%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI179_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 4.81s 1.52s
% Output : Refutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 52 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 9 ~; 0 |; 20 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 142 ( 33 atm; 32 fun; 60 num; 17 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 ( 2 usr; 8 con; 0-2 aty)
% Number of variables : 17 ( 11 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_9,type,
sK0: $int ).
tff(func_def_10,type,
sK1: $int ).
tff(f1,conjecture,
! [X2: $int,X1: $int,X0: $int] :
( ( $less(X1,3)
& $greater($sum(X0,$product(2,X1)),7)
& $less(X0,5) )
=> ( X1 = 2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ! [X2: $int,X1: $int,X0: $int] :
( ( $less(X1,3)
& $greater($sum(X0,$product(2,X1)),7)
& $less(X0,5) )
=> ( X1 = 2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X2: $int,X1: $int,X0: $int] :
( ( $less(X1,3)
& $less(7,$sum(X0,$product(2,X1)))
& $less(X0,5) )
=> ( X1 = 2 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
~ ! [X2: $int,X1: $int] :
( ( $less(X2,5)
& $less(7,$sum(X2,$product(2,X1)))
& $less(X1,3) )
=> ( X1 = 2 ) ),
inference(rectify,[],[f3]) ).
tff(f23,plain,
? [X2: $int,X1: $int] :
( ( 2 != X1 )
& $less(X2,5)
& $less(7,$sum(X2,$product(2,X1)))
& $less(X1,3) ),
inference(ennf_transformation,[],[f22]) ).
tff(f24,plain,
? [X1: $int,X2: $int] :
( $less(X1,3)
& ( 2 != X1 )
& $less(X2,5)
& $less(7,$sum(X2,$product(2,X1))) ),
inference(flattening,[],[f23]) ).
tff(f25,plain,
? [X0: $int,X1: $int] :
( $less(X0,3)
& ( 2 != X0 )
& $less(X1,5)
& $less(7,$sum(X1,$product(2,X0))) ),
inference(rectify,[],[f24]) ).
tff(f26,plain,
( $less(sK0,3)
& ( 2 != sK0 )
& $less(sK1,5)
& $less(7,$sum(sK1,$product(2,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f25]) ).
tff(f27,plain,
$less(7,$sum(sK1,$product(2,sK0))),
inference(cnf_transformation,[],[f26]) ).
tff(f28,plain,
$less(sK1,5),
inference(cnf_transformation,[],[f26]) ).
tff(f29,plain,
2 != sK0,
inference(cnf_transformation,[],[f26]) ).
tff(f30,plain,
$less(sK0,3),
inference(cnf_transformation,[],[f26]) ).
tff(f31,plain,
$less(0,$sum(5,$uminus(sK1))),
inference(evaluation,[],[f28]) ).
tff(f32,plain,
$less(0,$sum(3,$uminus(sK0))),
inference(evaluation,[],[f30]) ).
tff(f33,plain,
$less(0,$sum($sum(sK1,$product(2,sK0)),-7)),
inference(evaluation,[],[f27]) ).
tff(f35,definition,
( spl2_1
<=> $less(0,$sum(5,$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f38,plain,
spl2_1,
inference(avatar_split_clause,[],[f31,f35]) ).
tff(f40,definition,
( spl2_2
<=> $less(0,$sum(3,$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f43,plain,
spl2_2,
inference(avatar_split_clause,[],[f32,f40]) ).
tff(f45,definition,
( spl2_3
<=> ( 2 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f48,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f29,f45]) ).
tff(f50,definition,
( spl2_4
<=> $less(0,$sum($sum(sK1,$product(2,sK0)),-7)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f53,plain,
spl2_4,
inference(avatar_split_clause,[],[f33,f50]) ).
tff(f54,plain,
$false,
inference(avatar_smt_refutation,[],[f53,f48,f43,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI179_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n017.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 20:39:36 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running first-order theorem proving
% 0.11/0.23 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
% 4.81/1.52 % (3991445)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.81/1.52 % (3991518)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1439572849:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.81/1.52 % (3991521)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3884574358:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.81/1.52 % (3991519)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3865719388:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.81/1.52 % (3991517)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3996732921:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.81/1.52 % (3991522)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=508237478:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.81/1.52 % (3991516)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=617975481:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.81/1.52 % (3991519)Instruction limit reached!
