TSTP Solution File: DAT030_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT030_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 : n012.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 05:05:41 EDT 2024
% Result : Theorem 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 69
% Syntax : Number of formulae : 434 ( 50 unt; 10 typ; 0 def)
% Number of atoms : 1090 ( 125 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1210 ( 544 ~; 547 |; 58 &)
% ( 42 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 1792 ( 514 atm; 310 fun; 625 num; 343 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 43 ( 39 usr; 39 prp; 0-2 aty)
% Number of functors : 44 ( 8 usr; 38 con; 0-2 aty)
% Number of variables : 381 ( 347 !; 34 ?; 381 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_7,type,
sK0: collection ).
tff(func_def_8,type,
sK1: collection ).
tff(func_def_9,type,
sK2: $int ).
tff(func_def_10,type,
sK3: $int > $int ).
tff(func_def_11,type,
sK4: $int > $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f3892,plain,
$false,
inference(avatar_sat_refutation,[],[f195,f215,f250,f266,f289,f338,f468,f2772,f2783,f2975,f2977,f2979,f2991,f3018,f3079,f3106,f3183,f3258,f3396,f3423,f3508,f3617,f3703,f3731,f3765,f3804,f3871]) ).
tff(f3871,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f3870]) ).
tff(f3870,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f3869,f122]) ).
tff(f122,plain,
~ $less(sK4(sK2),1),
inference(resolution,[],[f116,f58]) ).
tff(f58,plain,
$less(0,sK4(sK2)),
inference(resolution,[],[f55,f41]) ).
tff(f41,plain,
in(sK2,sK0),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
( ~ $less(1,sK2)
& in(sK2,sK0)
& ! [X3: $int] :
( ( ( $sum(sK3(X3),sK4(X3)) = X3 )
& in(sK4(X3),sK1)
& in(sK3(X3),sK1) )
| ~ in(X3,sK0) )
& ! [X6: $int] :
( $less(0,X6)
| ~ in(X6,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f28,f31,f30,f29]) ).
tff(f29,plain,
( ? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,X0) )
& ! [X3: $int] :
( ? [X4: $int,X5: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,X1)
& in(X4,X1) )
| ~ in(X3,X0) )
& ! [X6: $int] :
( $less(0,X6)
| ~ in(X6,X1) ) )
=> ( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,sK0) )
& ! [X3: $int] :
( ? [X5: $int,X4: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,sK1)
& in(X4,sK1) )
| ~ in(X3,sK0) )
& ! [X6: $int] :
( $less(0,X6)
| ~ in(X6,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,sK0) )
=> ( ~ $less(1,sK2)
& in(sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
! [X3: $int] :
( ? [X5: $int,X4: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,sK1)
& in(X4,sK1) )
=> ( ( $sum(sK3(X3),sK4(X3)) = X3 )
& in(sK4(X3),sK1)
& in(sK3(X3),sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,X0) )
& ! [X3: $int] :
( ? [X4: $int,X5: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,X1)
& in(X4,X1) )
| ~ in(X3,X0) )
& ! [X6: $int] :
( $less(0,X6)
| ~ in(X6,X1) ) ),
inference(rectify,[],[f27]) ).
tff(f27,plain,
? [X0: collection,X1: collection] :
( ? [X6: $int] :
( ~ $less(1,X6)
& in(X6,X0) )
& ! [X2: $int] :
( ? [X3: $int,X4: $int] :
( ( $sum(X3,X4) = X2 )
& in(X4,X1)
& in(X3,X1) )
| ~ in(X2,X0) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,X1) ) ),
inference(flattening,[],[f26]) ).
tff(f26,plain,
? [X0: collection,X1: collection] :
( ? [X6: $int] :
( ~ $less(1,X6)
& in(X6,X0) )
& ! [X2: $int] :
( ? [X3: $int,X4: $int] :
( ( $sum(X3,X4) = X2 )
& in(X4,X1)
& in(X3,X1) )
| ~ in(X2,X0) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,X1) ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X0)
=> ? [X3: $int,X4: $int] :
( ( $sum(X3,X4) = X2 )
& in(X4,X1)
& in(X3,X1) ) )
& ! [X5: $int] :
( in(X5,X1)
=> $less(0,X5) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $less(1,X6) ) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int,X5: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,X1)
& in(X4,X1) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $less(1,X6) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X0: collection,X1: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int,X5: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,X1)
& in(X4,X1) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $greater(X6,1) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
! [X0: collection,X1: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int,X5: $int] :
( ( $sum(X4,X5) = X3 )
& in(X5,X1)
& in(X4,X1) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X6: $int] :
( in(X6,X0)
=> $greater(X6,1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f55,plain,
! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,sK4(X0)) ),
inference(resolution,[],[f39,f37]) ).
tff(f37,plain,
! [X6: $int] :
( ~ in(X6,sK1)
| $less(0,X6) ),
inference(cnf_transformation,[],[f32]) ).
tff(f39,plain,
! [X3: $int] :
( in(sK4(X3),sK1)
| ~ in(X3,sK0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f116,plain,
! [X0: $int] :
( ~ $less(0,X0)
| ~ $less(X0,1) ),
inference(superposition,[],[f86,f11]) ).
tff(f11,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f86,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f20,f9]) ).
tff(f9,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f3869,plain,
( $less(sK4(sK2),1)
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f3824,f214]) ).
tff(f214,plain,
( $less(1,sK3(sK2))
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f212]) ).
tff(f212,plain,
( spl5_4
<=> $less(1,sK3(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
tff(f3824,plain,
( ~ $less(1,sK3(sK2))
| $less(sK4(sK2),1)
| ~ spl5_2 ),
inference(resolution,[],[f308,f1134]) ).
tff(f1134,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1132]) ).
tff(f1132,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-1),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1124,f386]) ).
tff(f386,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f365]) ).
tff(f365,plain,
! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f10,f13]) ).
tff(f13,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f1124,plain,
( ! [X0: $int] :
( $less($sum(-1,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1080,f9]) ).
tff(f1080,plain,
( ! [X0: $int] :
( $less($sum(X0,-1),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f508]) ).
tff(f508,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-1,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f499,f15]) ).
tff(f15,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f499,plain,
( $less($sum(-1,sK2),1)
| ~ spl5_2 ),
inference(resolution,[],[f492,f470]) ).
