,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ~ inRange(X2,X3,X1)
| $less(read(X2,X0),X3)
| ( read(X2,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).
tff(f215,plain,
( ! [X2: array,X3: $int,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ~ inRange(X2,X3,X1)
| $less(read(X2,X0),X3)
| ( read(X2,X0) = X3 ) )
| ~ spl3_12
| ~ spl3_19 ),
inference(resolution,[],[f204,f122]) ).
tff(f1040,plain,
( spl3_64
| ~ spl3_6
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f242,f230,f91,f1038]) ).
tff(f1038,plain,
( spl3_64
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(sK1(init(X0),X2,X0),X2)
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).
tff(f242,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(sK1(init(X0),X2,X0),X2)
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) )
| ~ spl3_6
| ~ spl3_22 ),
inference(superposition,[],[f231,f92]) ).
tff(f1036,plain,
( spl3_63
| ~ spl3_6
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f235,f226,f91,f1034]) ).
tff(f1034,plain,
( spl3_63
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(sK1(init(X0),X2,X0),0)
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_63])]) ).
tff(f235,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(sK1(init(X0),X2,X0),0)
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) )
| ~ spl3_6
| ~ spl3_21 ),
inference(superposition,[],[f227,f92]) ).
tff(f1030,plain,
( spl3_62
| ~ spl3_10
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f223,f212,f107,f1028]) ).
tff(f1028,plain,
( spl3_62
<=> ! [X4: $int,X0: array,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less(X1,0)
| ~ $less(X1,X3)
| ~ inRange(write(X0,X1,X2),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_62])]) ).
tff(f223,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int,X4: $int] :
( ~ $less(X2,0)
| $less(X1,0)
| ~ $less(X1,X3)
| ~ inRange(write(X0,X1,X2),X4,X3) )
| ~ spl3_10
| ~ spl3_20 ),
inference(superposition,[],[f213,f108]) ).
tff(f1026,plain,
( spl3_61
| ~ spl3_10
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f218,f203,f107,f1024]) ).
tff(f1024,plain,
( spl3_61
<=> ! [X4: $int,X0: array,X3: $int,X2: $int,X1: $int] :
( ~ $less(X3,X2)
| $less(X1,0)
| ~ $less(X1,X4)
| ~ inRange(write(X0,X1,X2),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_61])]) ).
tff(f218,plain,
( ! [X2: $int,X3: $int,X0: array,X1: $int,X4: $int] :
( ~ $less(X3,X2)
| $less(X1,0)
| ~ $less(X1,X4)
| ~ inRange(write(X0,X1,X2),X3,X4) )
| ~ spl3_10
| ~ spl3_19 ),
inference(superposition,[],[f204,f108]) ).
tff(f1000,plain,
( spl3_60
| ~ spl3_6
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f279,f269,f91,f998]) ).
tff(f998,plain,
( spl3_60
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X0)
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).
tff(f279,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X0)
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) )
| ~ spl3_6
| ~ spl3_26 ),
inference(forward_demodulation,[],[f274,f92]) ).
tff(f274,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,read(init(X0),sK1(init(X0),X2,X0)))
| $less(X1,0)
| ~ $less(X1,X2)
| ( max(init(X0),X2) = X0 ) )
| ~ spl3_6
| ~ spl3_26 ),
inference(superposition,[],[f270,f92]) ).
tff(f996,plain,
( spl3_58
| spl3_59
| ~ spl3_1
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f989,f837,f71,f994,f991]) ).
tff(f71,plain,
( spl3_1
<=> ! [X0: array,X1: $int] :
( inRange(X0,max(X0,X1),X1)
| $less(X1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f837,plain,
( spl3_57
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,0)
| $less(X1,0)
| ~ $less(X1,X2)
| ~ inRange(init(X0),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_57])]) ).
tff(f989,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X0,X1)
| ~ $less(X2,0)
| $less(X1,0) )
| ~ spl3_1
| ~ spl3_57 ),
inference(resolution,[],[f838,f72]) ).
tff(f72,plain,
( ! [X0: array,X1: $int] :
( inRange(X0,max(X0,X1),X1)
| $less(X1,0) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f71]) ).
tff(f838,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ inRange(init(X0),X3,X2)
| $less(X1,0)
| ~ $less(X1,X2)
| ~ $less(X0,0) )
| ~ spl3_57 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f839,plain,
( spl3_57
| ~ spl3_6
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f222,f212,f91,f837]) ).
tff(f222,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,0)
| $less(X1,0)
| ~ $less(X1,X2)
| ~ inRange(init(X0),X3,X2) )
| ~ spl3_6
| ~ spl3_20 ),
inference(superposition,[],[f213,f92]) ).
