%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI296_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 : n001.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 09:32:53 AM UTC 2026
% Result : Theorem 2.77s 1.10s
% Output : Refutation 2.77s
% 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 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 24 ( 0 atm; 5 fun; 16 num; 3 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 3 ( 2 !; 1 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
sK0: $rat ).
tff(f1,conjecture,
! [X0: $rat] :
( ( $product(5/8,2/5) = X0 )
=> ( X0 = 1/4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_product_problem_13) ).
tff(f2,negated_conjecture,
~ ! [X0: $rat] :
( ( $product(5/8,2/5) = X0 )
=> ( X0 = 1/4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f20,plain,
? [X0: $rat] :
( ( $product(5/8,2/5) = X0 )
& ( 1/4 != X0 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f21,plain,
( ( $product(5/8,2/5) = sK0 )
& ( 1/4 != sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
tff(f22,plain,
1/4 != sK0,
inference(cnf_transformation,[],[f21]) ).
tff(f23,plain,
$product(5/8,2/5) = sK0,
inference(cnf_transformation,[],[f21]) ).
tff(f25,plain,
1/4 = sK0,
inference(evaluation,[],[f23]) ).
tff(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI296_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:52:32 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 2.77/1.10 % (719657)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.77/1.10 % (719665)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3765446171:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.77/1.10 % (719665)First to succeed.
% 2.77/1.10 % (719665)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-719657"
% 2.77/1.10 % (719664)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=633229717:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.77/1.10 % (719668)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1257036932:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.77/1.10 % (719663)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1932336797:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.77/1.10 % (719662)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=524718069:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.77/1.10 % (719666)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4150382212:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.77/1.10 % (719667)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=70244004:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.77/1.10 % (719666)Also succeeded, but the first one will report.
% 2.77/1.10 % (719664)Also succeeded, but the first one will report.
% 2.77/1.10 % (719667)Also succeeded, but the first one will report.
% 2.77/1.10 % (719662)Also succeeded, but the first one will report.
% 2.77/1.10 % (719663)Also succeeded, but the first one will report.
% 2.77/1.10 % (719668)Also succeeded, but the first one will report.
% 2.77/1.10 % (719665)Refutation found. Thanks to Tanya!
% 2.77/1.10 % SZS status Theorem for theBenchmark
% 2.77/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.10 % (719665)------------------------------
% 2.77/1.10 % (719665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.10 % (719665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.10 % (719665)CaDiCaL version: 2.1.3
% 2.77/1.10 % (719665)Termination reason: Refutation
% 2.77/1.10 % (719665)Time elapsed: 0.001 s
% 2.77/1.10 % (719665)Peak memory usage: 89 MB
% 2.77/1.10 % (719665)Instructions burned: 1 (million)
% 2.77/1.10 % (719665)------------------------------
% 2.77/1.10 % (719665)------------------------------
% 2.77/1.10 % (719657)Success in time 0.315 s
% 2.77/1.10 % Vampire exiting
%------------------------------------------------------------------------------