%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI670_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 : n008.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 3.92s 1.33s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 20 ( 7 atm; 11 fun; 2 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 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 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,
$lesseq(a,$product(a,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ $lesseq(a,$product(a,a)),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ~ $less($product(a,a),a),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
$less($product(a,a),a),
inference(flattening,[],[f3]) ).
tff(f23,plain,
$less($product(a,a),a),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
$less(0,$sum(a,$uminus($product(a,a)))),
inference(evaluation,[],[f23]) ).
tff(f26,definition,
( spl0_1
<=> $less(0,$sum(a,$uminus($product(a,a)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f29,plain,
spl0_1,
inference(avatar_split_clause,[],[f24,f26]) ).
tff(f30,plain,
$false,
inference(avatar_smt_refutation,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI670_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n008.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 20:56:24 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 3.92/1.33 % (2639648)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.92/1.33 % (2639657)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2803013958:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.92/1.33 % (2639657)Instruction limit reached!
% 3.92/1.33 % (2639657)------------------------------
% 3.92/1.33 % (2639657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (2639657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (2639657)CaDiCaL version: 2.1.3
% 3.92/1.33 % (2639657)Termination reason: Instruction limit
% 3.92/1.33 % (2639657)Termination phase: Saturation
% 3.92/1.33 % (2639657)Time elapsed: 0.003 s
% 3.92/1.33 % (2639657)Peak memory usage: 88 MB
% 3.92/1.33 % (2639657)Instructions burned: 7 (million)
% 3.92/1.33 % (2639656)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2200056281:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.92/1.33 % (2639655)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=372567955:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.92/1.33 % (2639653)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3829693051:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.92/1.33 % (2639654)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=963184134:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.92/1.33 % (2639656)Instruction limit reached!
% 3.92/1.33 % (2639656)------------------------------
% 3.92/1.33 % (2639656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (2639656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (2639656)CaDiCaL version: 2.1.3
% 3.92/1.33 % (2639656)Termination reason: Instruction limit
% 3.92/1.33 % (2639656)Termination phase: Saturation
% 3.92/1.33 % (2639656)Time elapsed: 0.006 s
% 3.92/1.33 % (2639656)Peak memory usage: 88 MB
% 3.92/1.33 % (2639656)Instructions burned: 8 (million)
% 3.92/1.33 % (2639658)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2627952324:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.92/1.33 % (2639659)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2003539041:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.92/1.33 % (2639653)First to succeed.
% 3.92/1.33 % (2639653)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2639648"
% 3.92/1.33 % (2639654)Also succeeded, but the first one will report.
% 3.92/1.33 % (2639658)Also succeeded, but the first one will report.
% 3.92/1.33 % (2639659)Also succeeded, but the first one will report.
% 3.92/1.33 % (2639661)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3596469812:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.92/1.33 % (2639661)Refutation not found, incomplete strategy
% 3.92/1.33 % (2639661)------------------------------
% 3.92/1.33 % (2639661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (2639661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (2639661)CaDiCaL version: 2.1.3
% 3.92/1.33 % (2639661)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.33 % (2639661)Time elapsed: 0.0000 s
% 3.92/1.33 % (2639661)Peak memory usage: 88 MB
% 3.92/1.33 % (2639655)Instruction limit reached!
% 3.92/1.33 % (2639655)------------------------------
% 3.92/1.33 % (2639655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (2639655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (2639655)CaDiCaL version: 2.1.3
% 3.92/1.33 % (2639655)Termination reason: Instruction limit
% 3.92/1.33 % (2639655)Termination phase: Saturation
% 3.92/1.33 % (2639655)Time elapsed: 0.150 s
% 3.92/1.33 % (2639655)Peak memory usage: 118 MB
% 3.92/1.33 % (2639655)Instructions burned: 202 (million)
% 3.92/1.33 % (2639667)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=1472553813:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.92/1.33 % (2639667)Instruction limit reached!
% 3.92/1.33 % (2639667)------------------------------
% 3.92/1.33 % (2639667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (2639667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (2639667)CaDiCaL version: 2.1.3
% 3.92/1.33 % (2639667)Termination reason: Instruction limit
% 3.92/1.33 % (2639667)Termination phase: Saturation
% 3.92/1.33 % (2639667)Time elapsed: 0.019 s
% 3.92/1.33 % (2639667)Peak memory usage: 88 MB
% 3.92/1.33 % (2639667)Instructions burned: 29 (million)
% 3.92/1.33 % (2639661)------------------------------
% 3.92/1.33 % (2639661)------------------------------
% 3.92/1.33 % (2639653)Refutation found. Thanks to Tanya!
% 3.92/1.33 % SZS status Theorem for theBenchmark
% 3.92/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.33 % (2639653)------------------------------
% 3.92/1.33 % (2639653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.33 % (2639653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.33 % (2639653)CaDiCaL version: 2.1.3
% 3.92/1.33 % (2639653)Termination reason: Refutation
% 3.92/1.33 % (2639653)Time elapsed: 0.031 s
% 3.92/1.33 % (2639653)Peak memory usage: 115 MB
% 3.92/1.33 % (2639653)Instructions burned: 8 (million)
% 3.92/1.33 % (2639653)------------------------------
% 3.92/1.33 % (2639653)------------------------------
% 3.92/1.33 % (2639648)Success in time 0.464 s
% 3.92/1.33 % Vampire exiting
%------------------------------------------------------------------------------