TSTP Solution File: ARI065_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI065_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 10:34:31 EDT 2024
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 75
% Syntax : Number of formulae : 230 ( 24 unt; 1 typ; 0 def)
% Number of atoms : 664 ( 76 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 805 ( 370 ~; 368 |; 4 &)
% ( 60 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 1047 ( 220 atm; 341 fun; 194 num; 292 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 63 ( 60 usr; 61 prp; 0-2 aty)
% Number of functors : 11 ( 1 usr; 9 con; 0-2 aty)
% Number of variables : 292 ( 290 !; 2 ?; 292 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(f1362,plain,
$false,
inference(avatar_sat_refutation,[],[f24,f29,f33,f37,f41,f45,f49,f53,f57,f67,f71,f83,f87,f101,f118,f141,f145,f159,f178,f182,f186,f190,f228,f232,f257,f261,f265,f269,f342,f346,f350,f355,f512,f516,f520,f587,f593,f597,f601,f703,f707,f711,f715,f883,f909,f913,f917,f921,f966,f970,f974,f978,f982,f986,f1053,f1340,f1345,f1350,f1355,f1360,f1361]) ).
tff(f1361,plain,
( spl1_1
| ~ spl1_22
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f1018,f964,f188,f21]) ).
tff(f21,plain,
( spl1_1
<=> ( 3 = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f188,plain,
( spl1_22
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f964,plain,
( spl1_49
<=> ! [X0: $int] : ( $sum(5,X0) = $sum(2,$sum(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
tff(f1018,plain,
( ( 3 = sK0 )
| ~ spl1_22
| ~ spl1_49 ),
inference(evaluation,[],[f992]) ).
tff(f992,plain,
( ( sK0 = $sum(5,$uminus(2)) )
| ~ spl1_22
| ~ spl1_49 ),
inference(superposition,[],[f965,f189]) ).
tff(f189,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f965,plain,
( ! [X0: $int] : ( $sum(5,X0) = $sum(2,$sum(X0,sK0)) )
| ~ spl1_49 ),
inference(avatar_component_clause,[],[f964]) ).
tff(f1360,plain,
( spl1_60
| ~ spl1_22
| ~ spl1_49
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f1346,f1343,f964,f188,f1358]) ).
tff(f1358,plain,
( spl1_60
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,3))
| ~ $less(2,X0)
| ~ $less(X1,5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
tff(f1343,plain,
( spl1_57
<=> ! [X0: $int,X1: $int] :
( ~ $less(2,X0)
| ~ $less(X1,5)
| $less(X1,$sum(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
tff(f1346,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,3))
| ~ $less(2,X0)
| ~ $less(X1,5) )
| ~ spl1_22
| ~ spl1_49
| ~ spl1_57 ),
inference(forward_demodulation,[],[f1344,f1018]) ).
tff(f1344,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(2,X0)
| ~ $less(X1,5)
| $less(X1,$sum(X0,sK0)) )
| ~ spl1_57 ),
inference(avatar_component_clause,[],[f1343]) ).
tff(f1355,plain,
( spl1_59
| ~ spl1_16
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f623,f591,f139,f1353]) ).
tff(f1353,plain,
( spl1_59
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(5,$sum(X1,sK0))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
tff(f139,plain,
( spl1_16
<=> ! [X0: $int] :
( $less(5,$sum(X0,sK0))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f591,plain,
( spl1_37
<=> ! [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,[spl1_37])]) ).
tff(f623,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(5,$sum(X1,sK0))
| ~ $less(2,X0) )
| ~ spl1_16
| ~ spl1_37 ),
inference(resolution,[],[f592,f140]) ).
tff(f140,plain,
( ! [X0: $int] :
( $less(5,$sum(X0,sK0))
| ~ $less(2,X0) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f139]) ).
tff(f592,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,X3))
| ~ $less(X0,X1)
| $less(X2,$sum(X1,X3)) )
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f591]) ).
tff(f1350,plain,
( spl1_58
| ~ spl1_10
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f151,f143,f65,f1348]) ).
