TSTP Solution File: ARI588_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI588_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.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 10:35:38 EDT 2024
% Result : Theorem 25.47s 4.59s
% Output : Refutation 25.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 30
% Syntax : Number of formulae : 168 ( 25 unt; 1 typ; 0 def)
% Number of atoms : 365 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 345 ( 147 ~; 173 |; 4 &)
% ( 20 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number arithmetic : 1064 ( 181 atm; 396 fun; 351 num; 136 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 8 ( 1 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 130 !; 6 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int > $int ).
tff(f104169,plain,
$false,
inference(avatar_sat_refutation,[],[f287,f1303,f1323,f1383,f1494,f1590,f101504,f101723,f101777,f101810,f102248,f102467,f102532,f102587,f102591,f102970,f103143,f104168]) ).
tff(f104168,plain,
( ~ spl1_1
| ~ spl1_5
| spl1_55
| spl1_63 ),
inference(avatar_contradiction_clause,[],[f104167]) ).
tff(f104167,plain,
( $false
| ~ spl1_1
| ~ spl1_5
| spl1_55
| spl1_63 ),
inference(subsumption_resolution,[],[f104166,f103146]) ).
tff(f103146,plain,
( $less(sK0(2),0)
| spl1_55 ),
inference(resolution,[],[f101502,f38]) ).
tff(f38,plain,
! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ),
inference(evaluation,[],[f37]) ).
tff(f37,plain,
! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) ),
inference(superposition,[],[f13,f22]) ).
tff(f22,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f8,f14]) ).
tff(f14,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f101502,plain,
( ~ $less(-1,sK0(2))
| spl1_55 ),
inference(avatar_component_clause,[],[f101501]) ).
tff(f101501,plain,
( spl1_55
<=> $less(-1,sK0(2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f104166,plain,
( ~ $less(sK0(2),0)
| ~ spl1_1
| ~ spl1_5
| spl1_63 ),
inference(resolution,[],[f103131,f101603]) ).
tff(f101603,plain,
( ~ $less(sK0(2),2)
| spl1_63 ),
inference(avatar_component_clause,[],[f101602]) ).
tff(f101602,plain,
( spl1_63
<=> $less(sK0(2),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
tff(f103131,plain,
( ! [X0: $int] :
( $less(X0,2)
| ~ $less(X0,0) )
| ~ spl1_1
| ~ spl1_5 ),
inference(forward_demodulation,[],[f1327,f190]) ).
tff(f190,plain,
( ( 0 = sK0(3) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f188,plain,
( spl1_5
<=> ( 0 = sK0(3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f1327,plain,
( ! [X0: $int] :
( ~ $less(X0,sK0(3))
| $less(X0,2) )
| ~ spl1_1 ),
inference(resolution,[],[f150,f10]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f150,plain,
( $less(sK0(3),2)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f149]) ).
tff(f149,plain,
( spl1_1
<=> $less(sK0(3),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f103143,plain,
( ~ spl1_63
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f103141,f101497,f101602]) ).
tff(f101497,plain,
( spl1_54
<=> $less(1,sK0(2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f103141,plain,
( ~ $less(sK0(2),2)
| ~ spl1_54 ),
inference(evaluation,[],[f103136]) ).
tff(f103136,plain,
( ~ $less(sK0(2),$sum(1,1))
| ~ spl1_54 ),
inference(resolution,[],[f101499,f15]) ).
tff(f15,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f101499,plain,
( $less(1,sK0(2))
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f101497]) ).
tff(f102970,plain,
( ~ spl1_21
| spl1_1 ),
inference(avatar_split_clause,[],[f102969,f149,f1214]) ).
tff(f1214,plain,
( spl1_21
<=> $less(0,$sum(1,sK0(3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f102969,plain,
( $less(sK0(3),2)
| ~ $less(0,$sum(1,sK0(3))) ),
inference(forward_demodulation,[],[f102968,f139]) ).
tff(f139,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f121]) ).
tff(f121,plain,
! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f5,f8]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f102968,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($sum(X0,X1),$sum($uminus($sum(X0,X1)),3))),2)
| ~ $less(0,$sum(1,sK0(3))) ),
inference(forward_demodulation,[],[f102967,f129]) ).
