%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI587_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 : n005.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 09:33:25 AM UTC 2026
% Result : Theorem 5.83s 1.68s
% Output : Refutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 30 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 5 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 131 ( 24 atm; 49 fun; 47 num; 11 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 : 9 ( 1 usr; 6 con; 0-2 aty)
% Number of variables : 11 ( 8 !; 3 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(f1,conjecture,
! [X0: $int] :
( $less(1,X0)
=> ? [X1: $int] :
( $less($sum(X0,2),X1)
& $less(X1,$product(X0,3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists_Y_between_Xplus2_and_3X) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( $less(1,X0)
=> ? [X1: $int] :
( $less($sum(X0,2),X1)
& $less(X1,$product(X0,3)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f21,plain,
? [X0: $int] :
( $less(1,X0)
& ! [X1: $int] :
( ~ $less(X1,$product(X0,3))
| ~ $less($sum(X0,2),X1) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( $less(1,sK0)
& ! [X1: $int] :
( ~ $less(X1,$product(sK0,3))
| ~ $less($sum(sK0,2),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
tff(f23,plain,
! [X1: $int] :
( ~ $less(X1,$product(sK0,3))
| ~ $less($sum(sK0,2),X1) ),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
$less(1,sK0),
inference(cnf_transformation,[],[f22]) ).
tff(f25,plain,
$less(0,$sum(sK0,-1)),
inference(evaluation,[],[f24]) ).
tff(f26,plain,
! [X1: $int] :
( $less(0,$sum($sum($sum(sK0,2),1),$uminus(X1)))
| $less(0,$sum($sum(X1,1),$uminus($product(sK0,3)))) ),
inference(evaluation,[],[f23]) ).
tff(f28,definition,
( spl1_1
<=> $less(0,$sum(sK0,-1)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f31,plain,
spl1_1,
inference(avatar_split_clause,[],[f25,f28]) ).
tff(f33,plain,
! [X0: $int] :
( ( 0 != $sum($sum($sum(sK0,2),1),$uminus(X0)) )
| $less(0,$sum($sum(X0,1),$uminus($product(sK0,3)))) ),
inference(constrained_resolution,[],[f8,f26]) ).
tff(f34,plain,
$less(0,$sum($sum($uminus($sum(0,$uminus($sum($sum(sK0,2),1)))),1),$uminus($product(sK0,3)))),
inference(gaussian_variable_elimination,[],[f33]) ).
tff(f35,plain,
$less(0,$sum($sum($sum($sum(sK0,2),1),1),$uminus($product(sK0,3)))),
inference(evaluation,[],[f34]) ).
tff(f37,definition,
( spl1_2
<=> $less(0,$sum($sum($sum($sum(sK0,2),1),1),$uminus($product(sK0,3)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f40,plain,
spl1_2,
inference(avatar_split_clause,[],[f35,f37]) ).
tff(f46,plain,
$false,
inference(avatar_smt_refutation,[],[f40,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI587_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n005.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 20:52:46 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running first-order theorem proving
% 0.24/0.28 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
% 5.83/1.68 % (1158800)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.83/1.68 % (1158806)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1182664215:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.83/1.68 % (1158809)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3480345076:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.83/1.68 % (1158809)Instruction limit reached!
% 5.83/1.68 % (1158809)------------------------------
% 5.83/1.68 % (1158809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158809)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158809)Termination reason: Instruction limit
% 5.83/1.68 % (1158809)Termination phase: Saturation
% 5.83/1.68 % (1158809)Time elapsed: 0.005 s
% 5.83/1.68 % (1158809)Peak memory usage: 89 MB
% 5.83/1.68 % (1158809)Instructions burned: 5 (million)
% 5.83/1.68 % (1158806)Refutation not found, incomplete strategy
% 5.83/1.68 % (1158806)------------------------------
% 5.83/1.68 % (1158806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158806)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158806)Termination reason: Refutation not found, incomplete strategy
% 5.83/1.68 % (1158806)Time elapsed: 0.024 s
% 5.83/1.68 % (1158806)Peak memory usage: 115 MB
% 5.83/1.68 % (1158806)Instructions burned: 6 (million)
% 5.83/1.68 % (1158807)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1906954668:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.83/1.68 % (1158805)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2784714072:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.83/1.68 % (1158810)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4069021912:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.83/1.68 % (1158811)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=757683736:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.83/1.68 % (1158808)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1012605485:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.83/1.68 % (1158808)Instruction limit reached!
