%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI669_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 : n009.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 09:33:37 AM UTC 2026
% Result : Theorem 3.60s 1.19s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 57 ( 42 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 60 ( 21 ~; 26 |; 6 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 78 ( 0 atm; 36 fun; 42 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
c: $int ).
tff(f1,conjecture,
( ( ( a = 0 )
| ( b = 0 )
| ( c = 0 ) )
<=> ( $product($product($product(a,b),b),c) = 0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( ( a = 0 )
| ( b = 0 )
| ( c = 0 ) )
<=> ( $product($product($product(a,b),b),c) = 0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
( ( $product($product($product(a,b),b),c) = 0 )
<~> ( ( a = 0 )
| ( b = 0 )
| ( c = 0 ) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( ( ( ( a != 0 )
& ( b != 0 )
& ( c != 0 ) )
| ( $product($product($product(a,b),b),c) != 0 ) )
& ( ( a = 0 )
| ( b = 0 )
| ( c = 0 )
| ( $product($product($product(a,b),b),c) = 0 ) ) ),
inference(nnf_transformation,[],[f21]) ).
tff(f23,plain,
( ( ( ( a != 0 )
& ( b != 0 )
& ( c != 0 ) )
| ( $product($product($product(a,b),b),c) != 0 ) )
& ( ( a = 0 )
| ( b = 0 )
| ( c = 0 )
| ( $product($product($product(a,b),b),c) = 0 ) ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
( ( $product($product($product(a,b),b),c) = 0 )
| ( c = 0 )
| ( a = 0 )
| ( b = 0 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f25,plain,
( ( c != 0 )
| ( $product($product($product(a,b),b),c) != 0 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f26,plain,
( ( $product($product($product(a,b),b),c) != 0 )
| ( b != 0 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f27,plain,
( ( $product($product($product(a,b),b),c) != 0 )
| ( a != 0 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f30,definition,
( spl0_1
<=> ( b = 0 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f34,definition,
( spl0_2
<=> ( $product($product($product(a,b),b),c) = 0 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f37,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f26,f34,f30]) ).
tff(f39,definition,
( spl0_3
<=> ( a = 0 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f43,definition,
( spl0_4
<=> ( c = 0 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f46,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f24,f30,f43,f39,f34]) ).
tff(f47,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f27,f34,f39]) ).
tff(f48,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f25,f34,f43]) ).
tff(f49,plain,
$false,
inference(avatar_smt_refutation,[],[f48,f47,f46,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI669_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 20:55:30 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 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
% 3.60/1.18 % (3466580)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.60/1.18 % (3466589)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3216688631:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.60/1.18 % (3466589)Instruction limit reached!
% 3.60/1.18 % (3466589)------------------------------
% 3.60/1.18 % (3466589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.18 % (3466589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.18 % (3466589)CaDiCaL version: 2.1.3
% 3.60/1.18 % (3466589)Termination reason: Instruction limit
% 3.60/1.18 % (3466589)Termination phase: Saturation
% 3.60/1.18 % (3466589)Time elapsed: 0.002 s
% 3.60/1.18 % (3466589)Peak memory usage: 89 MB
% 3.60/1.18 % (3466589)Instructions burned: 4 (million)
% 3.60/1.18 % (3466591)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3480295353:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.60/1.18 % (3466588)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=389225905:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.60/1.18 % (3466587)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=773785335:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.60/1.18 % (3466585)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3986298767:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.60/1.18 % (3466586)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1826264699:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.60/1.18 % (3466588)Instruction limit reached!
% 3.60/1.18 % (3466588)------------------------------
% 3.60/1.18 % (3466588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.18 % (3466588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.18 % (3466588)CaDiCaL version: 2.1.3
% 3.60/1.18 % (3466588)Termination reason: Instruction limit
% 3.60/1.18 % (3466588)Termination phase: Saturation
% 3.60/1.18 % (3466588)Time elapsed: 0.006 s
% 3.60/1.18 % (3466588)Peak memory usage: 88 MB
% 3.60/1.18 % (3466588)Instructions burned: 8 (million)
% 3.60/1.18 % (3466590)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3115781265:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.60/1.18 % (3466585)First to succeed.
% 3.60/1.18 % (3466585)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3466580"
% 3.60/1.18 % (3466590)Also succeeded, but the first one will report.
% 3.60/1.18 % (3466591)Also succeeded, but the first one will report.
% 3.60/1.18 % (3466586)Also succeeded, but the first one will report.
% 3.60/1.18 % (3466593)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=934590673:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.60/1.18 % (3466593)Refutation not found, incomplete strategy
% 3.60/1.18 % (3466593)------------------------------
% 3.60/1.18 % (3466593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.18 % (3466593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.18 % (3466593)CaDiCaL version: 2.1.3
% 3.60/1.19 % (3466593)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.19 % (3466593)Time elapsed: 0.001 s
% 3.60/1.19 % (3466593)Peak memory usage: 89 MB
% 3.60/1.19 % (3466593)Instructions burned: 1 (million)
% 3.60/1.19 % (3466587)Instruction limit reached!
% 3.60/1.19 % (3466587)------------------------------
% 3.60/1.19 % (3466587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.19 % (3466587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.19 % (3466587)CaDiCaL version: 2.1.3
% 3.60/1.19 % (3466587)Termination reason: Instruction limit
% 3.60/1.19 % (3466587)Termination phase: Saturation
% 3.60/1.19 % (3466587)Time elapsed: 0.134 s
% 3.60/1.19 % (3466587)Peak memory usage: 114 MB
% 3.60/1.19 % (3466587)Instructions burned: 201 (million)
% 3.60/1.19 % (3466600)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=4181108190:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.60/1.19 % (3466600)Instruction limit reached!
% 3.60/1.19 % (3466600)------------------------------
% 3.60/1.19 % (3466600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.19 % (3466600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.19 % (3466600)CaDiCaL version: 2.1.3
% 3.60/1.19 % (3466600)Termination reason: Instruction limit
% 3.60/1.19 % (3466600)Termination phase: Saturation
% 3.60/1.19 % (3466600)Time elapsed: 0.016 s
% 3.60/1.19 % (3466600)Peak memory usage: 88 MB
% 3.60/1.19 % (3466600)Instructions burned: 30 (million)
% 3.60/1.19 % (3466593)------------------------------
% 3.60/1.19 % (3466593)------------------------------
% 3.60/1.19 % (3466603)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1624294480:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.60/1.19 % (3466585)Refutation found. Thanks to Tanya!
% 3.60/1.19 % SZS status Theorem for theBenchmark
% 3.60/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.19 % (3466585)------------------------------
% 3.60/1.19 % (3466585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.19 % (3466585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.19 % (3466585)CaDiCaL version: 2.1.3
% 3.60/1.19 % (3466585)Termination reason: Refutation
% 3.60/1.19 % (3466585)Time elapsed: 0.031 s
% 3.60/1.19 % (3466585)Peak memory usage: 115 MB
% 3.60/1.19 % (3466585)Instructions burned: 10 (million)
% 3.60/1.19 % (3466585)------------------------------
% 3.60/1.19 % (3466585)------------------------------
% 3.60/1.19 % (3466580)Success in time 0.438 s
% 3.60/1.19 % Vampire exiting
%------------------------------------------------------------------------------