%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI646_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 : n018.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 3.94s 1.32s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 52 ( 1 unt; 0 typ; 14 def)
% Number of atoms : 221 ( 120 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 230 ( 61 ~; 121 |; 29 &)
% ( 17 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number arithmetic : 168 ( 24 atm; 0 fun; 144 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 : 19 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 12 ( 1 usr; 12 con; 0-0 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 ) )
<=> ( $lesseq(0,a)
& $greater(10,a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 ) )
<=> ( $lesseq(0,a)
& $greater(10,a) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 ) )
<=> ( ~ $less(a,0)
& $less(a,10) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ( ~ $less(a,0)
& $less(a,10) )
<~> ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 ) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,definition,
( sP0
<=> ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f6,plain,
( ( ~ $less(a,0)
& $less(a,10) )
<~> sP0 ),
inference(definition_folding,[],[f4,f5]) ).
tff(f7,plain,
( ( sP0
| ( ( a != 4 )
& ( a != 8 )
& ( a != 1 )
& ( a != 6 )
& ( a != 7 )
& ( a != 2 )
& ( a != 9 )
& ( a != 3 )
& ( a != 5 )
& ( a != 0 ) ) )
& ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f8,plain,
( ( sP0
| ( ( a != 4 )
& ( a != 8 )
& ( a != 1 )
& ( a != 6 )
& ( a != 7 )
& ( a != 2 )
& ( a != 9 )
& ( a != 3 )
& ( a != 5 )
& ( a != 0 ) ) )
& ( ( a = 4 )
| ( a = 8 )
| ( a = 1 )
| ( a = 6 )
| ( a = 7 )
| ( a = 2 )
| ( a = 9 )
| ( a = 3 )
| ( a = 5 )
| ( a = 0 )
| ~ sP0 ) ),
inference(flattening,[],[f7]) ).
tff(f9,plain,
( ( ~ sP0
| $less(a,0)
| ~ $less(a,10) )
& ( sP0
| ( ~ $less(a,0)
& $less(a,10) ) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f10,plain,
( ( ~ sP0
| $less(a,0)
| ~ $less(a,10) )
& ( sP0
| ( ~ $less(a,0)
& $less(a,10) ) ) ),
inference(flattening,[],[f9]) ).
tff(f11,plain,
( ( a = 9 )
| ( a = 3 )
| ~ sP0
| ( a = 7 )
| ( a = 5 )
| ( a = 1 )
| ( a = 8 )
| ( a = 6 )
| ( a = 2 )
| ( a = 0 )
| ( a = 4 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f12,plain,
( ( a != 0 )
| sP0 ),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
( ( a != 5 )
| sP0 ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
( ( a != 3 )
| sP0 ),
inference(cnf_transformation,[],[f8]) ).
tff(f15,plain,
( sP0
| ( a != 9 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f16,plain,
( sP0
| ( a != 2 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f17,plain,
( ( a != 7 )
| sP0 ),
inference(cnf_transformation,[],[f8]) ).
tff(f18,plain,
( sP0
| ( a != 6 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f19,plain,
( ( a != 1 )
| sP0 ),
inference(cnf_transformation,[],[f8]) ).
tff(f20,plain,
( ( a != 8 )
| sP0 ),
inference(cnf_transformation,[],[f8]) ).
tff(f21,plain,
( sP0
| ( a != 4 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f22,plain,
( sP0
| $less(a,10) ),
inference(cnf_transformation,[],[f10]) ).
tff(f23,plain,
( sP0
| ~ $less(a,0) ),
inference(cnf_transformation,[],[f10]) ).
tff(f24,plain,
( ~ $less(a,10)
| ~ sP0
| $less(a,0) ),
inference(cnf_transformation,[],[f10]) ).
tff(f26,definition,
( spl1_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f30,definition,
( spl1_2
<=> $less(a,10) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f33,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f22,f30,f26]) ).
tff(f35,definition,
( spl1_3
<=> $less(a,0) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f38,plain,
( spl1_3
| ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f24,f30,f26,f35]) ).
tff(f40,definition,
( spl1_4
<=> ( a = 1 ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
tff(f43,plain,
( spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f19,f40,f26]) ).