tff(f835,plain,
( spl3_56
| ~ spl3_6
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f217,f203,f91,f833]) ).
tff(f833,plain,
( spl3_56
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,X0)
| $less(X1,0)
| ~ $less(X1,X3)
| ~ inRange(init(X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_56])]) ).
tff(f217,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,X0)
| $less(X1,0)
| ~ $less(X1,X3)
| ~ inRange(init(X0),X2,X3) )
| ~ spl3_6
| ~ spl3_19 ),
inference(superposition,[],[f204,f92]) ).
tff(f831,plain,
( spl3_55
| ~ spl3_15
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f179,f166,f141,f829]) ).
tff(f829,plain,
( spl3_55
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).
tff(f141,plain,
( spl3_15
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
tff(f166,plain,
( spl3_16
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
tff(f179,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl3_15
| ~ spl3_16 ),
inference(superposition,[],[f142,f167]) ).
tff(f167,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f166]) ).
tff(f142,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f141]) ).
tff(f827,plain,
( spl3_54
| ~ spl3_15
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f178,f166,f141,f825]) ).
tff(f825,plain,
( spl3_54
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).
tff(f178,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl3_15
| ~ spl3_16 ),
inference(superposition,[],[f142,f167]) ).
tff(f823,plain,
( spl3_53
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f172,f166,f133,f821]) ).
tff(f821,plain,
( spl3_53
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).
tff(f133,plain,
( spl3_13
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
tff(f172,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(superposition,[],[f167,f134]) ).
tff(f134,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f734,plain,
( spl3_52
| ~ spl3_13
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f164,f141,f133,f732]) ).
tff(f732,plain,
( spl3_52
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_52])]) ).
tff(f164,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl3_13
| ~ spl3_15 ),
inference(superposition,[],[f142,f134]) ).
tff(f730,plain,
( spl3_51
| ~ spl3_13
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f160,f141,f133,f728]) ).
tff(f728,plain,
( spl3_51
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_51])]) ).
tff(f160,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl3_13
| ~ spl3_15 ),
inference(superposition,[],[f142,f134]) ).
tff(f726,plain,
( spl3_50
| ~ spl3_11
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f156,f141,f117,f724]) ).
tff(f724,plain,
( spl3_50
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_50])]) ).
tff(f156,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl3_11
| ~ spl3_15 ),
inference(resolution,[],[f142,f118]) ).
tff(f722,plain,
( spl3_49
| ~ spl3_9
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f126,f121,f103,f720]) ).
tff(f720,plain,
( spl3_49
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_49])]) ).
tff(f126,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl3_9
| ~ spl3_12 ),
inference(resolution,[],[f122,f104]) ).
tff(f714,plain,
( spl3_48
| ~ spl3_41
| ~ spl3_42 ),
inference(avatar_split_clause,[],[f625,f462,f458,f712]) ).
tff(f712,plain,
( spl3_48
<=> ! [X0: array] : ( rev(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_48])]) ).
tff(f458,plain,
( spl3_41
<=> ! [X0: array,X1: $int] :
( ( rev(X0,X1) = X0 )
| ~ $less(sK2(X0,X0,X1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
tff(f462,plain,
( spl3_42
<=> ! [X0: array,X1: $int] :
( ( rev(X0,X1) = X0 )
| $less(sK2(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
tff(f625,plain,
( ! [X0: array] : ( rev(X0,0) = X0 )
| ~ spl3_41
| ~ spl3_42 ),
inference(duplicate_literal_removal,[],[f619]) ).
tff(f619,plain,
( ! [X0: array] :
( ( rev(X0,0) = X0 )
| ( rev(X0,0) = X0 ) )
| ~ spl3_41
| ~ spl3_42 ),
inference(resolution,[],[f463,f459]) ).
tff(f459,plain,
( ! [X0: array,X1: $int] :
( ~ $less(sK2(X0,X0,X1),0)
| ( rev(X0,X1) = X0 ) )
| ~ spl3_41 ),
inference(avatar_component_clause,[],[f458]) ).
tff(f463,plain,
( ! [X0: array,X1: $int] :
( $less(sK2(X0,X0,X1),X1)
| ( rev(X0,X1) = X0 ) )
| ~ spl3_42 ),
inference(avatar_component_clause,[],[f462]) ).
tff(f645,plain,
( spl3_47
| ~ spl3_6
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f199,f194,f91,f643]) ).
tff(f643,plain,
( spl3_47
<=> ! [X0: $int,X1: array] :
( ( read(X1,sK0(X1,init(X0))) != X0 )
| ( init(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_47])]) ).
