%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT068_1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:47:13 AM UTC 2026
% Result : Theorem 0.19s 1.20s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 40 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 11 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 41 ( 7 atm; 8 fun; 8 num; 18 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 24 !; 3 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
heap: $tType ).
tff(func_def_0,type,
empty: heap ).
tff(func_def_1,type,
toop: heap > $int ).
tff(func_def_2,type,
sel: ( heap * $int ) > $int ).
tff(func_def_3,type,
length: heap > $int ).
tff(func_def_4,type,
app: ( heap * $int ) > heap ).
tff(func_def_5,type,
get: heap > heap ).
tff(func_def_9,type,
sK0: $int ).
tff(func_def_10,type,
sK1: heap ).
tff(func_def_11,type,
sK2: $int ).
tff(pred_def_1,type,
lsls: ( heap * heap ) > $o ).
tff(f3,axiom,
! [X0: $int,X2: $int,X1: heap] :
( ( X2 != $sum(1,length(X1)) )
=> ( sel(app(X1,X0),X2) = sel(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_3) ).
tff(f15,conjecture,
! [X0: $int,X2: heap,X1: $int] :
( ~ $less(X1,length(X2))
| ( sel(app(X2,X0),X1) = sel(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_3) ).
tff(f16,negated_conjecture,
~ ! [X0: $int,X2: heap,X1: $int] :
( ~ $less(X1,length(X2))
| ( sel(app(X2,X0),X1) = sel(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f24,plain,
~ ! [X1: heap,X2: $int,X0: $int] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ~ $less(X2,length(X1)) ),
inference(rectify,[],[f16]) ).
tff(f25,plain,
! [X2: heap,X1: $int,X0: $int] :
( ( $sum(1,length(X2)) != X1 )
=> ( sel(app(X2,X0),X1) = sel(X2,X1) ) ),
inference(rectify,[],[f3]) ).
tff(f29,plain,
? [X0: $int,X1: heap,X2: $int] :
( $less(X2,length(X1))
& ( sel(app(X1,X0),X2) != sel(X1,X2) ) ),
inference(ennf_transformation,[],[f24]) ).
tff(f30,plain,
! [X0: $int,X2: heap,X1: $int] :
( ( sel(app(X2,X0),X1) = sel(X2,X1) )
| ( $sum(1,length(X2)) = X1 ) ),
inference(ennf_transformation,[],[f25]) ).
tff(f33,plain,
( $less(sK2,length(sK1))
& ( sel(app(sK1,sK0),sK2) != sel(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
tff(f43,plain,
! [X0: $int,X1: heap,X2: $int] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ),
inference(rectify,[],[f30]) ).
tff(f49,plain,
sel(app(sK1,sK0),sK2) != sel(sK1,sK2),
inference(cnf_transformation,[],[f33]) ).
tff(f50,plain,
$less(sK2,length(sK1)),
inference(cnf_transformation,[],[f33]) ).
tff(f63,plain,
! [X2: $int,X0: $int,X1: heap] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f74,definition,
( spl3_2
<=> $less(sK2,length(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f77,plain,
spl3_2,
inference(avatar_split_clause,[],[f50,f74]) ).
tff(f79,definition,
( spl3_3
<=> ( sel(app(sK1,sK0),sK2) = sel(sK1,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f81,plain,
( ( sel(app(sK1,sK0),sK2) != sel(sK1,sK2) )
| spl3_3 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f82,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f49,f79]) ).
tff(f123,plain,
( ( sel(sK1,sK2) != sel(sK1,sK2) )
| ( $sum(1,length(sK1)) = sK2 )
| spl3_3 ),
inference(superposition,[],[f81,f63]) ).
tff(f124,plain,
( ( $sum(1,length(sK1)) = sK2 )
| spl3_3 ),
inference(trivial_inequality_removal,[],[f123]) ).
tff(f126,definition,
( spl3_4
<=> ( $sum(1,length(sK1)) = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f129,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f124,f79,f126]) ).
tff(f134,plain,
$false,
inference(avatar_smt_refutation,[],[f129,f82,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT068_1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:08:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 0.19/1.20 % (2782350)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.19/1.20 % (2782406)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=797482686:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.19/1.20 % (2782406)Instruction limit reached!
% 0.19/1.20 % (2782406)------------------------------
% 0.19/1.20 % (2782406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782406)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782406)Termination reason: Instruction limit
% 0.19/1.20 % (2782406)Termination phase: Saturation
% 0.19/1.20 % (2782406)Time elapsed: 0.002 s
% 0.19/1.20 % (2782406)Peak memory usage: 88 MB
% 0.19/1.20 % (2782406)Instructions burned: 4 (million)
% 0.19/1.20 % (2782407)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=179195431:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.19/1.20 % (2782403)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=364316767:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.19/1.20 % (2782405)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3017862018:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/1.20 % (2782404)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2146471189:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.19/1.20 % (2782402)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3300913993:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/1.20 % (2782405)Instruction limit reached!
