%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI284_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 : n017.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 2.41s 0.86s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 13 ( 9 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 : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 25 ( 0 atm; 6 fun; 19 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 : 5 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
sF0: $rat ).
tff(f1,conjecture,
$product(1/3,3/4) = 1/4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rat_product_problem_1) ).
tff(f2,negated_conjecture,
( ( ~ $product(1/3,3/4) ) = 1/4 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f20,plain,
$product(1/3,3/4) != 1/4,
inference(flattening,[],[f2]) ).
tff(f21,plain,
$product(1/3,3/4) != 1/4,
inference(cnf_transformation,[],[f20]) ).
tff(f23,definition,
sF0 = $product(1/3,3/4),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f24,plain,
$product(1/3,3/4) = sF0,
inference(reorient_equations,[],[f23]) ).
tff(f25,plain,
1/4 != sF0,
inference(definition_folding,[],[f21,f24]) ).
tff(f26,plain,
1/4 = sF0,
inference(evaluation,[],[f24]) ).
tff(f28,definition,
( spl1_1
<=> ( 1/4 = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f31,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f25,f28]) ).
tff(f32,plain,
spl1_1,
inference(avatar_split_clause,[],[f26,f28]) ).
tff(f33,plain,
$false,
inference(avatar_smt_refutation,[],[f32,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI284_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:41:21 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.41/0.86 % (3996000)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.41/0.86 % (3996085)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3592342809:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.41/0.86 % (3996085)First to succeed.
% 2.41/0.86 % (3996085)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3996000"
% 2.41/0.86 % (3996083)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1646692541:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.41/0.86 % (3996077)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=257055310:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.41/0.86 % (3996081)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=481275932:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.41/0.86 % (3996081)Also succeeded, but the first one will report.
% 2.41/0.86 % (3996083)Also succeeded, but the first one will report.
% 2.41/0.86 % (3996079)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2776253496:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.41/0.86 % (3996077)Also succeeded, but the first one will report.
% 2.41/0.86 % (3996079)Also succeeded, but the first one will report.
% 2.41/0.86 % (3996084)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3028377600:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.41/0.86 % (3996080)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=248702172:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.41/0.86 % (3996084)Also succeeded, but the first one will report.
% 2.41/0.86 % (3996080)Also succeeded, but the first one will report.
% 2.41/0.86 % (3996085)Refutation found. Thanks to Tanya!
% 2.41/0.86 % SZS status Theorem for theBenchmark
% 2.41/0.86 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/0.86 % (3996085)------------------------------
% 2.41/0.86 % (3996085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/0.86 % (3996085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.86 % (3996085)CaDiCaL version: 2.1.3
% 2.41/0.86 % (3996085)Termination reason: Refutation
% 2.41/0.86 % (3996085)Time elapsed: 0.019 s
% 2.41/0.86 % (3996085)Peak memory usage: 116 MB
% 2.41/0.86 % (3996085)Instructions burned: 8 (million)
% 2.41/0.86 % (3996085)------------------------------
% 2.41/0.86 % (3996085)------------------------------
% 2.41/0.86 % (3996000)Success in time 0.312 s
% 2.41/0.86 % Vampire exiting
%------------------------------------------------------------------------------