tff(f194,plain,
( spl3_18
<=> ! [X0: array,X1: array] :
( ( X0 = X1 )
| ( read(X0,sK0(X0,X1)) != read(X1,sK0(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
tff(f199,plain,
( ! [X0: $int,X1: array] :
( ( read(X1,sK0(X1,init(X0))) != X0 )
| ( init(X0) = X1 ) )
| ~ spl3_6
| ~ spl3_18 ),
inference(superposition,[],[f195,f92]) ).
tff(f195,plain,
( ! [X0: array,X1: array] :
( ( read(X0,sK0(X0,X1)) != read(X1,sK0(X0,X1)) )
| ( X0 = X1 ) )
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f194]) ).
tff(f641,plain,
( spl3_46
| ~ spl3_6
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f197,f194,f91,f639]) ).
tff(f639,plain,
( spl3_46
<=> ! [X0: $int,X1: array] :
( ( read(X1,sK0(init(X0),X1)) != X0 )
| ( init(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_46])]) ).
tff(f197,plain,
( ! [X0: $int,X1: array] :
( ( read(X1,sK0(init(X0),X1)) != X0 )
| ( init(X0) = X1 ) )
| ~ spl3_6
| ~ spl3_18 ),
inference(superposition,[],[f195,f92]) ).
tff(f637,plain,
( spl3_45
| ~ spl3_8
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f183,f166,f99,f635]) ).
tff(f635,plain,
( spl3_45
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).
tff(f99,plain,
( spl3_8
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
tff(f183,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl3_8
| ~ spl3_16 ),
inference(superposition,[],[f100,f167]) ).
tff(f100,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f99]) ).
tff(f633,plain,
( spl3_44
| ~ spl3_9
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f182,f166,f103,f631]) ).
tff(f631,plain,
( spl3_44
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).
tff(f182,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl3_9
| ~ spl3_16 ),
inference(superposition,[],[f104,f167]) ).
tff(f629,plain,
( spl3_43
| ~ spl3_11
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f127,f121,f117,f627]) ).
tff(f627,plain,
( spl3_43
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
tff(f127,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl3_11
| ~ spl3_12 ),
inference(resolution,[],[f122,f118]) ).
tff(f464,plain,
( spl3_42
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f267,f251,f462]) ).
tff(f267,plain,
( ! [X0: array,X1: $int] :
( ( rev(X0,X1) = X0 )
| $less(sK2(X0,X0,X1),X1) )
| ~ spl3_24 ),
inference(equality_resolution,[],[f252]) ).
tff(f460,plain,
( spl3_41
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f258,f247,f458]) ).
tff(f258,plain,
( ! [X0: array,X1: $int] :
( ( rev(X0,X1) = X0 )
| ~ $less(sK2(X0,X0,X1),0) )
| ~ spl3_23 ),
inference(equality_resolution,[],[f248]) ).
tff(f456,plain,
( spl3_40
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f175,f166,f95,f454]) ).
tff(f454,plain,
( spl3_40
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
tff(f95,plain,
( spl3_7
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
tff(f175,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl3_7
| ~ spl3_16 ),
inference(superposition,[],[f167,f96]) ).
tff(f96,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f95]) ).
tff(f452,plain,
( spl3_39
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f170,f166,f95,f450]) ).
tff(f450,plain,
( spl3_39
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
tff(f170,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(superposition,[],[f167,f96]) ).
tff(f448,plain,
( spl3_38
| ~ spl3_8
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f124,f117,f99,f446]) ).
tff(f446,plain,
( spl3_38
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
tff(f124,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl3_8
| ~ spl3_11 ),
inference(resolution,[],[f118,f100]) ).
tff(f406,plain,
( spl3_37
| ~ spl3_25
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f344,f302,f260,f404]) ).
tff(f302,plain,
( spl3_30
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
tff(f344,plain,
( ! [X0: $int] : $less($sum(-1,X0),X0)
| ~ spl3_25
| ~ spl3_30 ),
inference(evaluation,[],[f338]) ).
tff(f338,plain,
( ! [X0: $int] : $less($sum($uminus(1),X0),X0)
| ~ spl3_25
| ~ spl3_30 ),
inference(superposition,[],[f261,f303]) ).
tff(f303,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f302]) ).
tff(f384,plain,
( spl3_36
| ~ spl3_5
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f174,f166,f87,f382]) ).
tff(f382,plain,
( spl3_36
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
tff(f174,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl3_5
| ~ spl3_16 ),
inference(superposition,[],[f167,f88]) ).
tff(f380,plain,
( spl3_35
| ~ spl3_7
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f162,f141,f95,f378]) ).
tff(f378,plain,
( spl3_35
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
tff(f162,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl3_7
| ~ spl3_15 ),
inference(superposition,[],[f142,f96]) ).