tff(f129,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ),
inference(superposition,[],[f5,f4]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f102967,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($uminus($sum(X0,X1)),$sum(3,$sum(X0,X1)))),2)
| ~ $less(0,$sum(1,sK0(3))) ),
inference(forward_demodulation,[],[f102966,f4]) ).
tff(f102966,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1)))),2)
| ~ $less(0,$sum(1,sK0(3))) ),
inference(evaluation,[],[f102965]) ).
tff(f102965,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1)))),$sum(2,0))
| ~ $less(0,$sum(1,sK0(3))) ),
inference(forward_demodulation,[],[f102964,f8]) ).
tff(f102964,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1)))),$sum(2,$sum(X0,$uminus(X0))))
| ~ $less(0,$sum(1,sK0(3))) ),
inference(forward_demodulation,[],[f102963,f208]) ).
tff(f208,plain,
! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) ),
inference(superposition,[],[f139,f7]) ).
tff(f7,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f102963,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1)))),$sum(2,$sum(X0,$sum(X1,$uminus($sum(X0,X1))))))
| ~ $less(0,$sum(1,sK0(3))) ),
inference(evaluation,[],[f102962]) ).
tff(f102962,plain,
! [X0: $int,X1: $int] :
( $less(sK0($sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1)))),$sum(-1,$sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1)))))
| ~ $less(0,$sum(1,sK0(3))) ),
inference(forward_demodulation,[],[f51009,f262]) ).
tff(f262,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$uminus($sum(X0,X1))) = $uminus($sum(X0,$sum(X1,$uminus(X2)))) ),
inference(superposition,[],[f66,f5]) ).
tff(f66,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X1,$uminus(X0))) = $sum(X0,$uminus(X1)) ),
inference(superposition,[],[f7,f14]) ).
tff(f51009,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,$sum(1,sK0(3)))
| $less(sK0($uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1))))))),$sum(-1,$uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1)))))))) ),
inference(forward_demodulation,[],[f51008,f139]) ).
tff(f51008,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,$sum(1,sK0($sum($sum(X0,X1),$sum($uminus($sum(X0,X1)),3)))))
| $less(sK0($uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1))))))),$sum(-1,$uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1)))))))) ),
inference(forward_demodulation,[],[f51007,f129]) ).
tff(f51007,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,$sum(1,sK0($sum($uminus($sum(X0,X1)),$sum(3,$sum(X0,X1))))))
| $less(sK0($uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1))))))),$sum(-1,$uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1)))))))) ),
inference(forward_demodulation,[],[f51006,f4]) ).
tff(f51006,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,$sum(1,sK0($sum($sum(3,$sum(X0,X1)),$uminus($sum(X0,X1))))))
| $less(sK0($uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1))))))),$sum(-1,$uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1)))))))) ),
inference(forward_demodulation,[],[f50912,f262]) ).
tff(f50912,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,$sum(1,sK0($uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1)))))))))
| $less(sK0($uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1))))))),$sum(-1,$uminus($sum(X0,$sum(X1,$uminus($sum(3,$sum(X0,X1)))))))) ),
inference(superposition,[],[f1051,f414]) ).
tff(f414,plain,
! [X2: $int,X0: $int,X1: $int] : ( 0 = $sum(X2,$sum(X0,$sum(X1,$uminus($sum(X2,$sum(X0,X1)))))) ),
inference(superposition,[],[f128,f5]) ).
tff(f128,plain,
! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ),
inference(superposition,[],[f5,f8]) ).
tff(f1051,plain,
! [X0: $int] :
( ~ $less($sum(3,X0),$sum(1,sK0($uminus(X0))))
| $less(sK0($uminus(X0)),$sum(-1,$uminus(X0))) ),
inference(forward_demodulation,[],[f1046,f4]) ).
tff(f1046,plain,
! [X0: $int] :
( ~ $less($sum(3,X0),$sum(1,sK0($uminus(X0))))
| $less(sK0($uminus(X0)),$sum($uminus(X0),-1)) ),
inference(superposition,[],[f177,f14]) ).
tff(f177,plain,
! [X0: $int] :
( ~ $less($sum(3,$uminus(X0)),$sum(1,sK0(X0)))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(forward_demodulation,[],[f172,f4]) ).
tff(f172,plain,
! [X0: $int] :
( $less(sK0(X0),$sum(X0,-1))
| ~ $less($sum(3,$uminus(X0)),$sum(sK0(X0),1)) ),
inference(resolution,[],[f21,f15]) ).
