%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI573_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:33:23 AM UTC 2026
% Result : Theorem 2.41s 0.98s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 29 ~; 0 |; 20 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 241 ( 40 atm; 110 fun; 70 num; 21 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 12 !; 9 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sK1: $int ).
tff(func_def_7,type,
sK2: $int ).
tff(f1,conjecture,
! [X2: $int,X1: $int,X0: $int] :
( ( $lesseq(1,$sum($product(X2,2),$uminus(X0)))
& $lesseq(1,$sum($product(X0,2),$uminus(X1)))
& $lesseq(1,$sum($product(X1,2),$uminus(X2))) )
=> $lesseq(2,$sum($sum(X0,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_3_ineq) ).
tff(f2,negated_conjecture,
~ ! [X2: $int,X1: $int,X0: $int] :
( ( $lesseq(1,$sum($product(X2,2),$uminus(X0)))
& $lesseq(1,$sum($product(X0,2),$uminus(X1)))
& $lesseq(1,$sum($product(X1,2),$uminus(X2))) )
=> $lesseq(2,$sum($sum(X0,X1),X2)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X2: $int,X1: $int,X0: $int] :
( ( ~ $less($sum($product(X2,2),$uminus(X0)),1)
& ~ $less($sum($product(X0,2),$uminus(X1)),1)
& ~ $less($sum($product(X1,2),$uminus(X2)),1) )
=> ~ $less($sum($sum(X0,X1),X2),2) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
~ ! [X1: $int,X0: $int,X2: $int] :
( ( ~ $less($sum($product(X1,2),$uminus(X0)),1)
& ~ $less($sum($product(X2,2),$uminus(X1)),1)
& ~ $less($sum($product(X0,2),$uminus(X2)),1) )
=> ~ $less($sum($sum(X2,X1),X0),2) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
? [X1: $int,X0: $int,X2: $int] :
( $less($sum($sum(X2,X1),X0),2)
& ~ $less($sum($product(X1,2),$uminus(X0)),1)
& ~ $less($sum($product(X2,2),$uminus(X1)),1)
& ~ $less($sum($product(X0,2),$uminus(X2)),1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
? [X1: $int,X2: $int,X0: $int] :
( $less($sum($sum(X2,X1),X0),2)
& ~ $less($sum($product(X0,2),$uminus(X2)),1)
& ~ $less($sum($product(X1,2),$uminus(X0)),1)
& ~ $less($sum($product(X2,2),$uminus(X1)),1) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
? [X0: $int,X1: $int,X2: $int] :
( $less($sum($sum(X1,X0),X2),2)
& ~ $less($sum($product(X2,2),$uminus(X1)),1)
& ~ $less($sum($product(X0,2),$uminus(X2)),1)
& ~ $less($sum($product(X1,2),$uminus(X0)),1) ),
inference(rectify,[],[f6]) ).
tff(f8,plain,
( $less($sum($sum(sK1,sK0),sK2),2)
& ~ $less($sum($product(sK2,2),$uminus(sK1)),1)
& ~ $less($sum($product(sK0,2),$uminus(sK2)),1)
& ~ $less($sum($product(sK1,2),$uminus(sK0)),1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
tff(f9,plain,
~ $less($sum($product(sK1,2),$uminus(sK0)),1),
inference(cnf_transformation,[],[f8]) ).
tff(f10,plain,
~ $less($sum($product(sK0,2),$uminus(sK2)),1),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
~ $less($sum($product(sK2,2),$uminus(sK1)),1),
inference(cnf_transformation,[],[f8]) ).
tff(f12,plain,
$less($sum($sum(sK1,sK0),sK2),2),
inference(cnf_transformation,[],[f8]) ).
tff(f14,definition,
( spl3_1
<=> $less($sum($product(sK1,2),$uminus(sK0)),1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f17,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f9,f14]) ).
tff(f19,definition,
( spl3_2
<=> $less($sum($sum(sK1,sK0),sK2),2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f22,plain,
spl3_2,
inference(avatar_split_clause,[],[f12,f19]) ).
