%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI660_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 : n007.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 09:33:36 AM UTC 2026
% Result : Theorem 4.13s 1.62s
% Output : Refutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 1 unt; 0 typ; 2 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 12 ~; 6 |; 1 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 54 ( 18 atm; 18 fun; 18 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 : 5 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( $lesseq(11,$product($product(a,a),a))
<=> $lesseq(3,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( $lesseq(11,$product($product(a,a),a))
<=> $lesseq(3,a) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ~ $less($product($product(a,a),a),11)
<=> ~ $less(a,3) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ~ $less($product($product(a,a),a),11)
<~> ~ $less(a,3) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ( $less(a,3)
| $less($product($product(a,a),a),11) )
& ( ~ $less(a,3)
| ~ $less($product($product(a,a),a),11) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f6,plain,
( ~ $less(a,3)
| ~ $less($product($product(a,a),a),11) ),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
( $less($product($product(a,a),a),11)
| $less(a,3) ),
inference(cnf_transformation,[],[f5]) ).
tff(f9,definition,
( spl0_1
<=> $less($product($product(a,a),a),11) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f13,definition,
( spl0_2
<=> $less(a,3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f16,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f7,f13,f9]) ).
tff(f17,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f6,f9,f13]) ).
tff(f18,plain,
$false,
inference(avatar_smt_refutation,[],[f17,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI660_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n007.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 20:53:10 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.32 Running first-order theorem proving
% 0.27/0.32 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
% 4.13/1.62 % (2811622)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.13/1.62 % (2811632)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=201461083:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.13/1.62 % (2811633)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1047042086:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.13/1.62 % (2811632)First to succeed.
% 4.13/1.62 % (2811632)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2811622"
% 4.13/1.62 % (2811633)Also succeeded, but the first one will report.
% 4.13/1.62 % (2811628)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3220421479:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.13/1.62 % (2811629)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2284846670:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.13/1.62 % (2811631)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3202158275:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.13/1.62 % (2811630)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3216952179:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.13/1.62 % (2811631)Instruction limit reached!
% 4.13/1.62 % (2811631)------------------------------
% 4.13/1.62 % (2811631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.62 % (2811631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.62 % (2811631)CaDiCaL version: 2.1.3
% 4.13/1.62 % (2811631)Termination reason: Instruction limit
% 4.13/1.62 % (2811631)Termination phase: Saturation
% 4.13/1.62 % (2811631)Time elapsed: 0.008 s
% 4.13/1.62 % (2811631)Peak memory usage: 89 MB
% 4.13/1.62 % (2811631)Instructions burned: 5 (million)
% 4.13/1.62 % (2811630)Instruction limit reached!
% 4.13/1.62 % (2811630)------------------------------
% 4.13/1.62 % (2811630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.62 % (2811630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.62 % (2811630)CaDiCaL version: 2.1.3
% 4.13/1.62 % (2811630)Termination reason: Instruction limit
% 4.13/1.62 % (2811630)Termination phase: Saturation
% 4.13/1.62 % (2811630)Time elapsed: 0.009 s
% 4.13/1.62 % (2811630)Peak memory usage: 88 MB
% 4.13/1.62 % (2811630)Instructions burned: 7 (million)
% 4.13/1.62 % (2811628)Also succeeded, but the first one will report.
% 4.13/1.62 % (2811627)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3486245811:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.13/1.62 % (2811627)Also succeeded, but the first one will report.
% 4.13/1.62 % (2811632)Refutation found. Thanks to Tanya!
% 4.13/1.62 % SZS status Theorem for theBenchmark
% 4.13/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 4.13/1.62 % (2811632)------------------------------
% 4.13/1.62 % (2811632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.62 % (2811632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.62 % (2811632)CaDiCaL version: 2.1.3
% 4.13/1.62 % (2811632)Termination reason: Refutation
% 4.13/1.62 % (2811632)Time elapsed: 0.026 s
% 4.13/1.62 % (2811632)Peak memory usage: 116 MB
% 4.13/1.62 % (2811632)Instructions burned: 8 (million)
% 4.13/1.62 % (2811632)------------------------------
% 4.13/1.62 % (2811632)------------------------------
% 4.13/1.62 % (2811622)Success in time 0.458 s
% 4.13/1.62 % Vampire exiting
%------------------------------------------------------------------------------