%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI659_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 : n015.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 09:33:35 AM UTC 2026
% Result : Theorem 4.05s 1.38s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 10 ~; 8 |; 1 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 92 ( 24 atm; 36 fun; 32 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 : 8 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 1 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( $greatereq(3,$product($product(a,a),a))
<=> $lesseq(a,1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( $greatereq(3,$product($product(a,a),a))
<=> $lesseq(a,1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ~ $less(3,$product($product(a,a),a))
<=> ~ $less(1,a) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
( ~ $less(3,$product($product(a,a),a))
<~> ~ $less(1,a) ),
inference(ennf_transformation,[],[f3]) ).
tff(f23,plain,
( ( $less(1,a)
| $less(3,$product($product(a,a),a)) )
& ( ~ $less(1,a)
| ~ $less(3,$product($product(a,a),a)) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f24,plain,
( ~ $less(3,$product($product(a,a),a))
| ~ $less(1,a) ),
inference(cnf_transformation,[],[f23]) ).
tff(f25,plain,
( $less(3,$product($product(a,a),a))
| $less(1,a) ),
inference(cnf_transformation,[],[f23]) ).
tff(f26,plain,
( $less(0,$sum($product($product(a,a),a),-3))
| $less(0,$sum(a,-1)) ),
inference(evaluation,[],[f25]) ).
tff(f27,plain,
( $less(0,$sum(4,$uminus($product($product(a,a),a))))
| $less(0,$sum(2,$uminus(a))) ),
inference(evaluation,[],[f24]) ).
tff(f29,definition,
( spl0_1
<=> $less(0,$sum(a,-1)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f33,definition,
( spl0_2
<=> $less(0,$sum($product($product(a,a),a),-3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f36,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f26,f33,f29]) ).
tff(f38,definition,
( spl0_3
<=> $less(0,$sum(2,$uminus(a))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f42,definition,
( spl0_4
<=> $less(0,$sum(4,$uminus($product($product(a,a),a)))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f45,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f27,f42,f38]) ).
tff(f46,plain,
$false,
inference(avatar_smt_refutation,[],[f45,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI659_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:58:32 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.05/1.38 % (3011896)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.05/1.38 % (3011940)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2940317299:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.05/1.38 % (3011940)Instruction limit reached!
% 4.05/1.38 % (3011940)------------------------------
% 4.05/1.38 % (3011940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.38 % (3011940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.38 % (3011940)CaDiCaL version: 2.1.3
% 4.05/1.38 % (3011940)Termination reason: Instruction limit
% 4.05/1.38 % (3011940)Termination phase: Saturation
% 4.05/1.38 % (3011940)Time elapsed: 0.004 s
% 4.05/1.38 % (3011940)Peak memory usage: 89 MB
% 4.05/1.38 % (3011940)Instructions burned: 9 (million)
% 4.05/1.38 % (3011938)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=524714384:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.05/1.38 % (3011941)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2021839015:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.05/1.38 % (3011937)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=102008109:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.05/1.38 % (3011939)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2494766840:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.05/1.38 % (3011941)Instruction limit reached!
% 4.05/1.38 % (3011941)------------------------------
% 4.05/1.38 % (3011941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.38 % (3011941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.38 % (3011941)CaDiCaL version: 2.1.3
% 4.05/1.38 % (3011941)Termination reason: Instruction limit
% 4.05/1.38 % (3011941)Termination phase: Saturation
% 4.05/1.38 % (3011941)Time elapsed: 0.005 s
% 4.05/1.38 % (3011941)Peak memory usage: 89 MB
% 4.05/1.38 % (3011941)Instructions burned: 6 (million)
% 4.05/1.38 % (3011942)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1663030189:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.05/1.38 % (3011943)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3696346315:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.05/1.38 % (3011937)First to succeed.
% 4.05/1.38 % (3011937)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3011896"
% 4.05/1.38 % (3011938)Also succeeded, but the first one will report.
% 4.05/1.38 % (3011942)Also succeeded, but the first one will report.
% 4.05/1.38 % (3011943)Also succeeded, but the first one will report.
% 4.05/1.38 % (3011945)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3228394229:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.05/1.38 % (3011945)Refutation not found, incomplete strategy
% 4.05/1.38 % (3011945)------------------------------
% 4.05/1.38 % (3011945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.38 % (3011945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.38 % (3011945)CaDiCaL version: 2.1.3
% 4.05/1.38 % (3011945)Termination reason: Refutation not found, incomplete strategy
% 4.05/1.38 % (3011945)Time elapsed: 0.001 s
% 4.05/1.38 % (3011945)Peak memory usage: 88 MB
% 4.05/1.38 % (3011939)Instruction limit reached!
% 4.05/1.38 % (3011939)------------------------------
% 4.05/1.38 % (3011939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.38 % (3011939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.38 % (3011939)CaDiCaL version: 2.1.3
% 4.05/1.38 % (3011939)Termination reason: Instruction limit
% 4.05/1.38 % (3011939)Termination phase: Saturation
% 4.05/1.38 % (3011939)Time elapsed: 0.208 s
% 4.05/1.38 % (3011939)Peak memory usage: 118 MB
% 4.05/1.38 % (3011939)Instructions burned: 201 (million)
% 4.05/1.38 % (3011950)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=3654749479:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.05/1.38 % (3011950)Instruction limit reached!
% 4.05/1.38 % (3011950)------------------------------
% 4.05/1.38 % (3011950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.38 % (3011950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.38 % (3011950)CaDiCaL version: 2.1.3
% 4.05/1.38 % (3011950)Termination reason: Instruction limit
% 4.05/1.38 % (3011950)Termination phase: Saturation
% 4.05/1.38 % (3011950)Time elapsed: 0.034 s
% 4.05/1.38 % (3011950)Peak memory usage: 88 MB
% 4.05/1.38 % (3011950)Instructions burned: 30 (million)
% 4.05/1.38 % (3011945)------------------------------
% 4.05/1.38 % (3011945)------------------------------
% 4.05/1.38 % (3011937)Refutation found. Thanks to Tanya!
% 4.05/1.38 % SZS status Theorem for theBenchmark
% 4.05/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 4.05/1.38 % (3011937)------------------------------
% 4.05/1.38 % (3011937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.38 % (3011937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.38 % (3011937)CaDiCaL version: 2.1.3
% 4.05/1.38 % (3011937)Termination reason: Refutation
% 4.05/1.38 % (3011937)Time elapsed: 0.032 s
% 4.05/1.38 % (3011937)Peak memory usage: 116 MB
% 4.05/1.38 % (3011937)Instructions burned: 9 (million)
% 4.05/1.38 % (3011937)------------------------------
% 4.05/1.38 % (3011937)------------------------------
% 4.05/1.38 % (3011896)Success in time 0.497 s
% 4.05/1.38 % Vampire exiting
%------------------------------------------------------------------------------