tff(f1348,plain,
( spl1_58
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,2)
| ~ $less(X1,$sum(X0,sK0))
| $less(X1,5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
tff(f65,plain,
( spl1_10
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f143,plain,
( spl1_17
<=> ! [X0: $int] :
( $less($sum(X0,sK0),5)
| ~ $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f151,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,2)
| ~ $less(X1,$sum(X0,sK0))
| $less(X1,5) )
| ~ spl1_10
| ~ spl1_17 ),
inference(resolution,[],[f144,f66]) ).
tff(f66,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f65]) ).
tff(f144,plain,
( ! [X0: $int] :
( $less($sum(X0,sK0),5)
| ~ $less(X0,2) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f143]) ).
tff(f1345,plain,
( spl1_57
| ~ spl1_10
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f146,f139,f65,f1343]) ).
tff(f146,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(2,X0)
| ~ $less(X1,5)
| $less(X1,$sum(X0,sK0)) )
| ~ spl1_10
| ~ spl1_16 ),
inference(resolution,[],[f140,f66]) ).
tff(f1340,plain,
( spl1_56
| ~ spl1_18
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f221,f188,f157,f1338]) ).
tff(f1338,plain,
( spl1_56
<=> ! [X0: $int] : ( $sum(2,X0) = $sum(5,$sum($uminus(sK0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
tff(f157,plain,
( spl1_18
<=> ! [X0: $int] : ( $sum(2,$sum(sK0,X0)) = $sum(5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f221,plain,
( ! [X0: $int] : ( $sum(2,X0) = $sum(5,$sum($uminus(sK0),X0)) )
| ~ spl1_18
| ~ spl1_22 ),
inference(superposition,[],[f158,f189]) ).
tff(f158,plain,
( ! [X0: $int] : ( $sum(2,$sum(sK0,X0)) = $sum(5,X0) )
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f157]) ).
tff(f1053,plain,
( ~ spl1_55
| ~ spl1_21
| ~ spl1_47 ),
inference(avatar_split_clause,[],[f955,f915,f184,f1050]) ).
tff(f1050,plain,
( spl1_55
<=> $less(sK0,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f184,plain,
( spl1_21
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f915,plain,
( spl1_47
<=> ! [X0: $int] :
( $less(5,$sum(X0,2))
| ~ $less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
tff(f955,plain,
( ~ $less(sK0,1)
| ~ spl1_21
| ~ spl1_47 ),
inference(evaluation,[],[f947]) ).
tff(f947,plain,
( ~ $less(sK0,1)
| ~ $less(2,5)
| ~ spl1_21
| ~ spl1_47 ),
inference(resolution,[],[f916,f185]) ).
tff(f185,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f184]) ).
tff(f916,plain,
( ! [X0: $int] :
( $less(5,$sum(X0,2))
| ~ $less(sK0,X0) )
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f915]) ).
tff(f986,plain,
( spl1_54
| ~ spl1_2
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f698,f599,f26,f984]) ).
tff(f984,plain,
( spl1_54
<=> ! [X0: $int] :
( $less($sum(X0,-2),-5)
| ~ $less(X0,$uminus(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f26,plain,
( spl1_2
<=> ( 5 = $sum(2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f599,plain,
( spl1_39
<=> ! [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,[spl1_39])]) ).
tff(f698,plain,
( ! [X0: $int] :
( $less($sum(X0,-2),-5)
| ~ $less(X0,$uminus(sK0)) )
| ~ spl1_2
| ~ spl1_39 ),
inference(evaluation,[],[f687]) ).
tff(f687,plain,
( ! [X0: $int] :
( $less($sum(X0,$uminus(2)),$uminus(5))
| ~ $less(X0,$uminus(sK0)) )
| ~ spl1_2
| ~ spl1_39 ),
inference(superposition,[],[f600,f28]) ).
tff(f28,plain,
( ( 5 = $sum(2,sK0) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f26]) ).
tff(f600,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_39 ),
inference(avatar_component_clause,[],[f599]) ).
tff(f982,plain,
( spl1_53
| ~ spl1_2
| ~ spl1_38 ),
inference(avatar_split_clause,[],[f668,f595,f26,f980]) ).
tff(f980,plain,
( spl1_53
<=> ! [X0: $int] :
( $less(-5,$sum(X0,-2))
| ~ $less($uminus(sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f595,plain,
( spl1_38
<=> ! [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,[spl1_38])]) ).
