%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI658_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 : n010.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 3.91s 1.38s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 1 unt; 0 typ; 3 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51 ( 22 ~; 14 |; 8 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 80 ( 34 atm; 12 fun; 34 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 : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( ( $lesseq(a,1)
& $greatereq(a,-1) )
<=> $greatereq(3,$product(a,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( $lesseq(a,1)
& $greatereq(a,-1) )
<=> $greatereq(3,$product(a,a)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ~ $less(1,a)
& ~ $less(a,-1) )
<=> ~ $less(3,$product(a,a)) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ( ~ $less(1,a)
& ~ $less(a,-1) )
<~> ~ $less(3,$product(a,a)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ( $less(3,$product(a,a))
| $less(1,a)
| $less(a,-1) )
& ( ~ $less(3,$product(a,a))
| ( ~ $less(1,a)
& ~ $less(a,-1) ) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f6,plain,
( ( $less(3,$product(a,a))
| $less(1,a)
| $less(a,-1) )
& ( ~ $less(3,$product(a,a))
| ( ~ $less(1,a)
& ~ $less(a,-1) ) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ~ $less(a,-1)
| ~ $less(3,$product(a,a)) ),
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
( ~ $less(1,a)
| ~ $less(3,$product(a,a)) ),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
( $less(1,a)
| $less(a,-1)
| $less(3,$product(a,a)) ),
inference(cnf_transformation,[],[f6]) ).
tff(f11,definition,
( spl0_1
<=> $less(1,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f15,definition,
( spl0_2
<=> $less(3,$product(a,a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f18,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f8,f15,f11]) ).
tff(f20,definition,
( spl0_3
<=> $less(a,-1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f23,plain,
( spl0_2
| spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f9,f20,f11,f15]) ).
tff(f24,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f7,f15,f20]) ).
tff(f25,plain,
$false,
inference(avatar_smt_refutation,[],[f24,f23,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI658_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n010.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 20:55:32 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.28 Running first-order theorem proving
% 0.27/0.28 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
% 3.91/1.38 % (2323251)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.91/1.38 % (2323261)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=158703256:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.91/1.38 % (2323261)First to succeed.
% 3.91/1.38 % (2323261)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2323251"
% 3.91/1.38 % (2323259)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1341333740:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.91/1.38 % (2323256)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1379921184:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.91/1.38 % (2323257)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=65200574:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.91/1.38 % (2323260)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2717943491:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.91/1.38 % (2323258)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1269632678:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.91/1.38 % (2323260)Instruction limit reached!
% 3.91/1.38 % (2323260)------------------------------
% 3.91/1.38 % (2323260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.38 % (2323260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.38 % (2323260)CaDiCaL version: 2.1.3
% 3.91/1.38 % (2323260)Termination reason: Instruction limit
% 3.91/1.38 % (2323260)Termination phase: Saturation
% 3.91/1.38 % (2323260)Time elapsed: 0.006 s
% 3.91/1.38 % (2323260)Peak memory usage: 88 MB
% 3.91/1.38 % (2323260)Instructions burned: 4 (million)
% 3.91/1.38 % (2323259)Instruction limit reached!
% 3.91/1.38 % (2323259)------------------------------
% 3.91/1.38 % (2323259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.38 % (2323259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.38 % (2323259)CaDiCaL version: 2.1.3
% 3.91/1.38 % (2323259)Termination reason: Instruction limit
% 3.91/1.38 % (2323259)Termination phase: Saturation
% 3.91/1.38 % (2323259)Time elapsed: 0.009 s
% 3.91/1.38 % (2323259)Peak memory usage: 88 MB
% 3.91/1.38 % (2323259)Instructions burned: 7 (million)
% 3.91/1.38 % (2323262)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4232032474:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.91/1.38 % (2323257)Also succeeded, but the first one will report.
% 3.91/1.38 % (2323256)Also succeeded, but the first one will report.
% 3.91/1.38 % (2323262)Also succeeded, but the first one will report.
% 3.91/1.38 % (2323272)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=3842064897:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.91/1.38 % (2323261)Refutation found. Thanks to Tanya!
% 3.91/1.38 % SZS status Theorem for theBenchmark
% 3.91/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.38 % (2323261)------------------------------
% 3.91/1.38 % (2323261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.38 % (2323261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.38 % (2323261)CaDiCaL version: 2.1.3
% 3.91/1.38 % (2323261)Termination reason: Refutation
% 3.91/1.38 % (2323261)Time elapsed: 0.029 s
% 3.91/1.38 % (2323261)Peak memory usage: 116 MB
% 3.91/1.38 % (2323261)Instructions burned: 9 (million)
% 3.91/1.38 % (2323261)------------------------------
% 3.91/1.38 % (2323261)------------------------------
% 3.91/1.38 % (2323251)Success in time 0.455 s
% 3.91/1.38 % Vampire exiting
%------------------------------------------------------------------------------