tff(f470,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f194,f15]) ).
tff(f194,plain,
( $less(sK2,1)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f192]) ).
tff(f192,plain,
( spl5_2
<=> $less(sK2,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
tff(f492,plain,
! [X0: $int] : $less($sum(-1,X0),X0),
inference(evaluation,[],[f491]) ).
tff(f491,plain,
! [X0: $int] : $less($sum($uminus(1),X0),X0),
inference(superposition,[],[f76,f386]) ).
tff(f76,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f71,f9]) ).
tff(f71,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f18,f14]) ).
tff(f14,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f304,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ),
inference(superposition,[],[f17,f9]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_145,[]) ).
tff(f308,plain,
! [X0: $int] :
( $less($sum(X0,sK4(sK2)),sK2)
| ~ $less(X0,sK3(sK2)) ),
inference(superposition,[],[f17,f70]) ).
tff(f70,plain,
sK2 = $sum(sK3(sK2),sK4(sK2)),
inference(resolution,[],[f40,f41]) ).
tff(f40,plain,
! [X3: $int] :
( ~ in(X3,sK0)
| ( $sum(sK3(X3),sK4(X3)) = X3 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f3804,plain,
( ~ spl5_37
| spl5_38
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2746,f192,f3801,f3797]) ).
tff(f3797,plain,
( spl5_37
<=> $less(16,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
tff(f3801,plain,
( spl5_38
<=> ( sK2 = 17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
tff(f2746,plain,
( ( sK2 = 17 )
| ~ $less(16,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2698]) ).
tff(f2698,plain,
( ( sK2 = $sum(16,1) )
| ~ $less(16,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f2101]) ).
tff(f2101,plain,
( ! [X0: $int] :
( ~ $less($sum(16,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f2096]) ).
tff(f2096,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-16),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f2075,f386]) ).
tff(f2075,plain,
( ! [X0: $int] :
( $less($sum(-16,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1095,f9]) ).
tff(f1095,plain,
( ! [X0: $int] :
( $less($sum(X0,-16),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f937]) ).
tff(f937,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-16,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f935,f15]) ).
tff(f935,plain,
( $less($sum(-16,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f933]) ).
tff(f933,plain,
( $less($sum($sum(-15,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f916,f500]) ).
tff(f500,plain,
! [X0: $int] : $less($sum(X0,-1),X0),
inference(superposition,[],[f492,f9]) ).
tff(f916,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-15,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f914,f15]) ).
tff(f914,plain,
( $less($sum(-15,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f912]) ).
tff(f912,plain,
( $less($sum($sum(-14,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f895,f500]) ).
tff(f895,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-14,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f893,f15]) ).
tff(f893,plain,
( $less($sum(-14,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f891]) ).
tff(f891,plain,
( $less($sum($sum(-13,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f874,f500]) ).
tff(f874,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-13,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f872,f15]) ).
tff(f872,plain,
( $less($sum(-13,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f870]) ).
tff(f870,plain,
( $less($sum($sum(-12,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f853,f500]) ).
tff(f853,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-12,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f851,f15]) ).
tff(f851,plain,
( $less($sum(-12,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f849]) ).
tff(f849,plain,
( $less($sum($sum(-11,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f832,f500]) ).
tff(f832,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-11,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f830,f15]) ).
tff(f830,plain,
( $less($sum(-11,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f828]) ).
tff(f828,plain,
( $less($sum($sum(-10,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f773,f500]) ).
tff(f773,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-10,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f771,f15]) ).
tff(f771,plain,
( $less($sum(-10,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f769]) ).
tff(f769,plain,
( $less($sum($sum(-9,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f752,f500]) ).
tff(f752,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-9,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f750,f15]) ).
tff(f750,plain,
( $less($sum(-9,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f748]) ).
tff(f748,plain,
( $less($sum($sum(-8,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f700,f500]) ).
tff(f700,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-8,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f698,f15]) ).
tff(f698,plain,
( $less($sum(-8,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f696]) ).
tff(f696,plain,
( $less($sum($sum(-7,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f679,f500]) ).
tff(f679,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-7,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f677,f15]) ).
tff(f677,plain,
( $less($sum(-7,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f675]) ).
tff(f675,plain,
( $less($sum($sum(-6,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f635,f500]) ).
tff(f635,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-6,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f633,f15]) ).
tff(f633,plain,
( $less($sum(-6,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f631]) ).
tff(f631,plain,
( $less($sum($sum(-5,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f614,f500]) ).
tff(f614,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-5,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f612,f15]) ).
tff(f612,plain,
( $less($sum(-5,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f610]) ).
tff(f610,plain,
( $less($sum($sum(-4,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f583,f500]) ).
tff(f583,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-4,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f581,f15]) ).
tff(f581,plain,
( $less($sum(-4,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f579]) ).
tff(f579,plain,
( $less($sum($sum(-3,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f562,f500]) ).
tff(f562,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-3,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f548,f15]) ).
tff(f548,plain,
( $less($sum(-3,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f546]) ).
tff(f546,plain,
( $less($sum($sum(-2,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f535,f500]) ).
tff(f535,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(-2,sK2))
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f533,f15]) ).
tff(f533,plain,
( $less($sum(-2,sK2),1)
| ~ spl5_2 ),
inference(evaluation,[],[f531]) ).
tff(f531,plain,
( $less($sum($sum(-1,sK2),-1),1)
| ~ spl5_2 ),
inference(resolution,[],[f508,f500]) ).
tff(f163,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,1),X1)
| ( $sum(X0,1) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f20]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f3765,plain,
( ~ spl5_35
| spl5_36
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2747,f192,f3762,f3758]) ).
tff(f3758,plain,
( spl5_35
<=> $less(15,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
tff(f3762,plain,
( spl5_36
<=> ( sK2 = 16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
tff(f2747,plain,
( ( sK2 = 16 )
| ~ $less(15,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2697]) ).
tff(f2697,plain,
( ( sK2 = $sum(15,1) )
| ~ $less(15,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f2065]) ).
tff(f2065,plain,
( ! [X0: $int] :
( ~ $less($sum(15,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f2060]) ).
tff(f2060,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-15),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f2039,f386]) ).
