%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI549_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:33:20 AM UTC 2026
% Result : Theorem 2.77s 1.18s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 14 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 5 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 35 ( 0 atm; 11 fun; 24 num; 0 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 : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 2 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sF0: $int ).
tff(func_def_6,type,
sF1: $int ).
tff(f1,conjecture,
$product($sum(-2,-3),0) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_combined_problem_13) ).
tff(f2,negated_conjecture,
( ( ~ $product($sum(-2,-3),0) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
0 != $product($sum(-2,-3),0),
inference(flattening,[],[f2]) ).
tff(f4,plain,
0 != $product($sum(-2,-3),0),
inference(cnf_transformation,[],[f3]) ).
tff(f5,definition,
sF0 = $sum(-2,-3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f6,plain,
$sum(-2,-3) = sF0,
inference(reorient_equations,[],[f5]) ).
tff(f7,definition,
sF1 = $product(sF0,0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f8,plain,
0 != sF1,
inference(definition_folding,[],[f4,f7,f6]) ).
tff(f10,plain,
0 = sF1,
inference(evaluation,[],[f7]) ).
tff(f17,definition,
( spl2_2
<=> ( 0 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f20,plain,
spl2_2,
inference(avatar_split_clause,[],[f10,f17]) ).
tff(f21,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f8,f17]) ).
tff(f22,plain,
$false,
inference(avatar_smt_refutation,[],[f21,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI549_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n026.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 20:54:42 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 2.77/1.18 % (55301)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.77/1.18 % (55307)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=504516169:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.77/1.18 % (55307)First to succeed.
% 2.77/1.18 % (55307)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-55301"
% 2.77/1.18 % (55311)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=835231553:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.77/1.18 % (55310)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4101383079:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.77/1.18 % (55309)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=227210206:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.77/1.18 % (55308)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2371684871:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.77/1.18 % (55306)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4266993815:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.77/1.18 % (55309)Also succeeded, but the first one will report.
% 2.77/1.18 % (55310)Also succeeded, but the first one will report.
% 2.77/1.18 % (55312)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1631063445:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.77/1.18 % (55311)Also succeeded, but the first one will report.
% 2.77/1.18 % (55306)Also succeeded, but the first one will report.
% 2.77/1.18 % (55308)Also succeeded, but the first one will report.
% 2.77/1.18 % (55312)Also succeeded, but the first one will report.
% 2.77/1.18 % (55307)Refutation found. Thanks to Tanya!
% 2.77/1.18 % SZS status Theorem for theBenchmark
% 2.77/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.18 % (55307)------------------------------
% 2.77/1.18 % (55307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.18 % (55307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.18 % (55307)CaDiCaL version: 2.1.3
% 2.77/1.18 % (55307)Termination reason: Refutation
% 2.77/1.18 % (55307)Time elapsed: 0.019 s
% 2.77/1.18 % (55307)Peak memory usage: 115 MB
% 2.77/1.18 % (55307)Instructions burned: 7 (million)
% 2.77/1.18 % (55307)------------------------------
% 2.77/1.18 % (55307)------------------------------
% 2.77/1.18 % (55301)Success in time 0.297 s
% 2.77/1.18 % Vampire exiting
%------------------------------------------------------------------------------