%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI282_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 : 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 09:32:51 AM UTC 2026
% Result : Theorem 2.59s 1.17s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 24 ( 0 atm; 8 fun; 16 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_1,type,
p: $rat > $o ).
tff(f1,conjecture,
( p($difference(5/12,1/12))
=> p(1/3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rat_difference_problem_10) ).
tff(f2,negated_conjecture,
~ ( p($difference(5/12,1/12))
=> p(1/3) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( p($sum(5/12,$uminus(1/12)))
=> p(1/3) ),
inference(theory_normalization,[],[f2]) ).
tff(f15,plain,
( ~ p(1/3)
& p($sum(5/12,$uminus(1/12))) ),
inference(ennf_transformation,[],[f3]) ).
tff(f16,plain,
p($sum(5/12,$uminus(1/12))),
inference(cnf_transformation,[],[f15]) ).
tff(f17,plain,
~ p(1/3),
inference(cnf_transformation,[],[f15]) ).
tff(f18,plain,
p(1/3),
inference(evaluation,[],[f16]) ).
tff(f19,plain,
$false,
inference(forward_subsumption_resolution,[],[f18,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI282_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:46:40 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 2.59/1.17 % (2616808)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.59/1.17 % (2616825)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=906354474:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 2.59/1.17 % (2616825)First to succeed.
% 2.59/1.17 % (2616825)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2616808"
% 2.59/1.17 % (2616822)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=213398939:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 2.59/1.17 % (2616827)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4254101986:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 2.59/1.17 % (2616821)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2414974665:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 2.59/1.17 % (2616824)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=278147363:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 2.59/1.17 % (2616823)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3732780508:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 2.59/1.17 % (2616824)Also succeeded, but the first one will report.
% 2.59/1.17 % (2616822)Also succeeded, but the first one will report.
% 2.59/1.17 % (2616821)Also succeeded, but the first one will report.
% 2.59/1.17 % (2616827)Also succeeded, but the first one will report.
% 2.59/1.17 % (2616823)Also succeeded, but the first one will report.
% 2.59/1.17 % (2616826)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2943322482:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 2.59/1.17 % (2616826)Also succeeded, but the first one will report.
% 2.59/1.17 % (2616825)Refutation found. Thanks to Tanya!
% 2.59/1.17 % SZS status Theorem for theBenchmark
% 2.59/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.17 % (2616825)------------------------------
% 2.59/1.17 % (2616825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.17 % (2616825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.17 % (2616825)CaDiCaL version: 2.1.3
% 2.59/1.17 % (2616825)Termination reason: Refutation
% 2.59/1.17 % (2616825)Time elapsed: 0.001 s
% 2.59/1.17 % (2616825)Peak memory usage: 88 MB
% 2.59/1.17 % (2616825)------------------------------
% 2.59/1.17 % (2616825)------------------------------
% 2.59/1.17 % (2616808)Success in time 0.268 s
% 2.59/1.17 % Vampire exiting
%------------------------------------------------------------------------------