tff(f2039,plain,
( ! [X0: $int] :
( $less($sum(-15,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1094,f9]) ).
tff(f1094,plain,
( ! [X0: $int] :
( $less($sum(X0,-15),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f916]) ).
tff(f3731,plain,
( ~ spl5_33
| spl5_34
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2748,f192,f3728,f3724]) ).
tff(f3724,plain,
( spl5_33
<=> $less(14,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
tff(f3728,plain,
( spl5_34
<=> ( sK2 = 15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
tff(f2748,plain,
( ( sK2 = 15 )
| ~ $less(14,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2696]) ).
tff(f2696,plain,
( ( sK2 = $sum(14,1) )
| ~ $less(14,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f2029]) ).
tff(f2029,plain,
( ! [X0: $int] :
( ~ $less($sum(14,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f2024]) ).
tff(f2024,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-14),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f2003,f386]) ).
tff(f2003,plain,
( ! [X0: $int] :
( $less($sum(-14,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1093,f9]) ).
tff(f1093,plain,
( ! [X0: $int] :
( $less($sum(X0,-14),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f895]) ).
tff(f3703,plain,
( ~ spl5_31
| spl5_32
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2749,f192,f3700,f3696]) ).
tff(f3696,plain,
( spl5_31
<=> $less(13,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
tff(f3700,plain,
( spl5_32
<=> ( sK2 = 14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
tff(f2749,plain,
( ( sK2 = 14 )
| ~ $less(13,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2695]) ).
tff(f2695,plain,
( ( sK2 = $sum(13,1) )
| ~ $less(13,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1993]) ).
tff(f1993,plain,
( ! [X0: $int] :
( ~ $less($sum(13,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1988]) ).
tff(f1988,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-13),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1763,f386]) ).
tff(f1763,plain,
( ! [X0: $int] :
( $less($sum(-13,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1092,f9]) ).
tff(f1092,plain,
( ! [X0: $int] :
( $less($sum(X0,-13),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f874]) ).
tff(f3617,plain,
( ~ spl5_29
| spl5_30
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2750,f192,f3614,f3610]) ).
tff(f3610,plain,
( spl5_29
<=> $less(12,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
tff(f3614,plain,
( spl5_30
<=> ( sK2 = 13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
tff(f2750,plain,
( ( sK2 = 13 )
| ~ $less(12,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2694]) ).
tff(f2694,plain,
( ( sK2 = $sum(12,1) )
| ~ $less(12,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1753]) ).
tff(f1753,plain,
( ! [X0: $int] :
( ~ $less($sum(12,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1750]) ).
tff(f1750,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-12),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1731,f386]) ).
tff(f1731,plain,
( ! [X0: $int] :
( $less($sum(-12,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1091,f9]) ).
tff(f1091,plain,
( ! [X0: $int] :
( $less($sum(X0,-12),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f853]) ).
tff(f3508,plain,
( ~ spl5_27
| spl5_28
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2751,f192,f3505,f3501]) ).
tff(f3501,plain,
( spl5_27
<=> $less(11,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
tff(f3505,plain,
( spl5_28
<=> ( sK2 = 12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
tff(f2751,plain,
( ( sK2 = 12 )
| ~ $less(11,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2693]) ).
tff(f2693,plain,
( ( sK2 = $sum(11,1) )
| ~ $less(11,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1721]) ).
tff(f1721,plain,
( ! [X0: $int] :
( ~ $less($sum(11,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1718]) ).
tff(f1718,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-11),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1699,f386]) ).
tff(f1699,plain,
( ! [X0: $int] :
( $less($sum(-11,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1090,f9]) ).
tff(f1090,plain,
( ! [X0: $int] :
( $less($sum(X0,-11),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f832]) ).
tff(f3423,plain,
( ~ spl5_25
| spl5_26
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2752,f192,f3420,f3416]) ).
tff(f3416,plain,
( spl5_25
<=> $less(10,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
tff(f3420,plain,
( spl5_26
<=> ( sK2 = 11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
tff(f2752,plain,
( ( sK2 = 11 )
| ~ $less(10,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2692]) ).
tff(f2692,plain,
( ( sK2 = $sum(10,1) )
| ~ $less(10,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1689]) ).
tff(f1689,plain,
( ! [X0: $int] :
( ~ $less($sum(10,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1686]) ).
tff(f1686,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-10),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1667,f386]) ).
tff(f1667,plain,
( ! [X0: $int] :
( $less($sum(-10,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1089,f9]) ).
tff(f1089,plain,
( ! [X0: $int] :
( $less($sum(X0,-10),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f773]) ).
tff(f3396,plain,
( ~ spl5_23
| spl5_24
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2753,f192,f3393,f3389]) ).
tff(f3389,plain,
( spl5_23
<=> $less(9,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
tff(f3393,plain,
( spl5_24
<=> ( sK2 = 10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
tff(f2753,plain,
( ( sK2 = 10 )
| ~ $less(9,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2691]) ).
tff(f2691,plain,
( ( sK2 = $sum(9,1) )
| ~ $less(9,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1567]) ).
tff(f1567,plain,
( ! [X0: $int] :
( ~ $less($sum(9,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1564]) ).
tff(f1564,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-9),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1546,f386]) ).
tff(f1546,plain,
( ! [X0: $int] :
( $less($sum(-9,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1088,f9]) ).
tff(f1088,plain,
( ! [X0: $int] :
( $less($sum(X0,-9),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f752]) ).
tff(f3258,plain,
( ~ spl5_21
| spl5_22
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2754,f192,f3255,f3251]) ).
tff(f3251,plain,
( spl5_21
<=> $less(8,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
tff(f3255,plain,
( spl5_22
<=> ( sK2 = 9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
tff(f2754,plain,
( ( sK2 = 9 )
| ~ $less(8,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2690]) ).
tff(f2690,plain,
( ( sK2 = $sum(8,1) )
| ~ $less(8,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1398]) ).
tff(f1398,plain,
( ! [X0: $int] :
( ~ $less($sum(8,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1395]) ).
tff(f1395,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-8),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1378,f386]) ).
tff(f1378,plain,
( ! [X0: $int] :
( $less($sum(-8,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1087,f9]) ).
tff(f1087,plain,
( ! [X0: $int] :
( $less($sum(X0,-8),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f700]) ).