tff(f668,plain,
( ! [X0: $int] :
( $less(-5,$sum(X0,-2))
| ~ $less($uminus(sK0),X0) )
| ~ spl1_2
| ~ spl1_38 ),
inference(evaluation,[],[f649]) ).
tff(f649,plain,
( ! [X0: $int] :
( $less($uminus(5),$sum(X0,$uminus(2)))
| ~ $less($uminus(sK0),X0) )
| ~ spl1_2
| ~ spl1_38 ),
inference(superposition,[],[f596,f28]) ).
tff(f596,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl1_38 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f978,plain,
( spl1_52
| ~ spl1_2
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f437,f348,f26,f976]) ).
tff(f976,plain,
( spl1_52
<=> ! [X0: $int] : ( $sum(2,$sum(sK0,X0)) = $sum(X0,5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
tff(f348,plain,
( spl1_31
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
tff(f437,plain,
( ! [X0: $int] : ( $sum(2,$sum(sK0,X0)) = $sum(X0,5) )
| ~ spl1_2
| ~ spl1_31 ),
inference(superposition,[],[f349,f28]) ).
tff(f349,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f348]) ).
tff(f974,plain,
( spl1_51
| ~ spl1_2
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f417,f348,f26,f972]) ).
tff(f972,plain,
( spl1_51
<=> ! [X0: $int] : ( $sum(X0,5) = $sum(sK0,$sum(X0,2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
tff(f417,plain,
( ! [X0: $int] : ( $sum(X0,5) = $sum(sK0,$sum(X0,2)) )
| ~ spl1_2
| ~ spl1_31 ),
inference(superposition,[],[f349,f28]) ).
tff(f970,plain,
( spl1_50
| ~ spl1_2
| ~ spl1_30 ),
inference(avatar_split_clause,[],[f372,f344,f26,f968]) ).
tff(f968,plain,
( spl1_50
<=> ! [X0: $int] : ( $sum(5,X0) = $sum(sK0,$sum(2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
tff(f344,plain,
( spl1_30
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f372,plain,
( ! [X0: $int] : ( $sum(5,X0) = $sum(sK0,$sum(2,X0)) )
| ~ spl1_2
| ~ spl1_30 ),
inference(superposition,[],[f345,f28]) ).
tff(f345,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f344]) ).
tff(f966,plain,
( spl1_49
| ~ spl1_7
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f161,f157,f47,f964]) ).
tff(f47,plain,
( spl1_7
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f161,plain,
( ! [X0: $int] : ( $sum(5,X0) = $sum(2,$sum(X0,sK0)) )
| ~ spl1_7
| ~ spl1_18 ),
inference(superposition,[],[f158,f48]) ).
tff(f48,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f921,plain,
( spl1_48
| ~ spl1_2
| ~ spl1_27 ),
inference(avatar_split_clause,[],[f331,f263,f26,f919]) ).
tff(f919,plain,
( spl1_48
<=> ! [X0: $int] :
( $less($sum(X0,2),5)
| ~ $less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
tff(f263,plain,
( spl1_27
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f331,plain,
( ! [X0: $int] :
( $less($sum(X0,2),5)
| ~ $less(X0,sK0) )
| ~ spl1_2
| ~ spl1_27 ),
inference(superposition,[],[f264,f28]) ).
tff(f264,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl1_27 ),
inference(avatar_component_clause,[],[f263]) ).
tff(f917,plain,
( spl1_47
| ~ spl1_2
| ~ spl1_26 ),
inference(avatar_split_clause,[],[f295,f259,f26,f915]) ).
tff(f259,plain,
( spl1_26
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f295,plain,
( ! [X0: $int] :
( $less(5,$sum(X0,2))
| ~ $less(sK0,X0) )
| ~ spl1_2
| ~ spl1_26 ),
inference(superposition,[],[f260,f28]) ).
tff(f260,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl1_26 ),
inference(avatar_component_clause,[],[f259]) ).
tff(f913,plain,
( spl1_46
| ~ spl1_7
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f152,f143,f47,f911]) ).