tff(f376,plain,
( spl3_34
| ~ spl3_7
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f158,f141,f95,f374]) ).
tff(f374,plain,
( spl3_34
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
tff(f158,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl3_7
| ~ spl3_15 ),
inference(superposition,[],[f142,f96]) ).
tff(f372,plain,
( spl3_33
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f145,f133,f95,f370]) ).
tff(f370,plain,
( spl3_33
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
tff(f145,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(superposition,[],[f134,f96]) ).
tff(f353,plain,
( spl3_32
| ~ spl3_5
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f161,f141,f87,f351]) ).
tff(f351,plain,
( spl3_32
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
tff(f161,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl3_5
| ~ spl3_15 ),
inference(superposition,[],[f142,f88]) ).
tff(f349,plain,
( spl3_31
| ~ spl3_5
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f157,f141,f87,f347]) ).
tff(f347,plain,
( spl3_31
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
tff(f157,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl3_5
| ~ spl3_15 ),
inference(superposition,[],[f142,f88]) ).
tff(f304,plain,
( spl3_30
| ~ spl3_5
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f184,f166,f87,f302]) ).
tff(f184,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl3_5
| ~ spl3_16 ),
inference(evaluation,[],[f169]) ).
tff(f169,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl3_5
| ~ spl3_16 ),
inference(superposition,[],[f167,f88]) ).
tff(f300,plain,
( spl3_29
| ~ spl3_7
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f114,f103,f95,f298]) ).
tff(f298,plain,
( spl3_29
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
tff(f114,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl3_7
| ~ spl3_9 ),
inference(superposition,[],[f104,f96]) ).
tff(f296,plain,
( spl3_28
| ~ spl3_7
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f111,f99,f95,f294]) ).
tff(f294,plain,
( spl3_28
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
tff(f111,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl3_7
| ~ spl3_8 ),
inference(superposition,[],[f100,f96]) ).
tff(f285,plain,
spl3_27,
inference(avatar_split_clause,[],[f69,f283]) ).
tff(f69,plain,
! [X2: $int,X0: array,X1: array] :
( ( read(X1,sK2(X0,X1,X2)) != read(X0,$sum(X2,$uminus($sum(1,sK2(X0,X1,X2))))) )
| ( rev(X0,X2) = X1 )
| ~ $less(sK2(X0,X1,X2),X2)
| $less(sK2(X0,X1,X2),0) ),
inference(forward_demodulation,[],[f60,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f60,plain,
! [X2: $int,X0: array,X1: array] :
( ( rev(X0,X2) = X1 )
| ( read(X1,sK2(X0,X1,X2)) != read(X0,$sum(X2,$uminus($sum(sK2(X0,X1,X2),1)))) )
| ~ $less(sK2(X0,X1,X2),X2)
| $less(sK2(X0,X1,X2),0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: array,X1: array,X2: $int] :
( ( rev(X0,X2) = X1 )
| ( ( ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| ( $less(sK2(X0,X1,X2),X2)
& ~ $less(sK2(X0,X1,X2),0) ) )
& ( ( read(X1,sK2(X0,X1,X2)) != read(X0,$sum(X2,$uminus($sum(sK2(X0,X1,X2),1)))) )
| ~ $less(sK2(X0,X1,X2),X2)
| $less(sK2(X0,X1,X2),0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f44,f51]) ).
tff(f51,plain,
! [X0: array,X1: array,X2: $int] :
( ? [X3: $int] :
( ( ( read(X0,X3) != read(X1,X3) )
| ( $less(X3,X2)
& ~ $less(X3,0) ) )
& ( ( read(X1,X3) != read(X0,$sum(X2,$uminus($sum(X3,1)))) )
| ~ $less(X3,X2)
| $less(X3,0) ) )
=> ( ( ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| ( $less(sK2(X0,X1,X2),X2)
& ~ $less(sK2(X0,X1,X2),0) ) )
& ( ( read(X1,sK2(X0,X1,X2)) != read(X0,$sum(X2,$uminus($sum(sK2(X0,X1,X2),1)))) )
| ~ $less(sK2(X0,X1,X2),X2)
| $less(sK2(X0,X1,X2),0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f44,plain,
! [X0: array,X1: array,X2: $int] :
( ( rev(X0,X2) = X1 )
| ? [X3: $int] :
( ( ( read(X0,X3) != read(X1,X3) )
| ( $less(X3,X2)
& ~ $less(X3,0) ) )
& ( ( read(X1,X3) != read(X0,$sum(X2,$uminus($sum(X3,1)))) )
| ~ $less(X3,X2)
| $less(X3,0) ) ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: array,X1: array,X2: $int] :
( ! [X3: $int] :
( ( ( read(X0,X3) = read(X1,X3) )
& ( ~ $less(X3,X2)
| $less(X3,0) ) )
| ( ( read(X1,X3) = read(X0,$sum(X2,$uminus($sum(X3,1)))) )
& $less(X3,X2)
& ~ $less(X3,0) ) )
=> ( rev(X0,X2) = X1 ) ),
inference(rectify,[],[f16]) ).