tff(f21,plain,
! [X0: $int] :
( $less(sK0(X0),$sum(3,$uminus(X0)))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
! [X0: $int] :
( ( $less(sK0(X0),$sum(X0,-1))
| $less(sK0(X0),$sum(3,$uminus(X0))) )
& ( ~ $less(sK0(X0),$sum(3,$uminus(X0)))
| ~ $less(sK0(X0),$sum(X0,-1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18]) ).
tff(f18,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( $less(X1,$sum(X0,-1))
| $less(X1,$sum(3,$uminus(X0))) )
& ( ~ $less(X1,$sum(3,$uminus(X0)))
| ~ $less(X1,$sum(X0,-1)) ) )
=> ( ( $less(sK0(X0),$sum(X0,-1))
| $less(sK0(X0),$sum(3,$uminus(X0))) )
& ( ~ $less(sK0(X0),$sum(3,$uminus(X0)))
| ~ $less(sK0(X0),$sum(X0,-1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f17,plain,
! [X0: $int] :
? [X1: $int] :
( ( $less(X1,$sum(X0,-1))
| $less(X1,$sum(3,$uminus(X0))) )
& ( ~ $less(X1,$sum(3,$uminus(X0)))
| ~ $less(X1,$sum(X0,-1)) ) ),
inference(nnf_transformation,[],[f16]) ).
tff(f16,plain,
! [X0: $int] :
? [X1: $int] :
( $less(X1,$sum(X0,-1))
<=> ~ $less(X1,$sum(3,$uminus(X0))) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ? [X0: $int] :
! [X1: $int] :
~ ( $less(X1,$sum(X0,-1))
<=> ~ $less(X1,$sum(3,$uminus(X0))) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ? [X0: $int] :
! [X1: $int] :
~ ( $less(X1,$sum(X0,-1))
<=> $lesseq($sum(3,$uminus(X0)),X1) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
? [X0: $int] :
! [X1: $int] :
~ ( $less(X1,$sum(X0,-1))
<=> $lesseq($sum(3,$uminus(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists_X_complementary_halflines) ).
tff(f102591,plain,
( spl1_5
| ~ spl1_1
| spl1_6 ),
inference(avatar_split_clause,[],[f74455,f192,f149,f188]) ).
tff(f192,plain,
( spl1_6
<=> $less(0,sK0(3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f74455,plain,
( $less(0,sK0(3))
| ~ $less(sK0(3),2)
| ( 0 = sK0(3) ) ),
inference(evaluation,[],[f74447]) ).
tff(f74447,plain,
( $less(0,sK0(3))
| ~ $less(sK0(3),$sum(-1,3))
| ( 0 = sK0(3) ) ),
inference(superposition,[],[f1161,f8]) ).
tff(f1161,plain,
! [X0: $int] :
( $less($sum(3,$uminus(X0)),sK0(X0))
| ~ $less(sK0(X0),$sum(-1,X0))
| ( $sum(3,$uminus(X0)) = sK0(X0) ) ),
inference(superposition,[],[f142,f4]) ).
tff(f142,plain,
! [X0: $int] :
( ~ $less(sK0(X0),$sum(X0,-1))
| $less($sum(3,$uminus(X0)),sK0(X0))
| ( $sum(3,$uminus(X0)) = sK0(X0) ) ),
inference(resolution,[],[f20,f11]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f20,plain,
! [X0: $int] :
( ~ $less(sK0(X0),$sum(3,$uminus(X0)))
| ~ $less(sK0(X0),$sum(X0,-1)) ),
inference(cnf_transformation,[],[f19]) ).
tff(f102587,plain,
( ~ spl1_64
| ~ spl1_71 ),
inference(avatar_contradiction_clause,[],[f102586]) ).
tff(f102586,plain,
( $false
| ~ spl1_64
| ~ spl1_71 ),
inference(subsumption_resolution,[],[f102584,f101609]) ).
tff(f101609,plain,
( $less(sK0(2),1)
| ~ spl1_64 ),
inference(avatar_component_clause,[],[f101607]) ).
tff(f101607,plain,
( spl1_64
<=> $less(sK0(2),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
tff(f102584,plain,
( ~ $less(sK0(2),1)
| ~ spl1_71 ),
inference(evaluation,[],[f102579]) ).