tff(f3183,plain,
( ~ spl5_19
| spl5_20
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2755,f192,f3180,f3176]) ).
tff(f3176,plain,
( spl5_19
<=> $less(7,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
tff(f3180,plain,
( spl5_20
<=> ( sK2 = 8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
tff(f2755,plain,
( ( sK2 = 8 )
| ~ $less(7,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2689]) ).
tff(f2689,plain,
( ( sK2 = $sum(7,1) )
| ~ $less(7,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1370]) ).
tff(f1370,plain,
( ! [X0: $int] :
( ~ $less($sum(7,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1367]) ).
tff(f1367,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-7),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1350,f386]) ).
tff(f1350,plain,
( ! [X0: $int] :
( $less($sum(-7,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1086,f9]) ).
tff(f1086,plain,
( ! [X0: $int] :
( $less($sum(X0,-7),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f679]) ).
tff(f3106,plain,
( ~ spl5_17
| spl5_18
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2756,f192,f3103,f3099]) ).
tff(f3099,plain,
( spl5_17
<=> $less(6,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
tff(f3103,plain,
( spl5_18
<=> ( sK2 = 7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
tff(f2756,plain,
( ( sK2 = 7 )
| ~ $less(6,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2688]) ).
tff(f2688,plain,
( ( sK2 = $sum(6,1) )
| ~ $less(6,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1342]) ).
tff(f1342,plain,
( ! [X0: $int] :
( ~ $less($sum(6,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1339]) ).
tff(f1339,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-6),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1322,f386]) ).
tff(f1322,plain,
( ! [X0: $int] :
( $less($sum(-6,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1085,f9]) ).
tff(f1085,plain,
( ! [X0: $int] :
( $less($sum(X0,-6),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f635]) ).
tff(f3079,plain,
( ~ spl5_15
| spl5_16
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2757,f192,f3076,f3072]) ).
tff(f3072,plain,
( spl5_15
<=> $less(5,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
tff(f3076,plain,
( spl5_16
<=> ( sK2 = 6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
tff(f2757,plain,
( ( sK2 = 6 )
| ~ $less(5,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2687]) ).
tff(f2687,plain,
( ( sK2 = $sum(5,1) )
| ~ $less(5,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1314]) ).
tff(f1314,plain,
( ! [X0: $int] :
( ~ $less($sum(5,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1311]) ).
tff(f1311,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-5),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1214,f386]) ).
tff(f1214,plain,
( ! [X0: $int] :
( $less($sum(-5,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1084,f9]) ).
tff(f1084,plain,
( ! [X0: $int] :
( $less($sum(X0,-5),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f614]) ).
tff(f3018,plain,
( ~ spl5_13
| spl5_14
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2758,f192,f3015,f3011]) ).
tff(f3011,plain,
( spl5_13
<=> $less(4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
tff(f3015,plain,
( spl5_14
<=> ( sK2 = 5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
tff(f2758,plain,
( ( sK2 = 5 )
| ~ $less(4,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2686]) ).
tff(f2686,plain,
( ( sK2 = $sum(4,1) )
| ~ $less(4,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1206]) ).
tff(f1206,plain,
( ! [X0: $int] :
( ~ $less($sum(4,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1204]) ).
tff(f1204,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-4),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1188,f386]) ).
tff(f1188,plain,
( ! [X0: $int] :
( $less($sum(-4,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1083,f9]) ).
tff(f1083,plain,
( ! [X0: $int] :
( $less($sum(X0,-4),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f583]) ).
tff(f2991,plain,
( ~ spl5_11
| spl5_12
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2759,f192,f2988,f2984]) ).
tff(f2984,plain,
( spl5_11
<=> $less(3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
tff(f2988,plain,
( spl5_12
<=> ( sK2 = 4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
tff(f2759,plain,
( ( sK2 = 4 )
| ~ $less(3,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2685]) ).
tff(f2685,plain,
( ( sK2 = $sum(3,1) )
| ~ $less(3,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1180]) ).
tff(f1180,plain,
( ! [X0: $int] :
( ~ $less($sum(3,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1178]) ).
tff(f1178,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-3),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1162,f386]) ).
tff(f1162,plain,
( ! [X0: $int] :
( $less($sum(-3,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1082,f9]) ).
tff(f1082,plain,
( ! [X0: $int] :
( $less($sum(X0,-3),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f562]) ).
tff(f2979,plain,
~ spl5_9,
inference(avatar_contradiction_clause,[],[f2978]) ).
tff(f2978,plain,
( $false
| ~ spl5_9 ),
inference(evaluation,[],[f2785]) ).
tff(f2785,plain,
( ~ $less(1,2)
| ~ spl5_9 ),
inference(superposition,[],[f42,f2778]) ).
tff(f2778,plain,
( ( sK2 = 2 )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f2776]) ).
tff(f2776,plain,
( spl5_9
<=> ( sK2 = 2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
tff(f42,plain,
~ $less(1,sK2),
inference(cnf_transformation,[],[f32]) ).
tff(f2977,plain,
( ~ spl5_2
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f2976]) ).
tff(f2976,plain,
( $false
| ~ spl5_2
| ~ spl5_9 ),
inference(evaluation,[],[f2801]) ).
tff(f2801,plain,
( $less(2,1)
| ~ spl5_2
| ~ spl5_9 ),
inference(superposition,[],[f194,f2778]) ).
tff(f2975,plain,
( ~ spl5_2
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f2974]) ).
tff(f2974,plain,
( $false
| ~ spl5_2
| ~ spl5_9 ),
inference(evaluation,[],[f2810]) ).
tff(f2810,plain,
( $less($sum(-1,2),1)
| ~ spl5_2
| ~ spl5_9 ),
inference(superposition,[],[f499,f2778]) ).
tff(f2783,plain,
( spl5_9
| spl5_10
| spl5_7 ),
inference(avatar_split_clause,[],[f2773,f2765,f2780,f2776]) ).
tff(f2780,plain,
( spl5_10
<=> $less(sK2,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
tff(f2765,plain,
( spl5_7
<=> $less(2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
tff(f2773,plain,
( $less(sK2,2)
| ( sK2 = 2 )
| spl5_7 ),
inference(resolution,[],[f2767,f16]) ).