tff(f16,plain,
! [X0: array,X4: array,X5: $int] :
( ! [X1: $int] :
( ( ( read(X0,X1) = read(X4,X1) )
& ( ~ $less(X1,X5)
| $less(X1,0) ) )
| ( ( read(X4,X1) = read(X0,$sum(X5,$uminus($sum(X1,1)))) )
& $less(X1,X5)
& ~ $less(X1,0) ) )
=> ( rev(X0,X5) = X4 ) ),
inference(theory_normalization,[],[f9]) ).
tff(f9,axiom,
! [X0: array,X4: array,X5: $int] :
( ! [X1: $int] :
( ( ( read(X0,X1) = read(X4,X1) )
& ( $greatereq(X1,X5)
| $greater(0,X1) ) )
| ( ( read(X4,X1) = read(X0,$difference(X5,$sum(X1,1))) )
& $greater(X5,X1)
& $greatereq(X1,0) ) )
=> ( rev(X0,X5) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rev_n1_proper) ).
tff(f271,plain,
spl3_26,
inference(avatar_split_clause,[],[f66,f269]) ).
tff(f66,plain,
! [X3: $int,X0: array,X1: $int] :
( ( read(X0,X3) = max(X0,X1) )
| $less(X3,0)
| ~ $less(X3,X1)
| $less(read(X0,X3),read(X0,sK1(X0,X1,read(X0,X3)))) ),
inference(equality_resolution,[],[f59]) ).
tff(f59,plain,
! [X2: $int,X3: $int,X0: array,X1: $int] :
( ( max(X0,X1) = X2 )
| ( read(X0,X3) != X2 )
| $less(X3,0)
| ~ $less(X3,X1)
| $less(X2,read(X0,sK1(X0,X1,X2))) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: array,X1: $int,X2: $int] :
( ( max(X0,X1) = X2 )
| ! [X3: $int] :
( ( read(X0,X3) != X2 )
| $less(X3,0)
| ~ $less(X3,X1) )
| ( $less(X2,read(X0,sK1(X0,X1,X2)))
& ~ $less(sK1(X0,X1,X2),0)
& $less(sK1(X0,X1,X2),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f43,f49]) ).
tff(f49,plain,
! [X0: array,X1: $int,X2: $int] :
( ? [X4: $int] :
( $less(X2,read(X0,X4))
& ~ $less(X4,0)
& $less(X4,X1) )
=> ( $less(X2,read(X0,sK1(X0,X1,X2)))
& ~ $less(sK1(X0,X1,X2),0)
& $less(sK1(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f43,plain,
! [X0: array,X1: $int,X2: $int] :
( ( max(X0,X1) = X2 )
| ! [X3: $int] :
( ( read(X0,X3) != X2 )
| $less(X3,0)
| ~ $less(X3,X1) )
| ? [X4: $int] :
( $less(X2,read(X0,X4))
& ~ $less(X4,0)
& $less(X4,X1) ) ),
inference(flattening,[],[f42]) ).
tff(f42,plain,
! [X0: array,X1: $int,X2: $int] :
( ( max(X0,X1) = X2 )
| ! [X3: $int] :
( ( read(X0,X3) != X2 )
| $less(X3,0)
| ~ $less(X3,X1) )
| ? [X4: $int] :
( $less(X2,read(X0,X4))
& ~ $less(X4,0)
& $less(X4,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: array,X1: $int,X2: $int] :
( ( ? [X3: $int] :
( ( read(X0,X3) = X2 )
& ~ $less(X3,0)
& $less(X3,X1) )
& ! [X4: $int] :
( ( ~ $less(X4,0)
& $less(X4,X1) )
=> ~ $less(X2,read(X0,X4)) ) )
=> ( max(X0,X1) = X2 ) ),
inference(rectify,[],[f15]) ).
tff(f15,plain,
! [X0: array,X5: $int,X6: $int] :
( ( ? [X1: $int] :
( ( read(X0,X1) = X6 )
& ~ $less(X1,0)
& $less(X1,X5) )
& ! [X1: $int] :
( ( ~ $less(X1,0)
& $less(X1,X5) )
=> ~ $less(X6,read(X0,X1)) ) )
=> ( max(X0,X5) = X6 ) ),
inference(theory_normalization,[],[f5]) ).
