%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI571_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:33:23 AM UTC 2026
% Result : Theorem 2.80s 1.16s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 0 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 84 ( 16 atm; 38 fun; 22 num; 8 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 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 6 !; 2 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(func_def_8,type,
sK1: $int ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( $less(X1,X0)
=> $less($difference(2,X0),$difference(5,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',neg_weakening_ineq) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( $less(X1,X0)
=> $less($difference(2,X0),$difference(5,X1)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $int,X0: $int] :
( $less(X1,X0)
=> $less($sum(2,$uminus(X0)),$sum(5,$uminus(X1))) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
? [X0: $int,X1: $int] :
( $less(X1,X0)
& ~ $less($sum(2,$uminus(X0)),$sum(5,$uminus(X1))) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
( $less(sK1,sK0)
& ~ $less($sum(2,$uminus(sK0)),$sum(5,$uminus(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
tff(f18,plain,
~ $less($sum(2,$uminus(sK0)),$sum(5,$uminus(sK1))),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
$less(sK1,sK0),
inference(cnf_transformation,[],[f17]) ).
tff(f20,plain,
$less(0,$sum(sK0,$uminus(sK1))),
inference(evaluation,[],[f19]) ).
tff(f21,plain,
$less(0,$sum($sum($sum(2,$uminus(sK0)),1),$uminus($sum(5,$uminus(sK1))))),
inference(evaluation,[],[f18]) ).
tff(f23,definition,
( spl2_1
<=> $less(0,$sum(sK0,$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f26,plain,
spl2_1,
inference(avatar_split_clause,[],[f20,f23]) ).
tff(f28,definition,
( spl2_2
<=> $less(0,$sum($sum($sum(2,$uminus(sK0)),1),$uminus($sum(5,$uminus(sK1))))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f31,plain,
spl2_2,
inference(avatar_split_clause,[],[f21,f28]) ).
tff(f32,plain,
$false,
inference(avatar_smt_refutation,[],[f31,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI571_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n013.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 20:51:52 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 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
% 2.80/1.16 % (1561790)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.80/1.16 % (1561795)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3037189342:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.80/1.16 % (1561795)First to succeed.
% 2.80/1.16 % (1561795)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1561790"
% 2.80/1.16 % (1561801)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1982974249:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.80/1.16 % (1561800)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2454547469:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.80/1.16 % (1561796)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1070519381:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.80/1.16 % (1561799)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1462233893:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.80/1.16 % (1561797)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3064282800:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.80/1.16 % (1561798)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3352525634:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.80/1.16 % (1561799)Instruction limit reached!
% 2.80/1.16 % (1561799)------------------------------
% 2.80/1.16 % (1561799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (1561799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (1561799)CaDiCaL version: 2.1.3
% 2.80/1.16 % (1561799)Termination reason: Instruction limit
% 2.80/1.16 % (1561799)Termination phase: Saturation
% 2.80/1.16 % (1561799)Time elapsed: 0.004 s
% 2.80/1.16 % (1561799)Peak memory usage: 89 MB
% 2.80/1.16 % (1561799)Instructions burned: 5 (million)
% 2.80/1.16 % (1561798)Instruction limit reached!
% 2.80/1.16 % (1561798)------------------------------
% 2.80/1.16 % (1561798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (1561798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (1561798)CaDiCaL version: 2.1.3
% 2.80/1.16 % (1561798)Termination reason: Instruction limit
% 2.80/1.16 % (1561798)Termination phase: Saturation
% 2.80/1.16 % (1561798)Time elapsed: 0.005 s
% 2.80/1.16 % (1561798)Peak memory usage: 89 MB
% 2.80/1.16 % (1561798)Instructions burned: 7 (million)
% 2.80/1.16 % (1561801)Also succeeded, but the first one will report.
% 2.80/1.16 % (1561800)Also succeeded, but the first one will report.
% 2.80/1.16 % (1561796)Also succeeded, but the first one will report.
% 2.80/1.16 % (1561795)Refutation found. Thanks to Tanya!
% 2.80/1.16 % SZS status Theorem for theBenchmark
% 2.80/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.16 % (1561795)------------------------------
% 2.80/1.16 % (1561795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (1561795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (1561795)CaDiCaL version: 2.1.3
% 2.80/1.16 % (1561795)Termination reason: Refutation
% 2.80/1.16 % (1561795)Time elapsed: 0.020 s
% 2.80/1.16 % (1561795)Peak memory usage: 116 MB
% 2.80/1.16 % (1561795)Instructions burned: 8 (million)
% 2.80/1.16 % (1561795)------------------------------
% 2.80/1.16 % (1561795)------------------------------
% 2.80/1.16 % (1561790)Success in time 0.306 s
% 2.80/1.16 % Vampire exiting
%------------------------------------------------------------------------------