tff(f2767,plain,
( ~ $less(2,sK2)
| spl5_7 ),
inference(avatar_component_clause,[],[f2765]) ).
tff(f2772,plain,
( ~ spl5_7
| spl5_8
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f2760,f192,f2769,f2765]) ).
tff(f2769,plain,
( spl5_8
<=> ( sK2 = 3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
tff(f2760,plain,
( ( sK2 = 3 )
| ~ $less(2,sK2)
| ~ spl5_2 ),
inference(evaluation,[],[f2684]) ).
tff(f2684,plain,
( ( sK2 = $sum(2,1) )
| ~ $less(2,sK2)
| $less(1,1)
| ~ spl5_2 ),
inference(resolution,[],[f163,f1154]) ).
tff(f1154,plain,
( ! [X0: $int] :
( ~ $less($sum(2,X0),sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(evaluation,[],[f1152]) ).
tff(f1152,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less($sum($uminus(-2),X0),sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1136,f386]) ).
tff(f1136,plain,
( ! [X0: $int] :
( $less($sum(-2,X0),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(superposition,[],[f1081,f9]) ).
tff(f1081,plain,
( ! [X0: $int] :
( $less($sum(X0,-2),1)
| ~ $less(X0,sK2) )
| ~ spl5_2 ),
inference(resolution,[],[f304,f535]) ).
tff(f468,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f467]) ).
tff(f467,plain,
( $false
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f466,f316]) ).
tff(f316,plain,
( $less(0,sK3(1))
| ~ spl5_1 ),
inference(superposition,[],[f57,f190]) ).
tff(f190,plain,
( ( 1 = sK2 )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f188,plain,
( spl5_1
<=> ( 1 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
tff(f57,plain,
$less(0,sK3(sK2)),
inference(resolution,[],[f54,f41]) ).
tff(f54,plain,
! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,sK3(X0)) ),
inference(resolution,[],[f38,f37]) ).
tff(f38,plain,
! [X3: $int] :
( in(sK3(X3),sK1)
| ~ in(X3,sK0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f466,plain,
( ~ $less(0,sK3(1))
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f462,f320]) ).
tff(f320,plain,
( ~ $less(sK4(1),1)
| ~ spl5_1 ),
inference(superposition,[],[f122,f190]) ).
tff(f462,plain,
( $less(sK4(1),1)
| ~ $less(0,sK3(1))
| ~ spl5_1 ),
inference(superposition,[],[f444,f11]) ).
tff(f444,plain,
( ! [X0: $int] :
( $less($sum(sK4(1),X0),1)
| ~ $less(X0,sK3(1)) )
| ~ spl5_1 ),
inference(superposition,[],[f340,f9]) ).
tff(f340,plain,
( ! [X0: $int] :
( $less($sum(X0,sK4(1)),1)
| ~ $less(X0,sK3(1)) )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f339,f190]) ).
tff(f339,plain,
( ! [X0: $int] :
( $less($sum(X0,sK4(1)),1)
| ~ $less(X0,sK3(sK2)) )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f308,f190]) ).
tff(f338,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f337]) ).
tff(f337,plain,
( $false
| ~ spl5_1
| ~ spl5_5 ),
inference(global_subsumption,[],[f10,f52,f46,f51,f53,f41,f42,f14,f43,f37,f11,f19,f44,f45,f38,f39,f13,f54,f57,f55,f58,f56,f9,f40,f70,f18,f73,f71,f77,f76,f20,f87,f75,f92,f89,f94,f47,f49,f72,f100,f101,f109,f86,f110,f115,f116,f124,f127,f121,f15,f133,f134,f135,f136,f137,f138,f139,f140,f122,f131,f143,f146,f142,f147,f132,f151,f154,f150,f155,f149,f159,f158,f16,f163,f164,f165,f166,f173,f175,f176,f177,f178,f180,f183,f185,f167,f157,f202,f201,f168,f12,f228,f229,f232,f233,f236,f237,f171,f261,f270,f273,f276,f268,f279,f280,f281,f283,f284,f285,f282,f287,f179,f17,f291,f293,f295,f296,f297,f298,f299,f312,f301,f303,f304,f305,f306,f307,f313,f309,f190,f314,f316,f317,f318,f319,f320,f321,f322,f323,f324,f325,f326,f327,f328,f329,f330,f334,f335,f336]) ).
tff(f336,plain,
( $less(sK3(1),1)
| ~ spl5_1
| ~ spl5_5 ),
inference(superposition,[],[f282,f190]) ).
tff(f335,plain,
( ( 1 = $sum(sK3(1),1) )
| ~ spl5_1
| ~ spl5_5 ),
inference(superposition,[],[f268,f190]) ).
tff(f334,plain,
( ( 1 = sK4(1) )
| ~ spl5_1
| ~ spl5_5 ),
inference(superposition,[],[f261,f190]) ).
tff(f330,plain,
( ~ $less(sK4(1),-1)
| ~ spl5_1 ),
inference(superposition,[],[f201,f190]) ).
tff(f329,plain,
( ~ $less(sK3(1),-1)
| ~ spl5_1 ),
inference(superposition,[],[f158,f190]) ).
tff(f328,plain,
( ! [X0: $int] :
( $less(X0,sK4(1))
| ~ $less(X0,-1) )
| ~ spl5_1 ),
inference(superposition,[],[f157,f190]) ).
tff(f327,plain,
( $less(-1,sK4(1))
| ~ spl5_1 ),
inference(superposition,[],[f155,f190]) ).
tff(f326,plain,
( ~ $less(sK4(1),0)
| ~ spl5_1 ),
inference(superposition,[],[f150,f190]) ).
tff(f325,plain,
( ! [X0: $int] :
( $less(X0,sK3(1))
| ~ $less(X0,-1) )
| ~ spl5_1 ),
inference(superposition,[],[f149,f190]) ).
tff(f324,plain,
( $less(-1,sK3(1))
| ~ spl5_1 ),
inference(superposition,[],[f147,f190]) ).
tff(f323,plain,
( ~ $less(sK3(1),0)
| ~ spl5_1 ),
inference(superposition,[],[f142,f190]) ).
tff(f322,plain,
( ! [X0: $int] :
( $less(X0,sK4(1))
| ~ $less(X0,0) )
| ~ spl5_1 ),
inference(superposition,[],[f132,f190]) ).