tff(f5,axiom,
! [X0: array,X5: $int,X6: $int] :
( ( ? [X1: $int] :
( ( read(X0,X1) = X6 )
& $greatereq(X1,0)
& $greater(X5,X1) )
& ! [X1: $int] :
( ( $greatereq(X1,0)
& $greater(X5,X1) )
=> $lesseq(read(X0,X1),X6) ) )
=> ( max(X0,X5) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(f262,plain,
( spl3_25
| ~ spl3_7
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f208,f137,f95,f260]) ).
tff(f208,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl3_7
| ~ spl3_14 ),
inference(superposition,[],[f138,f96]) ).
tff(f253,plain,
spl3_24,
inference(avatar_split_clause,[],[f62,f251]) ).
tff(f62,plain,
! [X2: $int,X0: array,X1: array] :
( ( rev(X0,X2) = X1 )
| ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| $less(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f52]) ).
tff(f249,plain,
spl3_23,
inference(avatar_split_clause,[],[f61,f247]) ).
tff(f61,plain,
! [X2: $int,X0: array,X1: array] :
( ( rev(X0,X2) = X1 )
| ( read(X0,sK2(X0,X1,X2)) != read(X1,sK2(X0,X1,X2)) )
| ~ $less(sK2(X0,X1,X2),0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f232,plain,
spl3_22,
inference(avatar_split_clause,[],[f68,f230]) ).
tff(f68,plain,
! [X3: $int,X0: array,X1: $int] :
( ( read(X0,X3) = max(X0,X1) )
| $less(X3,0)
| ~ $less(X3,X1)
| $less(sK1(X0,X1,read(X0,X3)),X1) ),
inference(equality_resolution,[],[f57]) ).
tff(f57,plain,
! [X2: $int,X3: $int,X0: array,X1: $int] :
( ( max(X0,X1) = X2 )
| ( read(X0,X3) != X2 )
| $less(X3,0)
| ~ $less(X3,X1)
| $less(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f50]) ).
tff(f228,plain,
spl3_21,
inference(avatar_split_clause,[],[f67,f226]) ).
tff(f67,plain,
! [X3: $int,X0: array,X1: $int] :
( ( read(X0,X3) = max(X0,X1) )
| $less(X3,0)
| ~ $less(X3,X1)
| ~ $less(sK1(X0,X1,read(X0,X3)),0) ),
inference(equality_resolution,[],[f58]) ).
tff(f58,plain,
! [X2: $int,X3: $int,X0: array,X1: $int] :
( ( max(X0,X1) = X2 )
| ( read(X0,X3) != X2 )
| $less(X3,0)
| ~ $less(X3,X1)
| ~ $less(sK1(X0,X1,X2),0) ),
inference(cnf_transformation,[],[f50]) ).
tff(f214,plain,
spl3_20,
inference(avatar_split_clause,[],[f64,f212]) ).
tff(f64,plain,
! [X2: $int,X3: $int,X0: array,X1: $int] :
( ~ $less(read(X0,X3),0)
| $less(X3,0)
| ~ $less(X3,X2)
| ~ inRange(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: array,X1: $int,X2: $int] :
( ! [X3: $int] :
( ( ~ $less(read(X0,X3),0)
& ~ $less(X1,read(X0,X3)) )
| $less(X3,0)
| ~ $less(X3,X2) )
| ~ inRange(X0,X1,X2) ),
inference(flattening,[],[f45]) ).
tff(f45,plain,
! [X0: array,X1: $int,X2: $int] :
( ! [X3: $int] :
( ( ~ $less(read(X0,X3),0)
& ~ $less(X1,read(X0,X3)) )
| $less(X3,0)
| ~ $less(X3,X2) )
| ~ inRange(X0,X1,X2) ),
inference(ennf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: array,X1: $int,X2: $int] :
( inRange(X0,X1,X2)
=> ! [X3: $int] :
( ( ~ $less(X3,0)
& $less(X3,X2) )
=> ( ~ $less(read(X0,X3),0)
& ~ $less(X1,read(X0,X3)) ) ) ),
inference(unused_predicate_definition_removal,[],[f37]) ).
tff(f37,plain,
! [X0: array,X1: $int,X2: $int] :
( inRange(X0,X1,X2)
<=> ! [X3: $int] :
( ( ~ $less(X3,0)
& $less(X3,X2) )
=> ( ~ $less(read(X0,X3),0)
& ~ $less(X1,read(X0,X3)) ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,plain,
! [X0: array,X7: $int,X5: $int] :
( inRange(X0,X7,X5)
<=> ! [X1: $int] :
( ( ~ $less(X1,0)
& $less(X1,X5) )
=> ( ~ $less(read(X0,X1),0)
& ~ $less(X7,read(X0,X1)) ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,axiom,
! [X0: array,X7: $int,X5: $int] :
( inRange(X0,X7,X5)
<=> ! [X1: $int] :
( ( $greatereq(X1,0)
& $greater(X5,X1) )
=> ( $greatereq(read(X0,X1),0)
& $greatereq(X7,read(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).
