%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI647_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:33:34 AM UTC 2026
% Result : Theorem 3.79s 1.21s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 18 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 3 |; 1 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 66 ( 7 atm; 24 fun; 35 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 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 1 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( ( $product(3,a) != 3 )
| ~ $lesseq(-1,$product(-1,$product(2,a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( $product(3,a) != 3 )
| ~ $lesseq(-1,$product(-1,$product(2,a))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( $less($product(-1,$product(2,a)),-1)
| ( $product(3,a) != 3 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
( ~ $less($product(-1,$product(2,a)),-1)
& ( 3 = $product(3,a) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f23,plain,
3 = $product(3,a),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
~ $less($product(-1,$product(2,a)),-1),
inference(cnf_transformation,[],[f22]) ).
tff(f25,plain,
$less(0,$sum($sum($uminus($product(2,a)),1),1)),
inference(evaluation,[],[f24]) ).
tff(f27,definition,
( spl0_1
<=> ( 3 = $product(3,a) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f30,plain,
spl0_1,
inference(avatar_split_clause,[],[f23,f27]) ).
tff(f32,definition,
( spl0_2
<=> $less(0,$sum($sum($uminus($product(2,a)),1),1)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f35,plain,
spl0_2,
inference(avatar_split_clause,[],[f25,f32]) ).
tff(f36,plain,
$false,
inference(avatar_smt_refutation,[],[f35,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI647_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/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 20:54:45 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.79/1.21 % (2178158)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.79/1.21 % (2178167)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1303937309:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.79/1.21 % (2178167)Instruction limit reached!
% 3.79/1.21 % (2178167)------------------------------
% 3.79/1.21 % (2178167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.21 % (2178167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.21 % (2178167)CaDiCaL version: 2.1.3
% 3.79/1.21 % (2178167)Termination reason: Instruction limit
% 3.79/1.21 % (2178167)Termination phase: Saturation
% 3.79/1.21 % (2178167)Time elapsed: 0.003 s
% 3.79/1.21 % (2178167)Peak memory usage: 89 MB
% 3.79/1.21 % (2178167)Instructions burned: 7 (million)
% 3.79/1.21 % (2178163)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1537598560:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.79/1.21 % (2178164)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2273034372:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.79/1.21 % (2178165)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2652337434:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.79/1.21 % (2178166)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3594827165:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.79/1.21 % (2178166)Instruction limit reached!
% 3.79/1.21 % (2178166)------------------------------
% 3.79/1.21 % (2178166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.21 % (2178166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.21 % (2178166)CaDiCaL version: 2.1.3
% 3.79/1.21 % (2178166)Termination reason: Instruction limit
% 3.79/1.21 % (2178166)Termination phase: Saturation
% 3.79/1.21 % (2178166)Time elapsed: 0.005 s
% 3.79/1.21 % (2178166)Peak memory usage: 88 MB
% 3.79/1.21 % (2178166)Instructions burned: 7 (million)
% 3.79/1.21 % (2178168)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2332290968:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.79/1.21 % (2178169)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2786691368:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.79/1.21 % (2178163)First to succeed.
% 3.79/1.21 % (2178163)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2178158"
% 3.79/1.21 % (2178164)Also succeeded, but the first one will report.
% 3.79/1.21 % (2178165)Also succeeded, but the first one will report.
% 3.79/1.21 % (2178168)Also succeeded, but the first one will report.
% 3.79/1.21 % (2178169)Also succeeded, but the first one will report.
% 3.79/1.21 % (2178171)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2104252476:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.79/1.21 % (2178171)Refutation not found, incomplete strategy
% 3.79/1.21 % (2178171)------------------------------
% 3.79/1.21 % (2178171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.21 % (2178171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.21 % (2178171)CaDiCaL version: 2.1.3
% 3.79/1.21 % (2178171)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.21 % (2178171)Time elapsed: 0.001 s
% 3.79/1.21 % (2178171)Peak memory usage: 88 MB
% 3.79/1.21 % (2178176)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=373464261:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.79/1.21 % (2178176)Instruction limit reached!
% 3.79/1.21 % (2178176)------------------------------
% 3.79/1.21 % (2178176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.21 % (2178176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.21 % (2178176)CaDiCaL version: 2.1.3
% 3.79/1.21 % (2178176)Termination reason: Instruction limit
% 3.79/1.21 % (2178176)Termination phase: Saturation
% 3.79/1.21 % (2178176)Time elapsed: 0.019 s
% 3.79/1.21 % (2178176)Peak memory usage: 88 MB
% 3.79/1.21 % (2178176)Instructions burned: 30 (million)
% 3.79/1.21 % (2178171)------------------------------
% 3.79/1.21 % (2178171)------------------------------
% 3.79/1.21 % (2178163)Refutation found. Thanks to Tanya!
% 3.79/1.21 % SZS status Theorem for theBenchmark
% 3.79/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.21 % (2178163)------------------------------
% 3.79/1.21 % (2178163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.21 % (2178163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.21 % (2178163)CaDiCaL version: 2.1.3
% 3.79/1.21 % (2178163)Termination reason: Refutation
% 3.79/1.21 % (2178163)Time elapsed: 0.031 s
% 3.79/1.21 % (2178163)Peak memory usage: 114 MB
% 3.79/1.21 % (2178163)Instructions burned: 8 (million)
% 3.79/1.21 % (2178163)------------------------------
% 3.79/1.21 % (2178163)------------------------------
% 3.79/1.21 % (2178158)Success in time 0.457 s
% 3.79/1.21 % Vampire exiting
%------------------------------------------------------------------------------