%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT062_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 : n009.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 2.56s 0.93s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 81 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 29 ~; 27 |; 10 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 36 ( 16 atm; 4 fun; 4 num; 12 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 : 9 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 37 !; 3 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
heap: $tType ).
tff(func_def_0,type,
empty: heap ).
tff(func_def_1,type,
get: heap > heap ).
tff(func_def_2,type,
app: ( heap * $int ) > heap ).
tff(func_def_3,type,
toop: heap > $int ).
tff(func_def_4,type,
length: heap > $int ).
tff(func_def_8,type,
sK0: $int ).
tff(func_def_9,type,
sK1: heap ).
tff(func_def_10,type,
sK2: heap ).
tff(pred_def_1,type,
lsls: ( heap * heap ) > $o ).
tff(f7,axiom,
! [X0: $int,X1: heap] : ( length(app(X1,X0)) = $sum(1,length(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_23) ).
tff(f11,axiom,
! [X1: heap,X2: heap,X0: $int] :
( lsls(X1,app(X2,X0))
<=> ( lsls(X1,X2)
| ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_27) ).
tff(f12,conjecture,
! [X1: $int,X0: heap] :
( ~ ! [X2: heap] :
( lsls(X2,X0)
=> $less(length(X2),length(X0)) )
| ! [X2: heap] :
( lsls(X2,app(X0,X1))
=> $less(length(X2),length(app(X0,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_lem_1a) ).
tff(f13,negated_conjecture,
~ ! [X1: $int,X0: heap] :
( ~ ! [X2: heap] :
( lsls(X2,X0)
=> $less(length(X2),length(X0)) )
| ! [X2: heap] :
( lsls(X2,app(X0,X1))
=> $less(length(X2),length(app(X0,X1))) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
tff(f14,plain,
~ ! [X0: $int,X1: heap] :
( ~ ! [X2: heap] :
( lsls(X2,X1)
=> $less(length(X2),length(X1)) )
| ! [X3: heap] :
( lsls(X3,app(X1,X0))
=> $less(length(X3),length(app(X1,X0))) ) ),
inference(rectify,[],[f13]) ).
tff(f19,plain,
! [X2: $int,X1: heap,X0: heap] :
( lsls(X0,app(X1,X2))
<=> ( lsls(X0,X1)
| ( X0 = X1 ) ) ),
inference(rectify,[],[f11]) ).
tff(f22,plain,
? [X0: $int,X1: heap] :
( ! [X2: heap] :
( ~ lsls(X2,X1)
| $less(length(X2),length(X1)) )
& ? [X3: heap] :
( ~ $less(length(X3),length(app(X1,X0)))
& lsls(X3,app(X1,X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
tff(f27,plain,
( ! [X2: heap] :
( ~ lsls(X2,sK1)
| $less(length(X2),length(sK1)) )
& ~ $less(length(sK2),length(app(sK1,sK0)))
& lsls(sK2,app(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f22]) ).
tff(f28,plain,
! [X2: $int,X1: heap,X0: heap] :
( ( lsls(X0,app(X1,X2))
| ( ~ lsls(X0,X1)
& ( X0 != X1 ) ) )
& ( lsls(X0,X1)
| ( X0 = X1 )
| ~ lsls(X0,app(X1,X2)) ) ),
inference(nnf_transformation,[],[f19]) ).
tff(f29,plain,
! [X2: $int,X1: heap,X0: heap] :
( ( lsls(X0,app(X1,X2))
| ( ~ lsls(X0,X1)
& ( X0 != X1 ) ) )
& ( lsls(X0,X1)
| ( X0 = X1 )
| ~ lsls(X0,app(X1,X2)) ) ),
inference(flattening,[],[f28]) ).
tff(f30,plain,
! [X0: $int,X1: heap,X2: heap] :
( ( lsls(X2,app(X1,X0))
| ( ~ lsls(X2,X1)
& ( X1 != X2 ) ) )
& ( lsls(X2,X1)
| ( X1 = X2 )
| ~ lsls(X2,app(X1,X0)) ) ),
inference(rectify,[],[f29]) ).
tff(f34,plain,
! [X0: $int,X1: heap] : ( length(app(X1,X0)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f7]) ).
tff(f43,plain,
lsls(sK2,app(sK1,sK0)),
inference(cnf_transformation,[],[f27]) ).
tff(f44,plain,
~ $less(length(sK2),length(app(sK1,sK0))),
inference(cnf_transformation,[],[f27]) ).
tff(f45,plain,
! [X2: heap] :
( ~ lsls(X2,sK1)
| $less(length(X2),length(sK1)) ),
inference(cnf_transformation,[],[f27]) ).
tff(f46,plain,
! [X2: heap,X0: $int,X1: heap] :
( ~ lsls(X2,app(X1,X0))
| ( X1 = X2 )
| lsls(X2,X1) ),
inference(cnf_transformation,[],[f30]) ).
