%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI119_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 : n010.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 09:32:34 AM UTC 2026
% Result : Theorem 0.20s 1.21s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 22 ( 11 ~; 5 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 39 ( 0 atm; 7 fun; 21 num; 11 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 : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 5 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X1: $int,X0: $int] :
( ( X1 = 4 )
& ( X0 = 4 )
& ( $product(X0,X1) = 16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_4_4_16) ).
tff(f2,negated_conjecture,
~ ? [X1: $int,X0: $int] :
( ( X1 = 4 )
& ( X0 = 4 )
& ( $product(X0,X1) = 16 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ? [X1: $int,X0: $int] :
( ( 4 = X1 )
& ( 16 = $product(X1,X0) )
& ( 4 = X0 ) ),
inference(rectify,[],[f2]) ).
tff(f4,plain,
! [X0: $int,X1: $int] :
( ( 4 != X0 )
| ( 16 != $product(X1,X0) )
| ( 4 != X1 ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
! [X0: $int,X1: $int] :
( ( 4 != X0 )
| ( 16 != $product(X1,X0) )
| ( 4 != X1 ) ),
inference(cnf_transformation,[],[f4]) ).
tff(f6,plain,
! [X1: $int] :
( ( 16 != $product(X1,4) )
| ( 4 != X1 ) ),
inference(equality_resolution,[],[f5]) ).
tff(f7,plain,
16 != $product(4,4),
inference(equality_resolution,[],[f6]) ).
tff(f8,plain,
$false,
inference(evaluation,[],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI119_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.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 20:43:32 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.20/1.21 % (2295169)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.20/1.21 % (2295287)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=655307778:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.20/1.21 % (2295287)First to succeed.
% 0.20/1.21 % (2295287)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2295169"
% 0.20/1.21 % (2295281)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3794363860:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.20/1.21 % (2295279)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3997340739:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/1.21 % (2295283)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=850546333:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.20/1.21 % (2295284)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=615528600:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/1.21 % (2295284)Also succeeded, but the first one will report.
% 0.20/1.21 % (2295289)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1491319442:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.20/1.21 % (2295279)Also succeeded, but the first one will report.
% 0.20/1.21 % (2295283)Also succeeded, but the first one will report.
% 0.20/1.21 % (2295285)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1080083347:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.20/1.21 % (2295281)Also succeeded, but the first one will report.
% 0.20/1.21 % (2295285)Also succeeded, but the first one will report.
% 0.20/1.21 % (2295289)Also succeeded, but the first one will report.
% 0.20/1.21 % (2295287)Refutation found. Thanks to Tanya!
% 0.20/1.21 % SZS status Theorem for theBenchmark
% 0.20/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.21 % (2295287)------------------------------
% 0.20/1.21 % (2295287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.21 % (2295287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.21 % (2295287)CaDiCaL version: 2.1.3
% 0.20/1.21 % (2295287)Termination reason: Refutation
% 0.20/1.21 % (2295287)Time elapsed: 0.017 s
% 0.20/1.21 % (2295287)Peak memory usage: 111 MB
% 0.20/1.21 % (2295287)Instructions burned: 5 (million)
% 0.20/1.21 % (2295287)------------------------------
% 0.20/1.21 % (2295287)------------------------------
% 0.20/1.21 % (2295169)Success in time 0.327 s
% 0.20/1.21 % Vampire exiting
%------------------------------------------------------------------------------