%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI124_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:32:35 AM UTC 2026
% Result : Theorem 3.29s 1.26s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 18 ( 0 atm; 4 fun; 14 num; 0 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 4 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_1,type,
p: $int > $o ).
tff(f1,conjecture,
( p($product(5,3))
=> p(15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5_3_15_predicate) ).
tff(f2,negated_conjecture,
~ ( p($product(5,3))
=> p(15) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
( p($product(5,3))
& ~ p(15) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
~ p(15),
inference(cnf_transformation,[],[f21]) ).
tff(f23,plain,
p($product(5,3)),
inference(cnf_transformation,[],[f21]) ).
tff(f24,plain,
p(15),
inference(evaluation,[],[f23]) ).
tff(f26,definition,
( spl0_1
<=> p(15) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f29,plain,
spl0_1,
inference(avatar_split_clause,[],[f24,f26]) ).
tff(f30,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f22,f26]) ).
tff(f31,plain,
$false,
inference(avatar_smt_refutation,[],[f30,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI124_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:43:54 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.26 % (2609739)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.29/1.26 % (2609818)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=384812772:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.29/1.26 % (2609818)First to succeed.
% 3.29/1.26 % (2609818)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2609739"
% 3.29/1.26 % (2609820)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=907479984:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.29/1.26 % (2609822)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1012250429:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.29/1.26 % (2609821)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1639648659:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.29/1.26 % (2609827)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=187475791:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.29/1.26 % (2609825)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1781890640:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.29/1.26 % (2609824)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2901010301:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.29/1.26 % (2609824)Also succeeded, but the first one will report.
% 3.29/1.26 % (2609822)Also succeeded, but the first one will report.
% 3.29/1.26 % (2609821)Also succeeded, but the first one will report.
% 3.29/1.26 % (2609825)Also succeeded, but the first one will report.
% 3.29/1.26 % (2609820)Also succeeded, but the first one will report.
% 3.29/1.26 % (2609827)Also succeeded, but the first one will report.
% 3.29/1.26 % (2609818)Refutation found. Thanks to Tanya!
% 3.29/1.26 % SZS status Theorem for theBenchmark
% 3.29/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.29/1.26 % (2609818)------------------------------
% 3.29/1.26 % (2609818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.26 % (2609818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.26 % (2609818)CaDiCaL version: 2.1.3
% 3.29/1.26 % (2609818)Termination reason: Refutation
% 3.29/1.26 % (2609818)Time elapsed: 0.019 s
% 3.29/1.26 % (2609818)Peak memory usage: 115 MB
% 3.29/1.26 % (2609818)Instructions burned: 7 (million)
% 3.29/1.26 % (2609818)------------------------------
% 3.29/1.26 % (2609818)------------------------------
% 3.29/1.26 % (2609739)Success in time 0.38 s
% 3.29/1.26 % Vampire exiting
%------------------------------------------------------------------------------