%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI437_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 : n020.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 09:33:08 AM UTC 2026
% Result : Theorem 3.26s 1.04s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 5 ( 4 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 16 ( 0 atm; 4 fun; 12 num; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
$product(3/1,12/5) = 36/5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_product_problem_2) ).
tff(f2,negated_conjecture,
( ( ~ $product(3/1,12/5) ) = 36/5 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f20,plain,
$product(3/1,12/5) != 36/5,
inference(flattening,[],[f2]) ).
tff(f21,plain,
$product(3/1,12/5) != 36/5,
inference(cnf_transformation,[],[f20]) ).
tff(f23,plain,
$false,
inference(evaluation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI437_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n020.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 20:51:05 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 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
% 3.26/1.04 % (534970)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.26/1.04 % (534982)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=667767432:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.26/1.04 % (534985)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2214057287:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.26/1.04 % (534981)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2670757310:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.26/1.04 % (534984)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1236725317:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.26/1.04 % (534983)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2694360823:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.26/1.04 % (534985)Also succeeded, but the first one will report.
% 3.26/1.04 % (534984)First to succeed.
% 3.26/1.04 % (534984)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-534970"
% 3.26/1.04 % (534987)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3995170958:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.26/1.04 % (534986)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2393363268:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.26/1.04 % (534981)Also succeeded, but the first one will report.
% 3.26/1.04 % (534983)Also succeeded, but the first one will report.
% 3.26/1.04 % (534982)Also succeeded, but the first one will report.
% 3.26/1.04 % (534987)Also succeeded, but the first one will report.
% 3.26/1.04 % (534986)Also succeeded, but the first one will report.
% 3.26/1.04 % (534984)Refutation found. Thanks to Tanya!
% 3.26/1.04 % SZS status Theorem for theBenchmark
% 3.26/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 3.26/1.04 % (534984)------------------------------
% 3.26/1.04 % (534984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.04 % (534984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.04 % (534984)CaDiCaL version: 2.1.3
% 3.26/1.04 % (534984)Termination reason: Refutation
% 3.26/1.04 % (534984)Time elapsed: 0.001 s
% 3.26/1.04 % (534984)Peak memory usage: 88 MB
% 3.26/1.04 % (534984)------------------------------
% 3.26/1.04 % (534984)------------------------------
% 3.26/1.04 % (534970)Success in time 0.39 s
% 3.26/1.04 % Vampire exiting
%------------------------------------------------------------------------------