tff(f911,plain,
( spl1_46
<=> ! [X0: $int] :
( $less($sum(sK0,X0),5)
| ~ $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
tff(f152,plain,
( ! [X0: $int] :
( $less($sum(sK0,X0),5)
| ~ $less(X0,2) )
| ~ spl1_7
| ~ spl1_17 ),
inference(superposition,[],[f144,f48]) ).
tff(f909,plain,
( spl1_45
| ~ spl1_7
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f147,f139,f47,f907]) ).
tff(f907,plain,
( spl1_45
<=> ! [X0: $int] :
( $less(5,$sum(sK0,X0))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
tff(f147,plain,
( ! [X0: $int] :
( $less(5,$sum(sK0,X0))
| ~ $less(2,X0) )
| ~ spl1_7
| ~ spl1_16 ),
inference(superposition,[],[f140,f48]) ).
tff(f883,plain,
( spl1_44
| ~ spl1_2
| ~ spl1_18
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f581,f518,f157,f26,f881]) ).
tff(f881,plain,
( spl1_44
<=> ! [X0: $int] :
( $less(5,X0)
| $less(X0,6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
tff(f518,plain,
( spl1_35
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
tff(f581,plain,
( ! [X0: $int] :
( $less(5,X0)
| $less(X0,6) )
| ~ spl1_2
| ~ spl1_18
| ~ spl1_35 ),
inference(forward_demodulation,[],[f577,f28]) ).
tff(f577,plain,
( ! [X0: $int] :
( $less(X0,6)
| $less($sum(2,sK0),X0) )
| ~ spl1_18
| ~ spl1_35 ),
inference(evaluation,[],[f574]) ).
tff(f574,plain,
( ! [X0: $int] :
( $less(X0,$sum(5,1))
| $less($sum(2,sK0),X0) )
| ~ spl1_18
| ~ spl1_35 ),
inference(superposition,[],[f519,f158]) ).
tff(f519,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl1_35 ),
inference(avatar_component_clause,[],[f518]) ).
tff(f715,plain,
( spl1_43
| ~ spl1_2
| ~ spl1_18
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f556,f514,f157,f26,f713]) ).
tff(f713,plain,
( spl1_43
<=> ! [X0: $int] :
( ~ $less(5,X0)
| ~ $less(X0,6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
tff(f514,plain,
( spl1_34
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
tff(f556,plain,
( ! [X0: $int] :
( ~ $less(5,X0)
| ~ $less(X0,6) )
| ~ spl1_2
| ~ spl1_18
| ~ spl1_34 ),
inference(forward_demodulation,[],[f551,f28]) ).
tff(f551,plain,
( ! [X0: $int] :
( ~ $less(X0,6)
| ~ $less($sum(2,sK0),X0) )
| ~ spl1_18
| ~ spl1_34 ),
inference(evaluation,[],[f548]) ).
tff(f548,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(5,1))
| ~ $less($sum(2,sK0),X0) )
| ~ spl1_18
| ~ spl1_34 ),
inference(superposition,[],[f515,f158]) ).
tff(f515,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f514]) ).
tff(f711,plain,
( spl1_42
| ~ spl1_13
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f130,f116,f85,f709]) ).
tff(f709,plain,
( spl1_42
<=> ! [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,[spl1_42])]) ).
tff(f85,plain,
( spl1_13
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f116,plain,
( spl1_15
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f130,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl1_13
| ~ spl1_15 ),
inference(superposition,[],[f86,f117]) ).
tff(f117,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f86,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f707,plain,
( spl1_41
| ~ spl1_13
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f129,f116,f85,f705]) ).
tff(f705,plain,
( spl1_41
<=> ! [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,[spl1_41])]) ).
tff(f129,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl1_13
| ~ spl1_15 ),
inference(superposition,[],[f86,f117]) ).
tff(f703,plain,
( spl1_40
| ~ spl1_12
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f124,f116,f81,f701]) ).
tff(f701,plain,
( spl1_40
<=> ! [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,[spl1_40])]) ).
tff(f81,plain,
( spl1_12
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f124,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl1_12
| ~ spl1_15 ),
inference(superposition,[],[f117,f82]) ).
tff(f82,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f81]) ).
tff(f601,plain,
( spl1_39
| ~ spl1_12
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f114,f85,f81,f599]) ).