tff(f102579,plain,
( ~ $less(sK0(2),$sum(0,1))
| ~ spl1_71 ),
inference(resolution,[],[f101917,f15]) ).
tff(f101917,plain,
( $less(0,sK0(2))
| ~ spl1_71 ),
inference(avatar_component_clause,[],[f101915]) ).
tff(f101915,plain,
( spl1_71
<=> $less(0,sK0(2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
tff(f102532,plain,
( spl1_70
| spl1_71
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f102510,f101501,f101915,f101911]) ).
tff(f101911,plain,
( spl1_70
<=> ( 0 = sK0(2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
tff(f102510,plain,
( $less(0,sK0(2))
| ( 0 = sK0(2) )
| ~ spl1_55 ),
inference(resolution,[],[f101787,f11]) ).
tff(f101787,plain,
( ~ $less(sK0(2),0)
| ~ spl1_55 ),
inference(evaluation,[],[f101782]) ).
tff(f101782,plain,
( ~ $less(sK0(2),$sum(-1,1))
| ~ spl1_55 ),
inference(resolution,[],[f101503,f15]) ).
tff(f101503,plain,
( $less(-1,sK0(2))
| ~ spl1_55 ),
inference(avatar_component_clause,[],[f101501]) ).
tff(f102467,plain,
( spl1_64
| spl1_53
| spl1_54 ),
inference(avatar_split_clause,[],[f102466,f101497,f101493,f101607]) ).
tff(f101493,plain,
( spl1_53
<=> ( 1 = sK0(2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f102466,plain,
( $less(sK0(2),1)
| spl1_53
| spl1_54 ),
inference(subsumption_resolution,[],[f102438,f101494]) ).
tff(f101494,plain,
( ( 1 != sK0(2) )
| spl1_53 ),
inference(avatar_component_clause,[],[f101493]) ).
tff(f102438,plain,
( $less(sK0(2),1)
| ( 1 = sK0(2) )
| spl1_54 ),
inference(resolution,[],[f101498,f11]) ).
tff(f101498,plain,
( ~ $less(1,sK0(2))
| spl1_54 ),
inference(avatar_component_clause,[],[f101497]) ).
tff(f102248,plain,
~ spl1_70,
inference(avatar_contradiction_clause,[],[f102247]) ).
tff(f102247,plain,
( $false
| ~ spl1_70 ),
inference(evaluation,[],[f102203]) ).
tff(f102203,plain,
( ~ $less(0,$sum(3,$uminus(2)))
| ~ $less(0,$sum(2,-1))
| ~ spl1_70 ),
inference(superposition,[],[f20,f101913]) ).
tff(f101913,plain,
( ( 0 = sK0(2) )
| ~ spl1_70 ),
inference(avatar_component_clause,[],[f101911]) ).
tff(f101810,plain,
( ~ spl1_64
| ~ spl1_1
| ~ spl1_22
| spl1_63 ),
inference(avatar_split_clause,[],[f101791,f101602,f1255,f149,f101607]) ).
tff(f1255,plain,
( spl1_22
<=> ( 1 = sK0(3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f101791,plain,
( ~ $less(sK0(2),1)
| ~ spl1_1
| ~ spl1_22
| spl1_63 ),
inference(resolution,[],[f101603,f1664]) ).
tff(f1664,plain,
( ! [X0: $int] :
( $less(X0,2)
| ~ $less(X0,1) )
| ~ spl1_1
| ~ spl1_22 ),
inference(backward_demodulation,[],[f1327,f1257]) ).
tff(f1257,plain,
( ( 1 = sK0(3) )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f1255]) ).
tff(f101777,plain,
( spl1_64
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f101776,f101497,f101607]) ).
tff(f101776,plain,
( $less(sK0(2),1)
| ~ spl1_54 ),
inference(evaluation,[],[f101767]) ).
tff(f101767,plain,
( $less(sK0(2),$sum(2,-1))
| $less(1,$sum(3,$uminus(2)))
| ~ spl1_54 ),
inference(resolution,[],[f101499,f171]) ).
tff(f171,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,sK0(X0))
| $less(sK0(X0),$sum(X0,-1))
| $less(X1,$sum(3,$uminus(X0))) ),
inference(resolution,[],[f21,f10]) ).