% 5.83/1.68 % (1158808)------------------------------
% 5.83/1.68 % (1158808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158808)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158808)Termination reason: Instruction limit
% 5.83/1.68 % (1158808)Termination phase: Saturation
% 5.83/1.68 % (1158808)Time elapsed: 0.010 s
% 5.83/1.68 % (1158808)Peak memory usage: 88 MB
% 5.83/1.68 % (1158808)Instructions burned: 8 (million)
% 5.83/1.68 % (1158805)First to succeed.
% 5.83/1.68 % (1158810)Refutation not found, incomplete strategy
% 5.83/1.68 % (1158810)------------------------------
% 5.83/1.68 % (1158810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158810)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158810)Termination reason: Refutation not found, incomplete strategy
% 5.83/1.68 % (1158810)Time elapsed: 0.039 s
% 5.83/1.68 % (1158810)Peak memory usage: 115 MB
% 5.83/1.68 % (1158810)Instructions burned: 6 (million)
% 5.83/1.68 % (1158805)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1158800"
% 5.83/1.68 % (1158811)Also succeeded, but the first one will report.
% 5.83/1.68 % (1158806)------------------------------
% 5.83/1.68 % (1158806)------------------------------
% 5.83/1.68 % (1158814)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1999178843:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.83/1.68 % (1158814)Refutation not found, incomplete strategy
% 5.83/1.68 % (1158814)------------------------------
% 5.83/1.68 % (1158814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158814)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158814)Termination reason: Refutation not found, incomplete strategy
% 5.83/1.68 % (1158814)Time elapsed: 0.002 s
% 5.83/1.68 % (1158814)Peak memory usage: 88 MB
% 5.83/1.68 % (1158807)Instruction limit reached!
% 5.83/1.68 % (1158807)------------------------------
% 5.83/1.68 % (1158807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158807)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158807)Termination reason: Instruction limit
% 5.83/1.68 % (1158807)Termination phase: Saturation
% 5.83/1.68 % (1158807)Time elapsed: 0.266 s
% 5.83/1.68 % (1158807)Peak memory usage: 117 MB
% 5.83/1.68 % (1158807)Instructions burned: 201 (million)
% 5.83/1.68 % (1158820)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=2386044141:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.83/1.68 % (1158820)Instruction limit reached!
% 5.83/1.68 % (1158820)------------------------------
% 5.83/1.68 % (1158820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158820)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158820)Termination reason: Instruction limit
% 5.83/1.68 % (1158820)Termination phase: Saturation
% 5.83/1.68 % (1158820)Time elapsed: 0.034 s
% 5.83/1.68 % (1158820)Peak memory usage: 88 MB
% 5.83/1.68 % (1158820)Instructions burned: 29 (million)
% 5.83/1.68 % (1158821)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3165436839:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/16Mi)
% 5.83/1.68 % (1158821)Instruction limit reached!
% 5.83/1.68 % (1158821)------------------------------
% 5.83/1.68 % (1158821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158821)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158821)Termination reason: Instruction limit
% 5.83/1.68 % (1158821)Termination phase: Saturation
% 5.83/1.68 % (1158821)Time elapsed: 0.010 s
% 5.83/1.68 % (1158821)Peak memory usage: 90 MB
% 5.83/1.68 % (1158821)Instructions burned: 18 (million)
% 5.83/1.68 % (1158810)------------------------------
% 5.83/1.68 % (1158810)------------------------------
% 5.83/1.68 % (1158805)Refutation found. Thanks to Tanya!
% 5.83/1.68 % SZS status Theorem for theBenchmark
% 5.83/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 5.83/1.68 % (1158805)------------------------------
% 5.83/1.68 % (1158805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.68 % (1158805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.68 % (1158805)CaDiCaL version: 2.1.3
% 5.83/1.68 % (1158805)Termination reason: Refutation
% 5.83/1.68 % (1158805)Time elapsed: 0.046 s
% 5.83/1.68 % (1158805)Peak memory usage: 116 MB
% 5.83/1.68 % (1158805)Instructions burned: 9 (million)
% 5.83/1.68 % (1158805)------------------------------
% 5.83/1.68 % (1158805)------------------------------
% 5.83/1.68 % (1158800)Success in time 0.726 s
% 5.83/1.68 % Vampire exiting
%------------------------------------------------------------------------------