%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM878_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 : n015.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 12:17:21 PM UTC 2026
% Result : Theorem 4.55s 1.61s
% Output : Refutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 6 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 6 ( 5 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 12 ( 0 atm; 5 fun; 3 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,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotent_element) ).
tff(f2,negated_conjecture,
~ ? [X0: $int] : ( $product(X0,X0) = X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
! [X0: $int] : ( $product(X0,X0) != X0 ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
! [X0: $int] : ( $product(X0,X0) != X0 ),
inference(cnf_transformation,[],[f21]) ).
tff(f25,plain,
0 != $product(0,0),
inference(instantiation,[],[f22]) ).
tff(f26,plain,
$false,
inference(evaluation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM878_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:40:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 4.55/1.61 % (2028146)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.55/1.61 % (2028165)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=27080062:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.55/1.61 % (2028165)Refutation not found, incomplete strategy
% 4.55/1.61 % (2028165)------------------------------
% 4.55/1.61 % (2028165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.61 % (2028165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.61 % (2028165)CaDiCaL version: 2.1.3
% 4.55/1.61 % (2028165)Termination reason: Refutation not found, incomplete strategy
% 4.55/1.61 % (2028165)Time elapsed: 0.016 s
% 4.55/1.61 % (2028165)Peak memory usage: 112 MB
% 4.55/1.61 % (2028165)Instructions burned: 5 (million)
% 4.55/1.61 % (2028169)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1232907549:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.55/1.61 % (2028170)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4005184490:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.55/1.61 % (2028167)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3958445689:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.55/1.61 % (2028164)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1819731391:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.55/1.61 % (2028166)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4121984437:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.55/1.61 % (2028167)First to succeed.
% 4.55/1.61 % (2028167)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2028146"
% 4.55/1.61 % (2028168)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=288941113:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.55/1.61 % (2028168)Also succeeded, but the first one will report.
% 4.55/1.61 % (2028169)Refutation not found, incomplete strategy
% 4.55/1.61 % (2028169)------------------------------
% 4.55/1.61 % (2028169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.61 % (2028169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.61 % (2028169)CaDiCaL version: 2.1.3
% 4.55/1.61 % (2028169)Termination reason: Refutation not found, incomplete strategy
% 4.55/1.61 % (2028169)Time elapsed: 0.040 s
% 4.55/1.61 % (2028169)Peak memory usage: 112 MB
% 4.55/1.61 % (2028169)Instructions burned: 5 (million)
% 4.55/1.61 % (2028170)Also succeeded, but the first one will report.
% 4.55/1.61 % (2028164)Refutation not found, incomplete strategy
% 4.55/1.61 % (2028164)------------------------------
% 4.55/1.61 % (2028164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.61 % (2028164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.61 % (2028164)CaDiCaL version: 2.1.3
% 4.55/1.61 % (2028164)Termination reason: Refutation not found, incomplete strategy
% 4.55/1.61 % (2028164)Time elapsed: 0.040 s
% 4.55/1.61 % (2028164)Peak memory usage: 112 MB
% 4.55/1.61 % (2028164)Instructions burned: 5 (million)
% 4.55/1.61 % (2028166)Also succeeded, but the first one will report.
% 4.55/1.61 % (2028165)------------------------------
% 4.55/1.61 % (2028165)------------------------------
% 4.55/1.61 % (2028169)------------------------------
% 4.55/1.61 % (2028169)------------------------------
% 4.55/1.61 % (2028167)Refutation found. Thanks to Tanya!
% 4.55/1.61 % SZS status Theorem for theBenchmark
% 4.55/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 4.55/1.61 % (2028167)------------------------------
% 4.55/1.61 % (2028167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.61 % (2028167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.61 % (2028167)CaDiCaL version: 2.1.3
% 4.55/1.61 % (2028167)Termination reason: Refutation
% 4.55/1.61 % (2028167)Time elapsed: 0.003 s
% 4.55/1.61 % (2028167)Peak memory usage: 89 MB
% 4.55/1.61 % (2028167)Instructions burned: 1 (million)
% 4.55/1.61 % (2028167)------------------------------
% 4.55/1.61 % (2028167)------------------------------
% 4.55/1.61 % (2028146)Success in time 0.561 s
% 4.55/1.61 % Vampire exiting
%------------------------------------------------------------------------------