tff(f101723,plain,
~ spl1_53,
inference(avatar_contradiction_clause,[],[f101722]) ).
tff(f101722,plain,
( $false
| ~ spl1_53 ),
inference(evaluation,[],[f101721]) ).
tff(f101721,plain,
( $less(0,$sum(3,$uminus(3)))
| ~ spl1_53 ),
inference(forward_demodulation,[],[f101669,f208]) ).
tff(f101669,plain,
( ! [X0: $int] : $less(0,$sum(3,$sum(X0,$uminus($sum(3,X0)))))
| ~ spl1_53 ),
inference(evaluation,[],[f101668]) ).
tff(f101668,plain,
( ! [X0: $int] :
( $less(0,$sum(3,$sum(X0,$uminus($sum(2,$sum(1,X0))))))
| $less(1,$sum(2,-1)) )
| ~ spl1_53 ),
inference(superposition,[],[f73996,f101495]) ).
tff(f101495,plain,
( ( 1 = sK0(2) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f101493]) ).
tff(f73996,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(3,$sum(X1,$uminus($sum(X0,$sum(sK0(X0),X1))))))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(forward_demodulation,[],[f73995,f4]) ).
tff(f73995,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(3,$sum($uminus($sum(X0,$sum(sK0(X0),X1))),X1)))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(forward_demodulation,[],[f1094,f361]) ).
tff(f361,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X1,X2)),X0) = $sum($uminus(X1),$sum(X0,$uminus(X2))) ),
inference(forward_demodulation,[],[f360,f67]) ).
tff(f67,plain,
! [X0: $int,X1: $int] : ( $uminus($sum($uminus(X0),X1)) = $sum($uminus(X1),X0) ),
inference(superposition,[],[f7,f14]) ).
tff(f360,plain,
! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum($uminus(X0),$sum(X1,X2))) = $sum($uminus(X1),$sum(X0,$uminus(X2))) ),
inference(forward_demodulation,[],[f359,f5]) ).
tff(f359,plain,
! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum($sum($uminus(X0),X1),X2)) = $sum($uminus(X1),$sum(X0,$uminus(X2))) ),
inference(forward_demodulation,[],[f336,f5]) ).
tff(f336,plain,
! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum($sum($uminus(X0),X1),X2)) = $sum($sum($uminus(X1),X0),$uminus(X2)) ),
inference(superposition,[],[f70,f67]) ).
tff(f70,plain,
! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ),
inference(superposition,[],[f7,f4]) ).
tff(f1094,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(3,$sum($uminus(X0),$sum(X1,$uminus($sum(sK0(X0),X1))))))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(superposition,[],[f176,f128]) ).
tff(f176,plain,
! [X0: $int,X1: $int] :
( $less($sum(sK0(X0),X1),$sum(3,$sum($uminus(X0),X1)))
| $less(sK0(X0),$sum(X0,-1)) ),
inference(forward_demodulation,[],[f170,f5]) ).
tff(f170,plain,
! [X0: $int,X1: $int] :
( $less(sK0(X0),$sum(X0,-1))
| $less($sum(sK0(X0),X1),$sum($sum(3,$uminus(X0)),X1)) ),
inference(resolution,[],[f21,f12]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f101504,plain,
( spl1_53
| spl1_54
| spl1_55 ),
inference(avatar_split_clause,[],[f101443,f101501,f101497,f101493]) ).
tff(f101443,plain,
( $less(-1,sK0(2))
| $less(1,sK0(2))
| ( 1 = sK0(2) ) ),
inference(evaluation,[],[f101398]) ).
tff(f101398,plain,
( $less(-1,sK0(2))
| $less($sum(3,$uminus(2)),sK0(2))
| ( $sum(3,$uminus(2)) = sK0(2) ) ),
inference(resolution,[],[f3416,f142]) ).
tff(f3416,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum(2,X1))
| $less(X1,X0) ),
inference(evaluation,[],[f3382]) ).
tff(f3382,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum($sum(X1,1),1))
| $less(X1,X0) ),
inference(resolution,[],[f454,f39]) ).
tff(f39,plain,
! [X0: $int,X1: $int] :
( ~ $less($sum(X0,1),$sum(X1,1))
| $less(X0,X1) ),
inference(resolution,[],[f15,f13]) ).