% 0.19/1.20 % (2782405)------------------------------
% 0.19/1.20 % (2782405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782405)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782405)Termination reason: Instruction limit
% 0.19/1.20 % (2782405)Termination phase: Saturation
% 0.19/1.20 % (2782405)Time elapsed: 0.006 s
% 0.19/1.20 % (2782405)Peak memory usage: 88 MB
% 0.19/1.20 % (2782405)Instructions burned: 8 (million)
% 0.19/1.20 % (2782408)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=137902443:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.19/1.20 % (2782402)Instruction limit reached!
% 0.19/1.20 % (2782402)------------------------------
% 0.19/1.20 % (2782402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782402)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782402)Termination reason: Instruction limit
% 0.19/1.20 % (2782402)Termination phase: Saturation
% 0.19/1.20 % (2782402)Time elapsed: 0.031 s
% 0.19/1.20 % (2782402)Peak memory usage: 115 MB
% 0.19/1.20 % (2782402)Instructions burned: 12 (million)
% 0.19/1.20 % (2782407)First to succeed.
% 0.19/1.20 % (2782407)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2782350"
% 0.19/1.20 % (2782403)Also succeeded, but the first one will report.
% 0.19/1.20 % (2782404)Also succeeded, but the first one will report.
% 0.19/1.20 % (2782408)Instruction limit reached!
% 0.19/1.20 % (2782408)------------------------------
% 0.19/1.20 % (2782408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782408)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782408)Termination reason: Instruction limit
% 0.19/1.20 % (2782408)Termination phase: Saturation
% 0.19/1.20 % (2782408)Time elapsed: 0.047 s
% 0.19/1.20 % (2782408)Peak memory usage: 116 MB
% 0.19/1.20 % (2782408)Instructions burned: 33 (million)
% 0.19/1.20 % (2782410)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3316438603:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.19/1.20 % (2782410)Instruction limit reached!
% 0.19/1.20 % (2782410)------------------------------
% 0.19/1.20 % (2782410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782410)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782410)Termination reason: Instruction limit
% 0.19/1.20 % (2782410)Termination phase: Saturation
% 0.19/1.20 % (2782410)Time elapsed: 0.006 s
% 0.19/1.20 % (2782410)Peak memory usage: 88 MB
% 0.19/1.20 % (2782410)Instructions burned: 16 (million)
% 0.19/1.20 % (2782417)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=880268058:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.19/1.20 % (2782417)Instruction limit reached!
% 0.19/1.20 % (2782417)------------------------------
% 0.19/1.20 % (2782417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782417)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782417)Termination reason: Instruction limit
% 0.19/1.20 % (2782417)Termination phase: Saturation
% 0.19/1.20 % (2782417)Time elapsed: 0.021 s
% 0.19/1.20 % (2782417)Peak memory usage: 89 MB
% 0.19/1.20 % (2782417)Instructions burned: 29 (million)
% 0.19/1.20 % (2782418)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2095125736:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 0.19/1.20 % (2782418)Instruction limit reached!
% 0.19/1.20 % (2782418)------------------------------
% 0.19/1.20 % (2782418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782418)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782418)Termination reason: Instruction limit
% 0.19/1.20 % (2782418)Termination phase: Saturation
% 0.19/1.20 % (2782418)Time elapsed: 0.011 s
% 0.19/1.20 % (2782418)Peak memory usage: 90 MB
% 0.19/1.20 % (2782418)Instructions burned: 17 (million)
% 0.19/1.20 % (2782419)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1525143385:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 0.19/1.20 % (2782421)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=3250407116:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 0.19/1.20 % (2782419)Also succeeded, but the first one will report.
% 0.19/1.20 % (2782421)Instruction limit reached!
% 0.19/1.20 % (2782421)------------------------------
% 0.19/1.20 % (2782421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782421)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782421)Termination reason: Instruction limit
% 0.19/1.20 % (2782421)Termination phase: Saturation
% 0.19/1.20 % (2782421)Time elapsed: 0.009 s
% 0.19/1.20 % (2782421)Peak memory usage: 89 MB
% 0.19/1.20 % (2782421)Instructions burned: 28 (million)
% 0.19/1.20 % (2782407)Refutation found. Thanks to Tanya!
% 0.19/1.20 % SZS status Theorem for theBenchmark
% 0.19/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.20 % (2782407)------------------------------
% 0.19/1.20 % (2782407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2782407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2782407)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2782407)Termination reason: Refutation
% 0.19/1.20 % (2782407)Time elapsed: 0.035 s
% 0.19/1.20 % (2782407)Peak memory usage: 116 MB
% 0.19/1.20 % (2782407)Instructions burned: 13 (million)
% 0.19/1.20 % (2782407)------------------------------
% 0.19/1.20 % (2782407)------------------------------
% 0.19/1.20 % (2782350)Success in time 0.432 s
% 0.19/1.20 % Vampire exiting
%------------------------------------------------------------------------------