tff(f45,definition,
( spl1_5
<=> ( a = 9 ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
tff(f48,plain,
( ~ spl1_5
| spl1_1 ),
inference(avatar_split_clause,[],[f15,f26,f45]) ).
tff(f50,definition,
( spl1_6
<=> ( a = 7 ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
tff(f53,plain,
( ~ spl1_6
| spl1_1 ),
inference(avatar_split_clause,[],[f17,f26,f50]) ).
tff(f55,definition,
( spl1_7
<=> ( a = 5 ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
tff(f59,definition,
( spl1_8
<=> ( a = 6 ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
tff(f63,definition,
( spl1_9
<=> ( a = 3 ) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
tff(f67,definition,
( spl1_10
<=> ( a = 0 ) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
tff(f71,definition,
( spl1_11
<=> ( a = 4 ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
tff(f75,definition,
( spl1_12
<=> ( a = 2 ) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
tff(f79,definition,
( spl1_13
<=> ( a = 8 ) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
tff(f82,plain,
( spl1_7
| spl1_8
| spl1_6
| spl1_5
| spl1_9
| spl1_10
| spl1_11
| spl1_12
| spl1_4
| spl1_13
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f11,f26,f79,f40,f75,f71,f67,f63,f45,f50,f59,f55]) ).
tff(f83,plain,
( ~ spl1_11
| spl1_1 ),
inference(avatar_split_clause,[],[f21,f26,f71]) ).
tff(f84,plain,
( ~ spl1_10
| spl1_1 ),
inference(avatar_split_clause,[],[f12,f26,f67]) ).
tff(f85,plain,
( spl1_1
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f20,f79,f26]) ).
tff(f86,plain,
( spl1_1
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f18,f59,f26]) ).
tff(f87,plain,
( spl1_1
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f23,f35,f26]) ).
tff(f88,plain,
( ~ spl1_7
| spl1_1 ),
inference(avatar_split_clause,[],[f13,f26,f55]) ).
tff(f89,plain,
( ~ spl1_12
| spl1_1 ),
inference(avatar_split_clause,[],[f16,f26,f75]) ).
tff(f90,plain,
( spl1_1
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f14,f63,f26]) ).
tff(f91,plain,
$false,
inference(avatar_smt_refutation,[],[f90,f89,f88,f87,f86,f85,f84,f83,f82,f53,f48,f43,f38,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI646_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:56:55 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 3.09/1.12 % (3772774)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.09/1.12 % (3772783)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3386492587:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.09/1.12 % (3772783)Instruction limit reached!
% 3.09/1.12 % (3772783)------------------------------
% 3.09/1.12 % (3772783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.12 % (3772783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.12 % (3772783)CaDiCaL version: 2.1.3
% 3.09/1.12 % (3772783)Termination reason: Instruction limit
% 3.09/1.12 % (3772783)Termination phase: Saturation
% 3.09/1.12 % (3772783)Time elapsed: 0.003 s
% 3.09/1.12 % (3772783)Peak memory usage: 89 MB
% 3.09/1.12 % (3772783)Instructions burned: 7 (million)
% 3.09/1.12 % (3772784)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3721981949:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.09/1.12 % (3772782)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3234224099:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.09/1.12 % (3772779)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1068690017:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.09/1.12 % (3772781)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=414411752:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.09/1.12 % (3772780)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2597415615:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.09/1.12 % (3772785)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=347796412:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.09/1.12 % (3772782)Instruction limit reached!
% 3.09/1.12 % (3772782)------------------------------
% 3.09/1.12 % (3772782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.12 % (3772782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.12 % (3772782)CaDiCaL version: 2.1.3
% 3.09/1.12 % (3772782)Termination reason: Instruction limit
% 3.09/1.12 % (3772782)Termination phase: Saturation
% 3.09/1.12 % (3772782)Time elapsed: 0.005 s
% 3.09/1.12 % (3772782)Peak memory usage: 88 MB
% 3.09/1.12 % (3772782)Instructions burned: 7 (million)
% 3.09/1.12 % (3772779)Instruction limit reached!