tff(f454,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(X0,1)) ),
inference(resolution,[],[f49,f34]) ).
tff(f34,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f13,f9]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f49,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ),
inference(resolution,[],[f10,f13]) ).
tff(f1590,plain,
( ~ spl1_1
| ~ spl1_23 ),
inference(avatar_contradiction_clause,[],[f1589]) ).
tff(f1589,plain,
( $false
| ~ spl1_1
| ~ spl1_23 ),
inference(subsumption_resolution,[],[f1587,f150]) ).
tff(f1587,plain,
( ~ $less(sK0(3),2)
| ~ spl1_23 ),
inference(evaluation,[],[f1586]) ).
tff(f1586,plain,
( ~ $less(sK0(3),$sum(1,1))
| ~ spl1_23 ),
inference(resolution,[],[f1261,f15]) ).
tff(f1261,plain,
( $less(1,sK0(3))
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f1259]) ).
tff(f1259,plain,
( spl1_23
<=> $less(1,sK0(3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f1494,plain,
( spl1_22
| spl1_23
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f1492,f192,f1259,f1255]) ).
tff(f1492,plain,
( $less(1,sK0(3))
| ( 1 = sK0(3) )
| ~ spl1_6 ),
inference(resolution,[],[f1341,f11]) ).
tff(f1341,plain,
( ~ $less(sK0(3),1)
| ~ spl1_6 ),
inference(evaluation,[],[f1340]) ).
tff(f1340,plain,
( ~ $less(sK0(3),$sum(0,1))
| ~ spl1_6 ),
inference(resolution,[],[f194,f15]) ).
tff(f194,plain,
( $less(0,sK0(3))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f192]) ).
tff(f1383,plain,
( spl1_2
| spl1_21 ),
inference(avatar_contradiction_clause,[],[f1382]) ).
tff(f1382,plain,
( $false
| spl1_2
| spl1_21 ),
inference(subsumption_resolution,[],[f1379,f155]) ).
tff(f155,plain,
( ~ $less(sK0(3),0)
| spl1_2 ),
inference(avatar_component_clause,[],[f153]) ).
tff(f153,plain,
( spl1_2
<=> $less(sK0(3),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f1379,plain,
( $less(sK0(3),0)
| spl1_21 ),
inference(resolution,[],[f1216,f35]) ).
tff(f35,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f13,f4]) ).
tff(f1216,plain,
( ~ $less(0,$sum(1,sK0(3)))
| spl1_21 ),
inference(avatar_component_clause,[],[f1214]) ).
tff(f1323,plain,
( spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f1320,f164,f149]) ).
tff(f164,plain,
( spl1_4
<=> $less(2,sK0(3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f1320,plain,
( $less(sK0(3),2)
| ~ spl1_4 ),
inference(evaluation,[],[f1313]) ).
tff(f1313,plain,
( $less(sK0(3),$sum(3,-1))
| $less(2,$sum(3,$uminus(3)))
| ~ spl1_4 ),
inference(resolution,[],[f166,f171]) ).
tff(f166,plain,
( $less(2,sK0(3))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f164]) ).
tff(f1303,plain,
( spl1_3
| spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f1301,f149,f164,f160]) ).
tff(f160,plain,
( spl1_3
<=> ( 2 = sK0(3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f1301,plain,
( $less(2,sK0(3))
| ( 2 = sK0(3) )
| spl1_1 ),
inference(resolution,[],[f151,f11]) ).
tff(f151,plain,
( ~ $less(sK0(3),2)
| spl1_1 ),
inference(avatar_component_clause,[],[f149]) ).
tff(f287,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f286]) ).
tff(f286,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(evaluation,[],[f280]) ).
tff(f280,plain,
( $less(2,0)
| ~ spl1_2
| ~ spl1_3 ),
inference(backward_demodulation,[],[f154,f162]) ).
tff(f162,plain,
( ( 2 = sK0(3) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f160]) ).
tff(f154,plain,
( $less(sK0(3),0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI588_1 : TPTP v8.1.2. Released v5.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:29:33 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (10492)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (10494)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (10496)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38 % (10495)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.38 % (10493)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % (10497)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 % (10498)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 % (10499)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % (10494)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (10496)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (10494)Terminated due to inappropriate strategy.