tff(f321,plain,
( ! [X0: $int] :
( $less(X0,sK3(1))
| ~ $less(X0,0) )
| ~ spl5_1 ),
inference(superposition,[],[f131,f190]) ).
tff(f319,plain,
( ~ $less(sK3(1),1)
| ~ spl5_1 ),
inference(superposition,[],[f121,f190]) ).
tff(f318,plain,
( ( 1 = $sum(sK3(1),sK4(1)) )
| ~ spl5_1 ),
inference(superposition,[],[f70,f190]) ).
tff(f317,plain,
( $less(0,sK4(1))
| ~ spl5_1 ),
inference(superposition,[],[f58,f190]) ).
tff(f314,plain,
( in(1,sK0)
| ~ spl5_1 ),
inference(superposition,[],[f41,f190]) ).
tff(f309,plain,
( ! [X0: $int] :
( $less($sum(X0,1),sK2)
| ~ $less(X0,sK3(sK2)) )
| ~ spl5_5 ),
inference(superposition,[],[f17,f268]) ).
tff(f313,plain,
( ! [X0: $int] :
( $less($sum(X0,1),sK2)
| ~ $less(X0,sK3(sK2)) )
| ~ spl5_5 ),
inference(forward_demodulation,[],[f308,f261]) ).
tff(f307,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) ),
inference(superposition,[],[f17,f12]) ).
tff(f306,plain,
! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) ),
inference(superposition,[],[f17,f56]) ).
tff(f305,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ),
inference(superposition,[],[f17,f9]) ).
tff(f303,plain,
! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ),
inference(superposition,[],[f17,f13]) ).
tff(f301,plain,
( ! [X0: $int] :
( $less(sK2,$sum(X0,1))
| ~ $less(sK3(sK2),X0) )
| ~ spl5_5 ),
inference(superposition,[],[f17,f268]) ).
tff(f312,plain,
( ! [X0: $int] :
( $less(sK2,$sum(X0,1))
| ~ $less(sK3(sK2),X0) )
| ~ spl5_5 ),
inference(forward_demodulation,[],[f300,f261]) ).
tff(f300,plain,
! [X0: $int] :
( $less(sK2,$sum(X0,sK4(sK2)))
| ~ $less(sK3(sK2),X0) ),
inference(superposition,[],[f17,f70]) ).
tff(f299,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) ),
inference(superposition,[],[f17,f12]) ).
tff(f298,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) ),
inference(superposition,[],[f17,f56]) ).
tff(f297,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ),
inference(superposition,[],[f17,f9]) ).
tff(f296,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ),
inference(superposition,[],[f17,f9]) ).
tff(f295,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ),
inference(superposition,[],[f17,f13]) ).
tff(f293,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,X3))
| ~ $less(X0,X1)
| $less(X2,$sum(X1,X3)) ),
inference(resolution,[],[f17,f15]) ).
tff(f291,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X0,X1)) ),
inference(resolution,[],[f17,f86]) ).
tff(f179,plain,
( $less(sK2,1)
| ( 1 = sK2 ) ),
inference(resolution,[],[f16,f42]) ).
tff(f287,plain,
( ! [X0: $int] :
( ~ $less(X0,sK3(sK2))
| $less(X0,sK2) )
| ~ spl5_5 ),
inference(resolution,[],[f282,f15]) ).
tff(f282,plain,
( $less(sK3(sK2),sK2)
| ~ spl5_5 ),
inference(superposition,[],[f71,f268]) ).
tff(f285,plain,
( ( sK2 = $sum(1,sK3(sK2)) )
| ~ spl5_5 ),
inference(superposition,[],[f9,f268]) ).
tff(f284,plain,
( ( sK2 = $sum(1,sK3(sK2)) )
| ~ spl5_5 ),
inference(superposition,[],[f9,f268]) ).
tff(f283,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| $less(sK3(sK2),X0) )
| ~ spl5_5 ),
inference(superposition,[],[f18,f268]) ).
tff(f281,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| ~ $less(sK3(sK2),X0) )
| ~ spl5_5 ),
inference(superposition,[],[f20,f268]) ).
tff(f280,plain,
( ( sK2 = $sum(1,sK3(sK2)) )
| ~ spl5_5 ),
inference(superposition,[],[f268,f9]) ).
tff(f279,plain,
( ( sK2 = $sum(1,sK3(sK2)) )
| ~ spl5_5 ),
inference(superposition,[],[f268,f9]) ).
tff(f268,plain,
( ( sK2 = $sum(sK3(sK2),1) )
| ~ spl5_5 ),
inference(superposition,[],[f70,f261]) ).
tff(f276,plain,
( in(1,sK1)
| ~ spl5_5 ),
inference(subsumption_resolution,[],[f275,f41]) ).
tff(f275,plain,
( in(1,sK1)
| ~ in(sK2,sK0)
| ~ spl5_5 ),
inference(superposition,[],[f39,f261]) ).
tff(f273,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less(X0,-1) )
| ~ spl5_5 ),
inference(superposition,[],[f157,f261]) ).
tff(f270,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less(X0,0) )
| ~ spl5_5 ),
inference(superposition,[],[f132,f261]) ).
tff(f261,plain,
( ( 1 = sK4(sK2) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f259]) ).
tff(f259,plain,
( spl5_5
<=> ( 1 = sK4(sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
tff(f171,plain,
( $less(1,sK4(sK2))
| ( 1 = sK4(sK2) ) ),
inference(resolution,[],[f16,f122]) ).
tff(f237,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
inference(superposition,[],[f9,f12]) ).
tff(f236,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
inference(superposition,[],[f9,f12]) ).
tff(f233,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
inference(superposition,[],[f12,f9]) ).
tff(f232,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
inference(superposition,[],[f12,f9]) ).
tff(f229,plain,
! [X0: $int,X1: $int] : ( $uminus($sum($uminus(X0),X1)) = $sum($uminus(X1),X0) ),
inference(superposition,[],[f12,f19]) ).
tff(f228,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X1,$uminus(X0))) = $sum(X0,$uminus(X1)) ),
inference(superposition,[],[f12,f19]) ).
tff(f12,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f168,plain,
( $less(1,sK3(sK2))
| ( 1 = sK3(sK2) ) ),
inference(resolution,[],[f16,f121]) ).
