%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI183_1 : TPTP v9.3.1. Released v5.0.0.
% 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 09:32:38 AM UTC 2026
% Result : Theorem 5.24s 1.50s
% Output : Refutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 32 ( 14 ~; 7 |; 3 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 66 ( 25 atm; 11 fun; 11 num; 19 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 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 17 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_3,type,
sK0: $int ).
tff(f1,conjecture,
( ! [X0: $int,X1: $int] :
( $less(X0,X1)
=> $less(f(X0),f(X1)) )
=> ! [X2: $int] : $greater(f($sum(f(X2),2)),f(f(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int,X1: $int] :
( $less(X0,X1)
=> $less(f(X0),f(X1)) )
=> ! [X2: $int] : $greater(f($sum(f(X2),2)),f(f(X2))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int,X1: $int] :
( $less(X0,X1)
=> $less(f(X0),f(X1)) )
=> ! [X2: $int] : $less(f(f(X2)),f($sum(f(X2),2))) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ? [X2: $int] : ~ $less(f(f(X2)),f($sum(f(X2),2)))
& ! [X0: $int,X1: $int] :
( $less(f(X0),f(X1))
| ~ $less(X0,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ? [X0: $int] : ~ $less(f(f(X0)),f($sum(f(X0),2)))
& ! [X1: $int,X2: $int] :
( $less(f(X1),f(X2))
| ~ $less(X1,X2) ) ),
inference(rectify,[],[f4]) ).
tff(f6,plain,
( ~ $less(f(f(sK0)),f($sum(f(sK0),2)))
& ! [X1: $int,X2: $int] :
( $less(f(X1),f(X2))
| ~ $less(X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
tff(f7,plain,
! [X2: $int,X1: $int] :
( $less(f(X1),f(X2))
| ~ $less(X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
~ $less(f(f(sK0)),f($sum(f(sK0),2))),
inference(cnf_transformation,[],[f6]) ).
tff(f10,definition,
( spl1_1
<=> $less(f(f(sK0)),f($sum(f(sK0),2))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f12,plain,
( ~ $less(f(f(sK0)),f($sum(f(sK0),2)))
| spl1_1 ),
inference(avatar_component_clause,[],[f10]) ).
tff(f13,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f8,f10]) ).
tff(f14,plain,
( ~ $less(f(sK0),$sum(f(sK0),2))
| spl1_1 ),
inference(resolution,[],[f12,f7]) ).
tff(f16,definition,
( spl1_2
<=> $less(f(sK0),$sum(f(sK0),2)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f19,plain,
( ~ spl1_2
| spl1_1 ),
inference(avatar_split_clause,[],[f14,f10,f16]) ).
tff(f20,plain,
$false,
inference(avatar_smt_refutation,[],[f19,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI183_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:46:41 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 5.24/1.50 % (3748556)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.24/1.50 % (3748567)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1147797678:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 5.24/1.50 % (3748567)Refutation not found, incomplete strategy
% 5.24/1.50 % (3748567)------------------------------
% 5.24/1.50 % (3748567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748567)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748567)Termination reason: Refutation not found, incomplete strategy
% 5.24/1.50 % (3748567)Time elapsed: 0.034 s
% 5.24/1.50 % (3748567)Peak memory usage: 116 MB
% 5.24/1.50 % (3748567)Instructions burned: 10 (million)
% 5.24/1.50 % (3748572)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=551401635:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 5.24/1.50 % (3748571)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3462843015:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 5.24/1.50 % (3748568)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4013117492:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 5.24/1.50 % (3748570)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2344946684:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 5.24/1.50 % (3748569)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=974499894:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 5.24/1.50 % (3748571)Instruction limit reached!
% 5.24/1.50 % (3748571)------------------------------
% 5.24/1.50 % (3748571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748571)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748571)Termination reason: Instruction limit
% 5.24/1.50 % (3748571)Termination phase: Saturation
% 5.24/1.50 % (3748571)Time elapsed: 0.006 s
% 5.24/1.50 % (3748571)Peak memory usage: 88 MB
% 5.24/1.50 % (3748571)Instructions burned: 4 (million)
% 5.24/1.50 % (3748570)Instruction limit reached!