tff(f58,definition,
( spl3_2
<=> lsls(sK2,app(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f60,plain,
( lsls(sK2,app(sK1,sK0))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f58]) ).
tff(f61,plain,
spl3_2,
inference(avatar_split_clause,[],[f43,f58]) ).
tff(f62,plain,
~ $less(length(sK2),$sum(1,length(sK1))),
inference(forward_demodulation,[],[f44,f34]) ).
tff(f64,definition,
( spl3_3
<=> $less(length(sK2),$sum(1,length(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f67,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f62,f64]) ).
tff(f94,plain,
( ( sK1 = sK2 )
| lsls(sK2,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f46,f60]) ).
tff(f101,definition,
( spl3_4
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f105,definition,
( spl3_5
<=> lsls(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f107,plain,
( lsls(sK2,sK1)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f105]) ).
tff(f108,plain,
( spl3_4
| spl3_5
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f94,f58,f105,f101]) ).
tff(f109,plain,
( $less(length(sK2),length(sK1))
| ~ spl3_5 ),
inference(resolution,[],[f107,f45]) ).
tff(f112,definition,
( spl3_6
<=> $less(length(sK2),length(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f115,plain,
( spl3_6
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f109,f105,f112]) ).
tff(f116,plain,
$false,
inference(avatar_smt_refutation,[],[f115,f108,f67,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT062_1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:07:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.56/0.93 % (3620876)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.56/0.93 % (3620952)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3319866818:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 2.56/0.93 % (3620952)First to succeed.
% 2.56/0.93 % (3620952)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3620876"
% 2.56/0.93 % (3620949)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=647213343:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 2.56/0.93 % (3620946)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1281164480:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 2.56/0.93 % (3620948)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=415968281:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 2.56/0.93 % (3620950)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1341155548:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 2.56/0.93 % (3620951)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3305253171:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 2.56/0.93 % (3620953)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2500507202:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 2.56/0.93 % (3620951)Instruction limit reached!
% 2.56/0.93 % (3620951)------------------------------
% 2.56/0.93 % (3620951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/0.93 % (3620951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.93 % (3620951)CaDiCaL version: 2.1.3
% 2.56/0.93 % (3620951)Termination reason: Instruction limit
% 2.56/0.93 % (3620951)Termination phase: Saturation
% 2.56/0.93 % (3620951)Time elapsed: 0.004 s
% 2.56/0.93 % (3620951)Peak memory usage: 88 MB
% 2.56/0.93 % (3620951)Instructions burned: 5 (million)
% 2.56/0.93 % (3620950)Instruction limit reached!
% 2.56/0.93 % (3620950)------------------------------
% 2.56/0.93 % (3620950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/0.93 % (3620950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.93 % (3620950)CaDiCaL version: 2.1.3
% 2.56/0.93 % (3620950)Termination reason: Instruction limit
% 2.56/0.93 % (3620950)Termination phase: Saturation
% 2.56/0.93 % (3620950)Time elapsed: 0.006 s
% 2.56/0.93 % (3620950)Peak memory usage: 88 MB
% 2.56/0.93 % (3620950)Instructions burned: 7 (million)
% 2.56/0.93 % (3620946)Instruction limit reached!
% 2.56/0.93 % (3620946)------------------------------
% 2.56/0.93 % (3620946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/0.93 % (3620946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.93 % (3620946)CaDiCaL version: 2.1.3
% 2.56/0.93 % (3620946)Termination reason: Instruction limit
% 2.56/0.93 % (3620946)Termination phase: Saturation
% 2.56/0.93 % (3620946)Time elapsed: 0.032 s
% 2.56/0.93 % (3620946)Peak memory usage: 115 MB
% 2.56/0.93 % (3620946)Instructions burned: 13 (million)
% 2.56/0.93 % (3620949)Also succeeded, but the first one will report.
% 2.56/0.93 % (3620953)Also succeeded, but the first one will report.
% 2.56/0.93 % (3620952)Refutation found. Thanks to Tanya!
% 2.56/0.93 % SZS status Theorem for theBenchmark
% 2.56/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/0.93 % (3620952)------------------------------
% 2.56/0.93 % (3620952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/0.93 % (3620952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.93 % (3620952)CaDiCaL version: 2.1.3
% 2.56/0.93 % (3620952)Termination reason: Refutation
% 2.56/0.93 % (3620952)Time elapsed: 0.022 s
% 2.56/0.93 % (3620952)Peak memory usage: 116 MB
% 2.56/0.93 % (3620952)Instructions burned: 13 (million)
% 2.56/0.93 % (3620952)------------------------------
% 2.56/0.93 % (3620952)------------------------------
% 2.56/0.93 % (3620876)Success in time 0.293 s
% 2.56/0.93 % Vampire exiting
%------------------------------------------------------------------------------