%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI117_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 : n007.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 4.30s 1.65s
% Output : Refutation 4.30s
% 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 : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 12 ( 0 atm; 4 fun; 4 num; 4 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 : 2 ( 0 usr; 1 con; 0-2 aty)
% Number of variables : 4 ( 2 !; 2 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X0: $int] : ( $product(X0,1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_1_identity) ).
tff(f2,negated_conjecture,
~ ? [X0: $int] : ( $product(X0,1) = X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
! [X0: $int] : ( $product(X0,1) != X0 ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
! [X0: $int] : ( $product(X0,1) != X0 ),
inference(cnf_transformation,[],[f21]) ).
tff(f23,plain,
$false,
inference(evaluation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI117_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n007.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 20:40:56 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running first-order theorem proving
% 0.23/0.30 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
% 4.30/1.65 % (2783981)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.30/1.65 % (2783986)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3785383666:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.30/1.65 % (2783986)First to succeed.
% 4.30/1.65 % (2783986)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2783981"
% 4.30/1.65 % (2783987)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3964152959:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.30/1.65 % (2783989)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3587448857:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.30/1.65 % (2783992)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=430740381:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.30/1.65 % (2783990)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1871907896:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.30/1.65 % (2783991)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=153681869:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.30/1.65 % (2783988)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3783006250:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.30/1.65 % (2783990)Also succeeded, but the first one will report.
% 4.30/1.65 % (2783989)Also succeeded, but the first one will report.
% 4.30/1.65 % (2783987)Also succeeded, but the first one will report.
% 4.30/1.65 % (2783991)Also succeeded, but the first one will report.
% 4.30/1.65 % (2783992)Also succeeded, but the first one will report.
% 4.30/1.65 % (2783988)Also succeeded, but the first one will report.
% 4.30/1.65 % (2783986)Refutation found. Thanks to Tanya!
% 4.30/1.65 % SZS status Theorem for theBenchmark
% 4.30/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 4.30/1.65 % (2783986)------------------------------
% 4.30/1.65 % (2783986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.65 % (2783986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.65 % (2783986)CaDiCaL version: 2.1.3
% 4.30/1.65 % (2783986)Termination reason: Refutation
% 4.30/1.65 % (2783986)Time elapsed: 0.023 s
% 4.30/1.65 % (2783986)Peak memory usage: 112 MB
% 4.30/1.65 % (2783986)Instructions burned: 5 (million)
% 4.30/1.65 % (2783986)------------------------------
% 4.30/1.65 % (2783986)------------------------------
% 4.30/1.65 % (2783981)Success in time 0.472 s
% 4.30/1.65 % Vampire exiting
%------------------------------------------------------------------------------