tff(f114,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_12
| ~ spl1_13 ),
inference(superposition,[],[f86,f82]) ).
tff(f597,plain,
( spl1_38
| ~ spl1_12
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f109,f85,f81,f595]) ).
tff(f109,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl1_12
| ~ spl1_13 ),
inference(superposition,[],[f86,f82]) ).
tff(f593,plain,
( spl1_37
| ~ spl1_10
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f104,f85,f65,f591]) ).
tff(f104,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl1_10
| ~ spl1_13 ),
inference(resolution,[],[f86,f66]) ).
tff(f587,plain,
( spl1_36
| ~ spl1_9
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f74,f69,f55,f585]) ).
tff(f585,plain,
( spl1_36
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
tff(f55,plain,
( spl1_9
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f69,plain,
( spl1_11
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f74,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl1_9
| ~ spl1_11 ),
inference(resolution,[],[f70,f56]) ).
tff(f56,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f70,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f69]) ).
tff(f520,plain,
( spl1_35
| ~ spl1_8
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f134,f116,f51,f518]) ).
tff(f51,plain,
( spl1_8
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f134,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl1_8
| ~ spl1_15 ),
inference(superposition,[],[f52,f117]) ).
tff(f52,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f516,plain,
( spl1_34
| ~ spl1_9
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f133,f116,f55,f514]) ).
tff(f133,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_9
| ~ spl1_15 ),
inference(superposition,[],[f56,f117]) ).
tff(f512,plain,
( spl1_33
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f75,f69,f65,f510]) ).
tff(f510,plain,
( spl1_33
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
tff(f75,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl1_10
| ~ spl1_11 ),
inference(resolution,[],[f70,f66]) ).
tff(f355,plain,
( ~ spl1_32
| ~ spl1_19
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f253,f230,f175,f352]) ).
tff(f352,plain,
( spl1_32
<=> $less(5,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
tff(f175,plain,
( spl1_19
<=> ( 2 = $sum(5,$uminus(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f230,plain,
( spl1_24
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f253,plain,
( ~ $less(5,sK0)
| ~ spl1_19
| ~ spl1_24 ),
inference(evaluation,[],[f248]) ).
tff(f248,plain,
( $less(2,0)
| ~ $less(5,sK0)
| ~ spl1_19
| ~ spl1_24 ),
inference(superposition,[],[f231,f177]) ).
tff(f177,plain,
( ( 2 = $sum(5,$uminus(sK0)) )
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f175]) ).
tff(f231,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl1_24 ),
inference(avatar_component_clause,[],[f230]) ).
tff(f350,plain,
( spl1_31
| ~ spl1_7
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f126,f116,f47,f348]) ).
tff(f126,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl1_7
| ~ spl1_15 ),
inference(superposition,[],[f117,f48]) ).
tff(f346,plain,
( spl1_30
| ~ spl1_7
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f120,f116,f47,f344]) ).
tff(f120,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl1_7
| ~ spl1_15 ),
inference(superposition,[],[f117,f48]) ).
tff(f342,plain,
( spl1_29
| ~ spl1_8
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f72,f65,f51,f340]) ).
tff(f340,plain,
( spl1_29
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f72,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl1_8
| ~ spl1_10 ),
inference(resolution,[],[f66,f52]) ).
tff(f269,plain,
( spl1_28
| ~ spl1_6
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f125,f116,f43,f267]) ).
tff(f267,plain,
( spl1_28
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f43,plain,
( spl1_6
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f125,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl1_6
| ~ spl1_15 ),
inference(superposition,[],[f117,f44]) ).
tff(f44,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f265,plain,
( spl1_27
| ~ spl1_7
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f112,f85,f47,f263]) ).
tff(f112,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl1_7
| ~ spl1_13 ),
inference(superposition,[],[f86,f48]) ).
tff(f261,plain,
( spl1_26
| ~ spl1_7
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f107,f85,f47,f259]) ).
tff(f107,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl1_7
| ~ spl1_13 ),
inference(superposition,[],[f86,f48]) ).
tff(f257,plain,
( spl1_25
| ~ spl1_7
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f89,f81,f47,f255]) ).