% 0.14/0.38 % (10494)------------------------------
% 0.14/0.38 % (10494)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (10494)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (10494)Memory used [KB]: 719
% 0.14/0.38 % (10494)Time elapsed: 0.002 s
% 0.14/0.38 % (10494)Instructions burned: 2 (million)
% 0.14/0.38 % (10494)------------------------------
% 0.14/0.38 % (10494)------------------------------
% 0.14/0.38 % (10496)Terminated due to inappropriate strategy.
% 0.14/0.38 % (10496)------------------------------
% 0.14/0.38 % (10496)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (10496)Termination reason: Inappropriate
% 0.14/0.38 % (10493)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38
% 0.14/0.38 % (10496)Memory used [KB]: 719
% 0.14/0.38 % (10496)Time elapsed: 0.002 s
% 0.14/0.38 % (10496)Instructions burned: 2 (million)
% 0.14/0.38 % (10496)------------------------------
% 0.14/0.38 % (10496)------------------------------
% 0.14/0.38 % (10493)Terminated due to inappropriate strategy.
% 0.14/0.38 % (10493)------------------------------
% 0.14/0.38 % (10493)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (10493)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (10493)Memory used [KB]: 719
% 0.14/0.38 % (10493)Time elapsed: 0.002 s
% 0.14/0.38 % (10493)Instructions burned: 2 (million)
% 0.14/0.38 % (10493)------------------------------
% 0.14/0.38 % (10493)------------------------------
% 0.14/0.38 % (10499)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (10499)Terminated due to inappropriate strategy.
% 0.14/0.38 % (10499)------------------------------
% 0.14/0.38 % (10499)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (10499)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (10499)Memory used [KB]: 719
% 0.14/0.38 % (10499)Time elapsed: 0.002 s
% 0.14/0.38 % (10499)Instructions burned: 2 (million)
% 0.14/0.38 % (10499)------------------------------
% 0.14/0.38 % (10499)------------------------------
% 0.21/0.39 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.39 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.39 % (10500)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.39 % (10501)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.21/0.39 % (10502)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.39 % (10503)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.39 % (10500)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.39 % (10500)Terminated due to inappropriate strategy.
% 0.21/0.39 % (10500)------------------------------
% 0.21/0.39 % (10500)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.39 % (10500)Termination reason: Inappropriate
% 0.21/0.39
% 0.21/0.39 % (10500)Memory used [KB]: 719
% 0.21/0.39 % (10500)Time elapsed: 0.002 s
% 0.21/0.39 % (10500)Instructions burned: 2 (million)
% 0.21/0.39 % (10500)------------------------------
% 0.21/0.39 % (10500)------------------------------
% 0.21/0.39 % (10502)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.39 % (10502)Terminated due to inappropriate strategy.
% 0.21/0.39 % (10502)------------------------------
% 0.21/0.39 % (10502)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.39 % (10502)Termination reason: Inappropriate
% 0.21/0.39
% 0.21/0.39 % (10502)Memory used [KB]: 719
% 0.21/0.39 % (10502)Time elapsed: 0.002 s
% 0.21/0.39 % (10502)Instructions burned: 2 (million)
% 0.21/0.39 % (10502)------------------------------
% 0.21/0.39 % (10502)------------------------------
% 0.21/0.41 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.21/0.41 % (10504)dis+11_4:5_nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_216 on theBenchmark for (216ds/0Mi)
% 25.47/4.59 % (10498)First to succeed.
% 25.47/4.59 % (10498)Refutation found. Thanks to Tanya!
% 25.47/4.59 % SZS status Theorem for theBenchmark
% 25.47/4.59 % SZS output start Proof for theBenchmark
% See solution above
% 25.47/4.59 % (10498)------------------------------
% 25.47/4.59 % (10498)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 25.47/4.59 % (10498)Termination reason: Refutation
% 25.47/4.59
% 25.47/4.59 % (10498)Memory used [KB]: 52611
% 25.47/4.59 % (10498)Time elapsed: 4.214 s
% 25.47/4.59 % (10498)Instructions burned: 17137 (million)
% 25.47/4.59 % (10498)------------------------------
% 25.47/4.59 % (10498)------------------------------
% 25.47/4.59 % (10492)Success in time 4.231 s
%------------------------------------------------------------------------------