tff(f24,definition,
( spl3_3
<=> $less($sum($product(sK2,2),$uminus(sK1)),1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f27,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f11,f24]) ).
tff(f29,definition,
( spl3_4
<=> $less($sum($product(sK0,2),$uminus(sK2)),1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f32,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f10,f29]) ).
tff(f33,plain,
$false,
inference(avatar_smt_refutation,[],[f32,f27,f22,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI573_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n011.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 20:52:31 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running first-order theorem proving
% 0.10/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.41/0.98 % (3770513)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.41/0.98 % (3770523)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3819593137:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 2.41/0.98 % (3770523)First to succeed.
% 2.41/0.98 % (3770523)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3770513"
% 2.41/0.98 % (3770518)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1526618602:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 2.41/0.98 % (3770520)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3243466389:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 2.41/0.98 % (3770521)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4255372631:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 2.41/0.98 % (3770519)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3128623962:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 2.41/0.98 % (3770524)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1479830304:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 2.41/0.98 % (3770521)Instruction limit reached!
% 2.41/0.98 % (3770521)------------------------------
% 2.41/0.98 % (3770521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/0.98 % (3770521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.98 % (3770521)CaDiCaL version: 2.1.3
% 2.41/0.98 % (3770521)Termination reason: Instruction limit
% 2.41/0.98 % (3770521)Termination phase: Saturation
% 2.41/0.98 % (3770521)Time elapsed: 0.005 s
% 2.41/0.98 % (3770521)Peak memory usage: 88 MB
% 2.41/0.98 % (3770521)Instructions burned: 8 (million)
% 2.41/0.98 % (3770522)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1627770996:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 2.41/0.98 % (3770522)Instruction limit reached!
% 2.41/0.98 % (3770522)------------------------------
% 2.41/0.98 % (3770522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/0.98 % (3770522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.98 % (3770522)CaDiCaL version: 2.1.3
% 2.41/0.98 % (3770522)Termination reason: Instruction limit
% 2.41/0.98 % (3770522)Termination phase: Saturation
% 2.41/0.98 % (3770522)Time elapsed: 0.003 s
% 2.41/0.98 % (3770522)Peak memory usage: 88 MB
% 2.41/0.98 % (3770522)Instructions burned: 4 (million)
% 2.41/0.98 % (3770518)Also succeeded, but the first one will report.
% 2.41/0.98 % (3770519)Also succeeded, but the first one will report.
% 2.41/0.98 % (3770524)Also succeeded, but the first one will report.
% 2.41/0.98 % (3770532)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1597378517:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.41/0.98 % (3770532)Refutation not found, incomplete strategy
% 2.41/0.98 % (3770532)------------------------------
% 2.41/0.98 % (3770532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/0.98 % (3770532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.98 % (3770532)CaDiCaL version: 2.1.3
% 2.41/0.98 % (3770532)Termination reason: Refutation not found, incomplete strategy
% 2.41/0.98 % (3770532)Time elapsed: 0.001 s
% 2.41/0.98 % (3770532)Peak memory usage: 88 MB
% 2.41/0.98 % (3770523)Refutation found. Thanks to Tanya!
% 2.41/0.98 % SZS status Theorem for theBenchmark
% 2.41/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/0.98 % (3770523)------------------------------
% 2.41/0.98 % (3770523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/0.98 % (3770523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.98 % (3770523)CaDiCaL version: 2.1.3
% 2.41/0.98 % (3770523)Termination reason: Refutation
% 2.41/0.98 % (3770523)Time elapsed: 0.020 s
% 2.41/0.98 % (3770523)Peak memory usage: 115 MB
% 2.41/0.98 % (3770523)Instructions burned: 9 (million)
% 2.41/0.98 % (3770523)------------------------------
% 2.41/0.98 % (3770523)------------------------------
% 2.41/0.98 % (3770513)Success in time 0.274 s
% 2.41/0.98 % Vampire exiting
%------------------------------------------------------------------------------