tff(f255,plain,
( spl1_25
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f89,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl1_7
| ~ spl1_12 ),
inference(superposition,[],[f82,f48]) ).
tff(f232,plain,
( spl1_24
| ~ spl1_6
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f111,f85,f43,f230]) ).
tff(f111,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl1_6
| ~ spl1_13 ),
inference(superposition,[],[f86,f44]) ).
tff(f228,plain,
( spl1_23
| ~ spl1_6
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f106,f85,f43,f226]) ).
tff(f226,plain,
( spl1_23
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f106,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl1_6
| ~ spl1_13 ),
inference(superposition,[],[f86,f44]) ).
tff(f190,plain,
( spl1_22
| ~ spl1_6
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f135,f116,f43,f188]) ).
tff(f135,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl1_6
| ~ spl1_15 ),
inference(evaluation,[],[f119]) ).
tff(f119,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl1_6
| ~ spl1_15 ),
inference(superposition,[],[f117,f44]) ).
tff(f186,plain,
( spl1_21
| ~ spl1_7
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f62,f55,f47,f184]) ).
tff(f62,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl1_7
| ~ spl1_9 ),
inference(superposition,[],[f56,f48]) ).
tff(f182,plain,
( spl1_20
| ~ spl1_7
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f59,f51,f47,f180]) ).
tff(f180,plain,
( spl1_20
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f59,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl1_7
| ~ spl1_8 ),
inference(superposition,[],[f52,f48]) ).
tff(f178,plain,
( spl1_19
| ~ spl1_6
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f166,f157,f43,f175]) ).
tff(f166,plain,
( ( 2 = $sum(5,$uminus(sK0)) )
| ~ spl1_6
| ~ spl1_18 ),
inference(evaluation,[],[f160]) ).
tff(f160,plain,
( ( $sum(5,$uminus(sK0)) = $sum(2,0) )
| ~ spl1_6
| ~ spl1_18 ),
inference(superposition,[],[f158,f44]) ).
tff(f159,plain,
( spl1_18
| ~ spl1_2
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f122,f116,f26,f157]) ).
tff(f122,plain,
( ! [X0: $int] : ( $sum(2,$sum(sK0,X0)) = $sum(5,X0) )
| ~ spl1_2
| ~ spl1_15 ),
inference(superposition,[],[f117,f28]) ).
tff(f145,plain,
( spl1_17
| ~ spl1_2
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f110,f85,f26,f143]) ).
tff(f110,plain,
( ! [X0: $int] :
( $less($sum(X0,sK0),5)
| ~ $less(X0,2) )
| ~ spl1_2
| ~ spl1_13 ),
inference(superposition,[],[f86,f28]) ).
tff(f141,plain,
( spl1_16
| ~ spl1_2
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f105,f85,f26,f139]) ).
tff(f105,plain,
( ! [X0: $int] :
( $less(5,$sum(X0,sK0))
| ~ $less(2,X0) )
| ~ spl1_2
| ~ spl1_13 ),
inference(superposition,[],[f86,f28]) ).
tff(f118,plain,
spl1_15,
inference(avatar_split_clause,[],[f4,f116]) ).
tff(f4,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f101,plain,
( spl1_14
| ~ spl1_3
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f58,f51,f31,f99]) ).
tff(f99,plain,
( spl1_14
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f31,plain,
( spl1_3
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f58,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl1_3
| ~ spl1_8 ),
inference(resolution,[],[f52,f32]) ).
tff(f32,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f87,plain,
spl1_13,
inference(avatar_split_clause,[],[f11,f85]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f83,plain,
spl1_12,
inference(avatar_split_clause,[],[f6,f81]) ).
tff(f6,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f71,plain,
spl1_11,
inference(avatar_split_clause,[],[f10,f69]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f67,plain,
spl1_10,
inference(avatar_split_clause,[],[f9,f65]) ).
tff(f9,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f57,plain,
spl1_9,
inference(avatar_split_clause,[],[f14,f55]) ).
tff(f14,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f53,plain,
spl1_8,
inference(avatar_split_clause,[],[f12,f51]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f49,plain,
spl1_7,
inference(avatar_split_clause,[],[f3,f47]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f45,plain,
spl1_6,
inference(avatar_split_clause,[],[f7,f43]) ).