tff(f201,plain,
~ $less(sK4(sK2),-1),
inference(resolution,[],[f157,f14]) ).
tff(f202,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,-1)
| ~ $less(X1,X0)
| $less(X1,sK4(sK2)) ),
inference(resolution,[],[f157,f15]) ).
tff(f157,plain,
! [X0: $int] :
( $less(X0,sK4(sK2))
| ~ $less(X0,-1) ),
inference(resolution,[],[f155,f15]) ).
tff(f167,plain,
( $less(sK2,1)
| ( 1 = sK2 ) ),
inference(resolution,[],[f16,f42]) ).
tff(f185,plain,
! [X0: $int] :
( $less(X0,-1)
| ( -1 = X0 )
| ~ $less(X0,0) ),
inference(resolution,[],[f16,f89]) ).
tff(f183,plain,
( $less(1,sK4(sK2))
| ( 1 = sK4(sK2) ) ),
inference(resolution,[],[f16,f122]) ).
tff(f180,plain,
( $less(1,sK3(sK2))
| ( 1 = sK3(sK2) ) ),
inference(resolution,[],[f16,f121]) ).
tff(f178,plain,
! [X0: $int] :
( $less(X0,0)
| ( 0 = X0 )
| ~ $less(X0,1) ),
inference(resolution,[],[f16,f116]) ).
tff(f177,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X1)
| ( X0 = X1 )
| ~ $less(X2,X1)
| $less(X2,X0) ),
inference(resolution,[],[f16,f15]) ).
tff(f176,plain,
! [X0: $int,X1: $int] :
( $less($sum(1,X0),X1)
| ( $sum(1,X0) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f86]) ).
tff(f175,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,1),X1)
| ( $sum(X0,1) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f20]) ).
tff(f173,plain,
! [X0: $int] :
( $less(X0,-1)
| ( -1 = X0 )
| ~ $less(X0,0) ),
inference(resolution,[],[f16,f89]) ).
tff(f166,plain,
! [X0: $int] :
( $less(X0,0)
| ( 0 = X0 )
| ~ $less(X0,1) ),
inference(resolution,[],[f16,f116]) ).
tff(f165,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X1)
| ( X0 = X1 )
| $less(X0,X1)
| $less(X2,X0) ),
inference(resolution,[],[f16,f15]) ).
tff(f164,plain,
! [X0: $int,X1: $int] :
( $less($sum(1,X0),X1)
| ( $sum(1,X0) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f86]) ).
tff(f158,plain,
~ $less(sK3(sK2),-1),
inference(resolution,[],[f149,f14]) ).
tff(f159,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,-1)
| ~ $less(X1,X0)
| $less(X1,sK3(sK2)) ),
inference(resolution,[],[f149,f15]) ).
tff(f149,plain,
! [X0: $int] :
( $less(X0,sK3(sK2))
| ~ $less(X0,-1) ),
inference(resolution,[],[f147,f15]) ).
tff(f155,plain,
$less(-1,sK4(sK2)),
inference(resolution,[],[f150,f75]) ).
tff(f150,plain,
~ $less(sK4(sK2),0),
inference(resolution,[],[f132,f14]) ).
tff(f154,plain,
~ $less(sK4(sK2),0),
inference(evaluation,[],[f153]) ).
tff(f153,plain,
( ~ $less(-1,0)
| ~ $less(sK4(sK2),0) ),
inference(resolution,[],[f132,f89]) ).
tff(f151,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,X0)
| $less(X1,sK4(sK2)) ),
inference(resolution,[],[f132,f15]) ).
tff(f132,plain,
! [X0: $int] :
( $less(X0,sK4(sK2))
| ~ $less(X0,0) ),
inference(resolution,[],[f15,f58]) ).
tff(f147,plain,
$less(-1,sK3(sK2)),
inference(resolution,[],[f142,f75]) ).
tff(f142,plain,
~ $less(sK3(sK2),0),
inference(resolution,[],[f131,f14]) ).
tff(f146,plain,
~ $less(sK3(sK2),0),
inference(evaluation,[],[f145]) ).
tff(f145,plain,
( ~ $less(-1,0)
| ~ $less(sK3(sK2),0) ),
inference(resolution,[],[f131,f89]) ).
tff(f143,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,X0)
| $less(X1,sK3(sK2)) ),
inference(resolution,[],[f131,f15]) ).
tff(f131,plain,
! [X0: $int] :
( $less(X0,sK3(sK2))
| ~ $less(X0,0) ),
inference(resolution,[],[f15,f57]) ).
tff(f140,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,-1)
| $less(X0,X1)
| $less(X1,0) ),
inference(resolution,[],[f15,f75]) ).
tff(f139,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,1)
| $less(0,X1) ),
inference(resolution,[],[f15,f101]) ).
tff(f138,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,0)
| $less(-1,X1) ),
inference(resolution,[],[f15,f75]) ).
tff(f137,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(1,X2))
| $less(X2,X1) ),
inference(resolution,[],[f15,f72]) ).
tff(f136,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(1,X1)) ),
inference(resolution,[],[f15,f76]) ).
tff(f135,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) ),
inference(resolution,[],[f15,f71]) ).
tff(f134,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ),
inference(resolution,[],[f15,f18]) ).
tff(f133,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| $less(X0,X1)
| $less(X1,1) ),
inference(resolution,[],[f15,f101]) ).
tff(f121,plain,
~ $less(sK3(sK2),1),
inference(resolution,[],[f116,f57]) ).
tff(f127,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,0) ),
inference(resolution,[],[f116,f72]) ).
tff(f124,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,0) ),
inference(resolution,[],[f116,f18]) ).
tff(f115,plain,
! [X0: $int] :
( ~ $less(X0,-1)
| $less($sum(1,X0),0) ),
inference(resolution,[],[f86,f75]) ).
tff(f110,plain,
! [X0: $int] :
( ~ $less(X0,0)
| $less($sum(1,X0),1) ),
inference(resolution,[],[f86,f101]) ).
tff(f109,plain,
! [X0: $int] :
( $less($sum(X0,1),1)
| ~ $less(X0,0) ),
inference(resolution,[],[f101,f20]) ).
