%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI643_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:33:33 AM UTC 2026
% Result : Theorem 2.82s 1.09s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 15 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 0 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 20 ( 0 atm; 5 fun; 15 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( ( a != 0 )
=> ( $quotient_e(0,a) = 0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( a != 0 )
=> ( $quotient_e(0,a) = 0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f26,plain,
( ( 0 != $quotient_e(0,a) )
& ( a != 0 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f27,plain,
a != 0,
inference(cnf_transformation,[],[f26]) ).
tff(f28,plain,
0 != $quotient_e(0,a),
inference(cnf_transformation,[],[f26]) ).
tff(f31,definition,
( spl0_1
<=> ( a = 0 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f34,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f27,f31]) ).
tff(f36,definition,
( spl0_2
<=> ( 0 = $quotient_e(0,a) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f39,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f28,f36]) ).
tff(f40,plain,
$false,
inference(avatar_smt_refutation,[],[f39,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI643_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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 20:54:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.82/1.09 % (2177382)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.82/1.09 % (2177387)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4244030149:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.82/1.09 % (2177387)First to succeed.
% 2.82/1.09 % (2177387)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2177382"
% 2.82/1.09 % (2177390)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1406630718:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.82/1.09 % (2177389)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2144272415:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.82/1.09 % (2177392)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1500298172:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.82/1.09 % (2177393)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3164735466:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.82/1.09 % (2177388)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=141042839:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.82/1.09 % (2177391)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1780930827:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.82/1.09 % (2177391)Instruction limit reached!
% 2.82/1.09 % (2177391)------------------------------
% 2.82/1.09 % (2177391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.09 % (2177391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.09 % (2177391)CaDiCaL version: 2.1.3
% 2.82/1.09 % (2177391)Termination reason: Instruction limit
% 2.82/1.09 % (2177391)Termination phase: Saturation
% 2.82/1.09 % (2177391)Time elapsed: 0.004 s
% 2.82/1.09 % (2177391)Peak memory usage: 88 MB
% 2.82/1.09 % (2177391)Instructions burned: 6 (million)
% 2.82/1.09 % (2177390)Instruction limit reached!
% 2.82/1.09 % (2177390)------------------------------
% 2.82/1.09 % (2177390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.09 % (2177390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.09 % (2177390)CaDiCaL version: 2.1.3
% 2.82/1.09 % (2177390)Termination reason: Instruction limit
% 2.82/1.09 % (2177390)Termination phase: Saturation
% 2.82/1.09 % (2177390)Time elapsed: 0.005 s
% 2.82/1.09 % (2177390)Peak memory usage: 88 MB
% 2.82/1.09 % (2177390)Instructions burned: 7 (million)
% 2.82/1.09 % (2177392)Also succeeded, but the first one will report.
% 2.82/1.09 % (2177388)Also succeeded, but the first one will report.
% 2.82/1.09 % (2177393)Also succeeded, but the first one will report.
% 2.82/1.09 % (2177389)Instruction limit reached!
% 2.82/1.09 % (2177389)------------------------------
% 2.82/1.09 % (2177389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.09 % (2177389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.09 % (2177389)CaDiCaL version: 2.1.3
% 2.82/1.09 % (2177389)Termination reason: Instruction limit
% 2.82/1.09 % (2177389)Termination phase: Saturation
% 2.82/1.09 % (2177389)Time elapsed: 0.133 s
% 2.82/1.09 % (2177389)Peak memory usage: 113 MB
% 2.82/1.09 % (2177389)Instructions burned: 202 (million)
% 2.82/1.09 % (2177387)Refutation found. Thanks to Tanya!
% 2.82/1.09 % SZS status Theorem for theBenchmark
% 2.82/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.09 % (2177387)------------------------------
% 2.82/1.09 % (2177387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.09 % (2177387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.09 % (2177387)CaDiCaL version: 2.1.3
% 2.82/1.09 % (2177387)Termination reason: Refutation
% 2.82/1.09 % (2177387)Time elapsed: 0.021 s
% 2.82/1.09 % (2177387)Peak memory usage: 116 MB
% 2.82/1.09 % (2177387)Instructions burned: 9 (million)
% 2.82/1.09 % (2177387)------------------------------
% 2.82/1.09 % (2177387)------------------------------
% 2.82/1.09 % (2177382)Success in time 0.328 s
% 2.82/1.10 % Vampire exiting
%------------------------------------------------------------------------------