tff(f205,plain,
spl3_19,
inference(avatar_split_clause,[],[f63,f203]) ).
tff(f63,plain,
! [X2: $int,X3: $int,X0: array,X1: $int] :
( ~ $less(X1,read(X0,X3))
| $less(X3,0)
| ~ $less(X3,X2)
| ~ inRange(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tff(f196,plain,
spl3_18,
inference(avatar_split_clause,[],[f55,f194]) ).
tff(f55,plain,
! [X0: array,X1: array] :
( ( X0 = X1 )
| ( read(X0,sK0(X0,X1)) != read(X1,sK0(X0,X1)) ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: array,X1: array] :
( ( X0 = X1 )
| ( read(X0,sK0(X0,X1)) != read(X1,sK0(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f41,f47]) ).
tff(f47,plain,
! [X0: array,X1: array] :
( ? [X2: $int] : ( read(X0,X2) != read(X1,X2) )
=> ( read(X0,sK0(X0,X1)) != read(X1,sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
! [X0: array,X1: array] :
( ( X0 = X1 )
| ? [X2: $int] : ( read(X0,X2) != read(X1,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: array,X1: array] :
( ! [X2: $int] : ( read(X0,X2) = read(X1,X2) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: array,X4: array] :
( ! [X1: $int] : ( read(X0,X1) = read(X4,X1) )
=> ( X0 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ext) ).
tff(f190,plain,
spl3_17,
inference(avatar_split_clause,[],[f65,f188]) ).
tff(f65,plain,
! [X2: $int,X3: $int,X0: array,X1: $int] :
( ( read(X0,X2) = read(write(X0,X1,X3),X2) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0: array,X1: $int,X2: $int,X3: $int] :
( ( read(X0,X2) = read(write(X0,X1,X3),X2) )
| ( X1 = X2 ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: array,X1: $int,X3: $int,X2: $int] :
( ( read(write(X0,X1,X2),X3) = read(X0,X3) )
| ( X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f168,plain,
spl3_16,
inference(avatar_split_clause,[],[f19,f166]) ).
tff(f19,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f143,plain,
spl3_15,
inference(avatar_split_clause,[],[f26,f141]) ).
tff(f26,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f139,plain,
( spl3_14
| ~ spl3_2
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f110,f99,f75,f137]) ).
tff(f75,plain,
( spl3_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f110,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl3_2
| ~ spl3_8 ),
inference(resolution,[],[f100,f76]) ).
tff(f76,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f135,plain,
spl3_13,
inference(avatar_split_clause,[],[f21,f133]) ).
tff(f21,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f123,plain,
spl3_12,
inference(avatar_split_clause,[],[f25,f121]) ).
tff(f25,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f119,plain,
spl3_11,
inference(avatar_split_clause,[],[f24,f117]) ).
tff(f24,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f109,plain,
spl3_10,
inference(avatar_split_clause,[],[f56,f107]) ).
tff(f56,plain,
! [X2: $int,X0: array,X1: $int] : ( read(write(X0,X1,X2),X1) = X2 ),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: array,X1: $int,X2: $int] : ( read(write(X0,X1,X2),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f105,plain,
spl3_9,
inference(avatar_split_clause,[],[f29,f103]) ).
tff(f29,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f101,plain,
spl3_8,
inference(avatar_split_clause,[],[f27,f99]) ).
tff(f27,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f97,plain,
spl3_7,
inference(avatar_split_clause,[],[f18,f95]) ).
tff(f93,plain,
spl3_6,
inference(avatar_split_clause,[],[f54,f91]) ).
tff(f54,plain,
! [X0: $int,X1: $int] : ( read(init(X0),X1) = X0 ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: $int,X1: $int] : ( read(init(X0),X1) = X0 ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X2: $int,X1: $int] : ( read(init(X2),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f89,plain,
spl3_5,
inference(avatar_split_clause,[],[f22,f87]) ).
tff(f22,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f85,plain,
spl3_4,
inference(avatar_split_clause,[],[f28,f83]) ).
tff(f83,plain,
( spl3_4
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
tff(f28,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f81,plain,
spl3_3,
inference(avatar_split_clause,[],[f20,f79]) ).
tff(f79,plain,
( spl3_3
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
tff(f20,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f77,plain,
spl3_2,
inference(avatar_split_clause,[],[f23,f75]) ).