% 3.09/1.12 % (3772779)------------------------------
% 3.09/1.12 % (3772779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.12 % (3772779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.12 % (3772779)CaDiCaL version: 2.1.3
% 3.09/1.12 % (3772779)Termination reason: Instruction limit
% 3.09/1.12 % (3772779)Termination phase: Saturation
% 3.09/1.12 % (3772779)Time elapsed: 0.031 s
% 3.09/1.12 % (3772779)Peak memory usage: 114 MB
% 3.09/1.12 % (3772779)Instructions burned: 12 (million)
% 3.09/1.12 % (3772784)First to succeed.
% 3.09/1.12 % (3772780)Also succeeded, but the first one will report.
% 3.09/1.12 % (3772785)Also succeeded, but the first one will report.
% 3.09/1.12 % (3772784)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3772774"
% 3.09/1.12 % (3772787)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2680656120:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.09/1.12 % (3772787)Refutation not found, incomplete strategy
% 3.09/1.12 % (3772787)------------------------------
% 3.09/1.12 % (3772787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.12 % (3772787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.12 % (3772787)CaDiCaL version: 2.1.3
% 3.09/1.12 % (3772787)Termination reason: Refutation not found, incomplete strategy
% 3.09/1.12 % (3772787)Time elapsed: 0.001 s
% 3.09/1.12 % (3772787)Peak memory usage: 89 MB
% 3.09/1.12 % (3772787)Instructions burned: 1 (million)
% 3.09/1.12 % (3772781)Instruction limit reached!
% 3.09/1.12 % (3772781)------------------------------
% 3.09/1.12 % (3772781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.12 % (3772781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.12 % (3772781)CaDiCaL version: 2.1.3
% 3.09/1.12 % (3772781)Termination reason: Instruction limit
% 3.09/1.12 % (3772781)Termination phase: Saturation
% 3.94/1.32 % (3772781)Time elapsed: 0.176 s
% 3.94/1.32 % (3772781)Peak memory usage: 116 MB
% 3.94/1.32 % (3772781)Instructions burned: 201 (million)
% 3.94/1.32 % (3772794)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=1743987082:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.94/1.32 % (3772794)Instruction limit reached!
% 3.94/1.32 % (3772794)------------------------------
% 3.94/1.32 % (3772794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.32 % (3772794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.32 % (3772794)CaDiCaL version: 2.1.3
% 3.94/1.32 % (3772794)Termination reason: Instruction limit
% 3.94/1.32 % (3772794)Termination phase: Saturation
% 3.94/1.32 % (3772794)Time elapsed: 0.021 s
% 3.94/1.32 % (3772794)Peak memory usage: 88 MB
% 3.94/1.32 % (3772794)Instructions burned: 30 (million)
% 3.94/1.32 % (3772795)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=27730238:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.94/1.32 % (3772795)Refutation not found, incomplete strategy
% 3.94/1.32 % (3772795)------------------------------
% 3.94/1.32 % (3772795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.32 % (3772795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.32 % (3772795)CaDiCaL version: 2.1.3
% 3.94/1.32 % (3772795)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.32 % (3772795)Time elapsed: 0.007 s
% 3.94/1.32 % (3772795)Peak memory usage: 91 MB
% 3.94/1.32 % (3772795)Instructions burned: 9 (million)
% 3.94/1.32 % (3772787)------------------------------
% 3.94/1.32 % (3772787)------------------------------
% 3.94/1.32 % (3772784)Refutation found. Thanks to Tanya!
% 3.94/1.32 % SZS status Theorem for theBenchmark
% 3.94/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.32 % (3772784)------------------------------
% 3.94/1.32 % (3772784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.32 % (3772784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.32 % (3772784)CaDiCaL version: 2.1.3
% 3.94/1.32 % (3772784)Termination reason: Refutation
% 3.94/1.32 % (3772784)Time elapsed: 0.035 s
% 3.94/1.32 % (3772784)Peak memory usage: 115 MB
% 3.94/1.32 % (3772784)Instructions burned: 14 (million)
% 3.94/1.32 % (3772784)------------------------------
% 3.94/1.32 % (3772784)------------------------------
% 3.94/1.32 % (3772774)Success in time 0.465 s
% 3.94/1.32 % Vampire exiting
%------------------------------------------------------------------------------