tff(f101,plain,
! [X0: $int] :
( $less(X0,1)
| $less(0,X0) ),
inference(superposition,[],[f72,f11]) ).
tff(f100,plain,
! [X0: $int] :
( $less(X0,-1)
| ~ $less($sum(1,X0),0) ),
inference(resolution,[],[f72,f89]) ).
tff(f72,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f18,f9]) ).
tff(f49,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f35]) ).
tff(f35,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f47,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f94,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),0)
| $less(X0,-1) ),
inference(resolution,[],[f89,f18]) ).
tff(f89,plain,
! [X0: $int] :
( ~ $less(-1,X0)
| ~ $less(X0,0) ),
inference(evaluation,[],[f88]) ).
tff(f88,plain,
! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) ),
inference(superposition,[],[f20,f56]) ).
tff(f92,plain,
! [X0: $int] :
( $less($sum(X0,1),0)
| ~ $less(X0,-1) ),
inference(resolution,[],[f75,f20]) ).
tff(f75,plain,
! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ),
inference(evaluation,[],[f74]) ).
tff(f74,plain,
! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) ),
inference(superposition,[],[f18,f56]) ).
tff(f87,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f20,f9]) ).
tff(f77,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f71,f9]) ).
tff(f73,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f18,f9]) ).
tff(f56,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f13,f19]) ).
tff(f45,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f44,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f19,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f43,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f53,plain,
! [X2: $int,X1: collection] : in(X2,add(X2,X1)),
inference(equality_resolution,[],[f50]) ).
tff(f50,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f36]) ).
tff(f51,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f36]) ).
tff(f46,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f52,plain,
! [X2: $int,X1: collection] : ~ in(X2,remove(X2,X1)),
inference(equality_resolution,[],[f48]) ).
tff(f48,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 != X2 )
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f289,plain,
( ~ spl5_2
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f288]) ).
tff(f288,plain,
( $false
| ~ spl5_2
| ~ spl5_5 ),
inference(subsumption_resolution,[],[f286,f121]) ).
tff(f286,plain,
( $less(sK3(sK2),1)
| ~ spl5_2
| ~ spl5_5 ),
inference(resolution,[],[f282,f196]) ).
tff(f196,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| $less(X0,1) )
| ~ spl5_2 ),
inference(resolution,[],[f194,f15]) ).
tff(f266,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f171,f263,f259]) ).
tff(f263,plain,
( spl5_6
<=> $less(1,sK4(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
tff(f250,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f249]) ).
tff(f249,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f247,f122]) ).
tff(f247,plain,
( $less(sK4(sK2),1)
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f246,f196]) ).
tff(f246,plain,
( $less(sK4(sK2),sK2)
| ~ spl5_3 ),
inference(superposition,[],[f76,f217]) ).
tff(f217,plain,
( ( sK2 = $sum(1,sK4(sK2)) )
| ~ spl5_3 ),
inference(superposition,[],[f70,f210]) ).
tff(f210,plain,
( ( 1 = sK3(sK2) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f208]) ).
tff(f208,plain,
( spl5_3
<=> ( 1 = sK3(sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
tff(f215,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f168,f212,f208]) ).
tff(f195,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f167,f192,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT030_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
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 12:53:55 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (14172)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (14175)WARNING: value z3 for option sas not known
% 0.15/0.38 % (14176)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (14174)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (14173)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (14177)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)
% 0.15/0.38 % (14178)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)
% 0.15/0.38 % (14179)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)
% 0.15/0.38 % (14175)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)
% 0.15/0.38 % (14174)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (14176)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (14173)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (14176)Terminated due to inappropriate strategy.
% 0.15/0.38 % (14176)------------------------------
% 0.15/0.38 % (14176)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (14176)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (14176)Memory used [KB]: 747
% 0.15/0.38 % (14173)Terminated due to inappropriate strategy.
% 0.15/0.38 % (14173)------------------------------
% 0.15/0.38 % (14173)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (14176)Time elapsed: 0.003 s
% 0.15/0.38 % (14173)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (14176)Instructions burned: 3 (million)
% 0.15/0.38 % (14173)Memory used [KB]: 747
% 0.15/0.38 % (14174)Terminated due to inappropriate strategy.
% 0.15/0.38 % (14174)------------------------------
% 0.15/0.38 % (14174)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (14173)Time elapsed: 0.003 s
% 0.15/0.38 % (14174)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (14173)Instructions burned: 3 (million)
% 0.15/0.38 % (14174)Memory used [KB]: 747
% 0.15/0.38 % (14174)Time elapsed: 0.003 s
% 0.15/0.38 % (14174)Instructions burned: 3 (million)
% 0.15/0.38 % (14176)------------------------------
% 0.15/0.38 % (14176)------------------------------
% 0.15/0.38 % (14173)------------------------------
% 0.15/0.38 % (14173)------------------------------
% 0.15/0.38 % (14174)------------------------------
% 0.15/0.38 % (14174)------------------------------
% 0.15/0.39 % (14180)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.39 % (14181)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)
% 0.15/0.39 % (14182)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)
% 0.15/0.39 % (14180)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (14180)Terminated due to inappropriate strategy.
% 0.15/0.39 % (14180)------------------------------
% 0.15/0.39 % (14180)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (14180)Termination reason: Inappropriate
% 0.15/0.39
% 0.15/0.39 % (14180)Memory used [KB]: 746
% 0.15/0.39 % (14180)Time elapsed: 0.002 s
% 0.15/0.39 % (14180)Instructions burned: 2 (million)
% 0.15/0.40 % (14180)------------------------------
% 0.15/0.40 % (14180)------------------------------
% 0.22/0.41 % (14183)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)
% 0.22/0.53 % (14175)First to succeed.
% 0.22/0.53 % (14175)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14172"
% 0.22/0.53 % (14175)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Theorem for theBenchmark
% 0.22/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54 % (14175)------------------------------
% 0.22/0.54 % (14175)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.54 % (14175)Termination reason: Refutation
% 0.22/0.54
% 0.22/0.54 % (14175)Memory used [KB]: 2434
% 0.22/0.54 % (14175)Time elapsed: 0.158 s
% 0.22/0.54 % (14175)Instructions burned: 291 (million)
% 0.22/0.54 % (14172)Success in time 0.174 s
%------------------------------------------------------------------------------