tff(f23,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f73,plain,
spl3_1,
inference(avatar_split_clause,[],[f53,f71]) ).
tff(f53,plain,
! [X0: array,X1: $int] :
( inRange(X0,max(X0,X1),X1)
| $less(X1,0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: array,X1: $int] :
( inRange(X0,max(X0,X1),X1)
| $less(X1,0) ),
inference(ennf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: array,X1: $int] :
( ~ $less(X1,0)
=> inRange(X0,max(X0,X1),X1) ),
inference(rectify,[],[f12]) ).
tff(f12,plain,
! [X0: array,X5: $int] :
( ~ $less(X5,0)
=> inRange(X0,max(X0,X5),X5) ),
inference(theory_normalization,[],[f11]) ).
tff(f11,negated_conjecture,
~ ~ ! [X0: array,X5: $int] :
( $greatereq(X5,0)
=> inRange(X0,max(X0,X5),X5) ),
inference(negated_conjecture,[],[f10]) ).
tff(f10,conjecture,
~ ! [X0: array,X5: $int] :
( $greatereq(X5,0)
=> inRange(X0,max(X0,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT073_1 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32 % Computer : n031.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri May 3 13:24:32 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % (24849)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.34 % (24852)WARNING: value z3 for option sas not known
% 0.19/0.34 % (24852)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)
% 0.19/0.34 % (24856)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)
% 0.19/0.34 % (24854)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)
% 0.19/0.34 % (24851)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.34 % (24850)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.34 % (24855)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)
% 0.19/0.34 % (24853)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.35 % (24851)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.35 % (24850)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.35 % (24850)Terminated due to inappropriate strategy.
% 0.19/0.35 % (24850)------------------------------
% 0.19/0.35 % (24850)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.35 % (24850)Termination reason: Inappropriate
% 0.19/0.35
% 0.19/0.35 % (24850)Memory used [KB]: 800
% 0.19/0.35 % (24850)Time elapsed: 0.003 s
% 0.19/0.35 % (24850)Instructions burned: 3 (million)
% 0.19/0.35 % (24851)Terminated due to inappropriate strategy.
% 0.19/0.35 % (24851)------------------------------
% 0.19/0.35 % (24851)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.35 % (24851)Termination reason: Inappropriate
% 0.19/0.35
% 0.19/0.35 % (24851)Memory used [KB]: 801
% 0.19/0.35 % (24851)Time elapsed: 0.003 s
% 0.19/0.35 % (24851)Instructions burned: 3 (million)
% 0.19/0.35 % (24850)------------------------------
% 0.19/0.35 % (24850)------------------------------
% 0.19/0.35 % (24853)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.35 % (24851)------------------------------
% 0.19/0.35 % (24851)------------------------------
% 0.19/0.35 % (24853)Terminated due to inappropriate strategy.
% 0.19/0.35 % (24853)------------------------------
% 0.19/0.35 % (24853)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.35 % (24853)Termination reason: Inappropriate
% 0.19/0.35
% 0.19/0.35 % (24853)Memory used [KB]: 800
% 0.19/0.35 % (24853)Time elapsed: 0.002 s
% 0.19/0.35 % (24853)Instructions burned: 3 (million)
% 0.19/0.35 % (24853)------------------------------
% 0.19/0.35 % (24853)------------------------------
% 0.19/0.36 % (24858)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.19/0.36 % (24859)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.19/0.36 % (24857)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.36 % (24857)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.36 % (24857)Terminated due to inappropriate strategy.
% 0.19/0.36 % (24857)------------------------------
% 0.19/0.36 % (24857)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.36 % (24857)Termination reason: Inappropriate
% 0.19/0.36
% 0.19/0.36 % (24857)Memory used [KB]: 800
% 0.19/0.36 % (24857)Time elapsed: 0.003 s
% 0.19/0.36 % (24857)Instructions burned: 3 (million)
% 0.19/0.36 % (24857)------------------------------
% 0.19/0.36 % (24857)------------------------------
% 0.19/0.38 % (24860)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.19/0.44 % (24854)First to succeed.
% 0.19/0.44 % (24854)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24849"
% 0.19/0.45 % (24854)Refutation found. Thanks to Tanya!
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45 % (24854)------------------------------
% 0.19/0.45 % (24854)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.45 % (24854)Termination reason: Refutation
% 0.19/0.45
% 0.19/0.45 % (24854)Memory used [KB]: 1764
% 0.19/0.45 % (24854)Time elapsed: 0.102 s
% 0.19/0.45 % (24854)Instructions burned: 195 (million)
% 0.19/0.45 % (24849)Success in time 0.115 s
%------------------------------------------------------------------------------