% 5.24/1.50 % (3748570)------------------------------
% 5.24/1.50 % (3748570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748570)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748570)Termination reason: Instruction limit
% 5.24/1.50 % (3748570)Termination phase: Saturation
% 5.24/1.50 % (3748570)Time elapsed: 0.009 s
% 5.24/1.50 % (3748570)Peak memory usage: 88 MB
% 5.24/1.50 % (3748570)Instructions burned: 7 (million)
% 5.24/1.50 % (3748573)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2118410319:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 5.24/1.50 % (3748572)First to succeed.
% 5.24/1.50 % (3748572)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3748556"
% 5.24/1.50 % (3748568)Also succeeded, but the first one will report.
% 5.24/1.50 % (3748573)Also succeeded, but the first one will report.
% 5.24/1.50 % (3748567)------------------------------
% 5.24/1.50 % (3748567)------------------------------
% 5.24/1.50 % (3748582)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=169433772:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.24/1.50 % (3748582)Refutation not found, incomplete strategy
% 5.24/1.50 % (3748582)------------------------------
% 5.24/1.50 % (3748582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748582)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748582)Termination reason: Refutation not found, incomplete strategy
% 5.24/1.50 % (3748582)Time elapsed: 0.002 s
% 5.24/1.50 % (3748582)Peak memory usage: 88 MB
% 5.24/1.50 % (3748583)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=3744953289:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.24/1.50 % (3748569)Instruction limit reached!
% 5.24/1.50 % (3748569)------------------------------
% 5.24/1.50 % (3748569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748569)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748569)Termination reason: Instruction limit
% 5.24/1.50 % (3748569)Termination phase: Saturation
% 5.24/1.50 % (3748569)Time elapsed: 0.257 s
% 5.24/1.50 % (3748569)Peak memory usage: 117 MB
% 5.24/1.50 % (3748569)Instructions burned: 201 (million)
% 5.24/1.50 % (3748583)Instruction limit reached!
% 5.24/1.50 % (3748583)------------------------------
% 5.24/1.50 % (3748583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748583)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748583)Termination reason: Instruction limit
% 5.24/1.50 % (3748583)Termination phase: Saturation
% 5.24/1.50 % (3748583)Time elapsed: 0.032 s
% 5.24/1.50 % (3748583)Peak memory usage: 88 MB
% 5.24/1.50 % (3748583)Instructions burned: 29 (million)
% 5.24/1.50 % (3748588)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3690984314:i=24:canc=force:rtra=on_2995 on theBenchmark for (2995ds/24Mi)
% 5.24/1.50 % (3748588)Also succeeded, but the first one will report.
% 5.24/1.50 % (3748585)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3636470934:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/16Mi)
% 5.24/1.50 % (3748589)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=3372001180:i=27:canc=cautious:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/27Mi)
% 5.24/1.50 % (3748585)Also succeeded, but the first one will report.
% 5.24/1.50 % (3748572)Refutation found. Thanks to Tanya!
% 5.24/1.50 % SZS status Theorem for theBenchmark
% 5.24/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 5.24/1.50 % (3748572)------------------------------
% 5.24/1.50 % (3748572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.50 % (3748572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.50 % (3748572)CaDiCaL version: 2.1.3
% 5.24/1.50 % (3748572)Termination reason: Refutation
% 5.24/1.50 % (3748572)Time elapsed: 0.043 s
% 5.24/1.50 % (3748572)Peak memory usage: 116 MB
% 5.24/1.50 % (3748572)Instructions burned: 8 (million)
% 5.24/1.50 % (3748572)------------------------------
% 5.24/1.50 % (3748572)------------------------------
% 5.24/1.50 % (3748556)Success in time 0.667 s
% 5.24/1.50 % Vampire exiting
%------------------------------------------------------------------------------