% 4.81/1.52 % (3991519)------------------------------
% 4.81/1.52 % (3991519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991519)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991519)Termination reason: Instruction limit
% 4.81/1.52 % (3991519)Termination phase: Saturation
% 4.81/1.52 % (3991519)Time elapsed: 0.005 s
% 4.81/1.52 % (3991519)Peak memory usage: 88 MB
% 4.81/1.52 % (3991519)Instructions burned: 7 (million)
% 4.81/1.52 % (3991520)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3779930338:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.81/1.52 % (3991520)Instruction limit reached!
% 4.81/1.52 % (3991520)------------------------------
% 4.81/1.52 % (3991520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991520)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991520)Termination reason: Instruction limit
% 4.81/1.52 % (3991520)Termination phase: Saturation
% 4.81/1.52 % (3991520)Time elapsed: 0.004 s
% 4.81/1.52 % (3991520)Peak memory usage: 88 MB
% 4.81/1.52 % (3991520)Instructions burned: 4 (million)
% 4.81/1.52 % (3991521)Also succeeded, but the first one will report.
% 4.81/1.52 % (3991516)First to succeed.
% 4.81/1.52 % (3991517)Also succeeded, but the first one will report.
% 4.81/1.52 % (3991516)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3991445"
% 4.81/1.52 % (3991522)Also succeeded, but the first one will report.
% 4.81/1.52 % (3991518)Instruction limit reached!
% 4.81/1.52 % (3991518)------------------------------
% 4.81/1.52 % (3991518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991518)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991518)Termination reason: Instruction limit
% 4.81/1.52 % (3991518)Termination phase: Saturation
% 4.81/1.52 % (3991518)Time elapsed: 0.098 s
% 4.81/1.52 % (3991518)Peak memory usage: 117 MB
% 4.81/1.52 % (3991518)Instructions burned: 201 (million)
% 4.81/1.52 % (3991567)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=104254918:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.81/1.52 % (3991567)Refutation not found, incomplete strategy
% 4.81/1.52 % (3991567)------------------------------
% 4.81/1.52 % (3991567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991567)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991567)Termination reason: Refutation not found, incomplete strategy
% 4.81/1.52 % (3991567)Time elapsed: 0.002 s
% 4.81/1.52 % (3991567)Peak memory usage: 89 MB
% 4.81/1.52 % (3991572)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=2775984155:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.81/1.52 % (3991572)Instruction limit reached!
% 4.81/1.52 % (3991572)------------------------------
% 4.81/1.52 % (3991572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991572)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991572)Termination reason: Instruction limit
% 4.81/1.52 % (3991572)Termination phase: Saturation
% 4.81/1.52 % (3991572)Time elapsed: 0.031 s
% 4.81/1.52 % (3991572)Peak memory usage: 89 MB
% 4.81/1.52 % (3991572)Instructions burned: 29 (million)
% 4.81/1.52 % (3991585)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2624028203:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.81/1.52 % (3991585)Refutation not found, incomplete strategy
% 4.81/1.52 % (3991585)------------------------------
% 4.81/1.52 % (3991585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991585)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991585)Termination reason: Refutation not found, incomplete strategy
% 4.81/1.52 % (3991585)Time elapsed: 0.005 s
% 4.81/1.52 % (3991585)Peak memory usage: 90 MB
% 4.81/1.52 % (3991585)Instructions burned: 6 (million)
% 4.81/1.52 % (3991516)Refutation found. Thanks to Tanya!
% 4.81/1.52 % SZS status Theorem for theBenchmark
% 4.81/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 4.81/1.52 % (3991516)------------------------------
% 4.81/1.52 % (3991516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.52 % (3991516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.52 % (3991516)CaDiCaL version: 2.1.3
% 4.81/1.52 % (3991516)Termination reason: Refutation
% 4.81/1.52 % (3991516)Time elapsed: 0.032 s
% 4.81/1.52 % (3991516)Peak memory usage: 115 MB
% 4.81/1.52 % (3991516)Instructions burned: 9 (million)
% 4.81/1.52 % (3991516)------------------------------
% 4.81/1.52 % (3991516)------------------------------
% 4.81/1.52 % (3991445)Success in time 0.605 s
% 4.81/1.52 % Vampire exiting
%------------------------------------------------------------------------------