tff(f7,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f41,plain,
spl1_5,
inference(avatar_split_clause,[],[f13,f39]) ).
tff(f39,plain,
( spl1_5
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f13,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f37,plain,
spl1_4,
inference(avatar_split_clause,[],[f5,f35]) ).
tff(f35,plain,
( spl1_4
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f33,plain,
spl1_3,
inference(avatar_split_clause,[],[f8,f31]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f29,plain,
spl1_2,
inference(avatar_split_clause,[],[f18,f26]) ).
tff(f18,plain,
5 = $sum(2,sK0),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
( ( 3 != sK0 )
& ( 5 = $sum(2,sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16]) ).
tff(f16,plain,
( ? [X0: $int] :
( ( 3 != X0 )
& ( $sum(2,X0) = 5 ) )
=> ( ( 3 != sK0 )
& ( 5 = $sum(2,sK0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f15,plain,
? [X0: $int] :
( ( 3 != X0 )
& ( $sum(2,X0) = 5 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( ( $sum(2,X0) = 5 )
=> ( 3 = X0 ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
! [X0: $int] :
( ( $sum(2,X0) = 5 )
=> ( 3 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum2_only_3_5) ).
tff(f24,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f19,f21]) ).
tff(f19,plain,
3 != sK0,
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI065_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 30 05:52:18 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (27923)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (27930)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.36 % (27928)WARNING: value z3 for option sas not known
% 0.14/0.37 % (27926)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (27927)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (27928)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (27931)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (27926)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (27932)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (27929)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (27927)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (27926)Terminated due to inappropriate strategy.
% 0.14/0.37 % (27926)------------------------------
% 0.14/0.37 % (27926)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37 % (27926)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (27926)Memory used [KB]: 722
% 0.14/0.37 % (27926)Time elapsed: 0.002 s
% 0.14/0.37 % (27927)Terminated due to inappropriate strategy.
% 0.14/0.37 % (27927)------------------------------
% 0.14/0.37 % (27927)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37 % (27927)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (27926)Instructions burned: 2 (million)
% 0.14/0.37 % (27926)------------------------------
% 0.14/0.37 % (27926)------------------------------
% 0.14/0.37 % (27927)Memory used [KB]: 722
% 0.14/0.37 % (27927)Time elapsed: 0.002 s
% 0.14/0.37 % (27927)Instructions burned: 2 (million)
% 0.14/0.37 % (27927)------------------------------
% 0.14/0.37 % (27927)------------------------------
% 0.14/0.37 % (27929)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (27929)Terminated due to inappropriate strategy.
% 0.14/0.37 % (27929)------------------------------
% 0.14/0.37 % (27929)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37 % (27929)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (27929)Memory used [KB]: 722
% 0.14/0.37 % (27929)Time elapsed: 0.002 s
% 0.14/0.37 % (27929)Instructions burned: 2 (million)
% 0.14/0.37 % (27929)------------------------------
% 0.14/0.37 % (27929)------------------------------
% 0.14/0.38 % (27940)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.38 % (27941)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.14/0.38 % (27942)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.14/0.38 % (27940)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (27940)Terminated due to inappropriate strategy.
% 0.14/0.38 % (27940)------------------------------
% 0.14/0.38 % (27940)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (27940)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (27940)Memory used [KB]: 722
% 0.14/0.38 % (27940)Time elapsed: 0.002 s
% 0.14/0.38 % (27940)Instructions burned: 2 (million)
% 0.14/0.38 % (27940)------------------------------
% 0.14/0.38 % (27940)------------------------------
% 0.14/0.40 % (27950)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)
% 0.21/0.41 % (27930)First to succeed.
% 0.21/0.41 % (27930)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for theBenchmark
% 0.21/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (27930)------------------------------
% 0.21/0.41 % (27930)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41 % (27930)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (27930)Memory used [KB]: 1532
% 0.21/0.41 % (27930)Time elapsed: 0.051 s
% 0.21/0.41 % (27930)Instructions burned: 110 (million)
% 0.21/0.41 % (27930)------------------------------
% 0.21/0.41 % (27930)------------------------------
% 0.21/0.41 % (27923)Success in time 0.061 s
%------------------------------------------------------------------------------