%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW551_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:30:47 PM UTC 2026
% Result : Theorem 4.98s 1.77s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 6 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-5 aty)
% Number of functors : 48 ( 48 usr; 13 con; 0-6 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
exp: $tType > $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
option: $tType > $tType ).
tff(type_def_10,type,
char: $tType ).
tff(type_def_11,type,
ty: $tType ).
tff(type_def_12,type,
val: $tType ).
tff(type_def_13,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_14,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
start_heap:
!>[X0: $tType] : ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) > fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) ).
tff(func_def_5,type,
new:
!>[X0: $tType] : ( list(char) > exp(X0) ) ).
tff(func_def_6,type,
fun_upd:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * X1 ) > fun(X0,X1) ) ).
tff(func_def_7,type,
map_comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,option(X1)) * fun(X2,option(X0)) * X2 ) > option(X1) ) ).
tff(func_def_8,type,
ran:
!>[X0: $tType,X1: $tType] : ( fun(X0,option(X1)) > fun(X1,bool) ) ).
tff(func_def_9,type,
init_fields: list(product_prod(product_prod(list(char),list(char)),ty)) > fun(product_prod(list(char),list(char)),option(val)) ).
tff(func_def_10,type,
new_Addr: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) > option(nat) ).
tff(func_def_11,type,
bind:
!>[X0: $tType,X1: $tType] : fun(option(X0),fun(fun(X0,option(X1)),option(X1))) ).
tff(func_def_12,type,
map:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > fun(option(X0),option(X1)) ) ).
tff(func_def_13,type,
none:
!>[X0: $tType] : option(X0) ).
tff(func_def_14,type,
some:
!>[X0: $tType] : fun(X0,option(X0)) ).
tff(func_def_15,type,
option_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,X0) ) > fun(option(X1),X0) ) ).
tff(func_def_16,type,
option_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,X0) * option(X1) ) > X0 ) ).
tff(func_def_17,type,
set:
!>[X0: $tType] : ( option(X0) > fun(X0,bool) ) ).
tff(func_def_18,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_19,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_20,type,
quickcheck_orelse:
!>[X0: $tType] : ( ( option(X0) * option(X0) ) > option(X0) ) ).
tff(func_def_21,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_22,type,
insert:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > fun(X0,bool) ) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fNot: fun(bool,bool) ).
tff(func_def_26,type,
fTrue: bool ).
tff(func_def_27,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_28,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_29,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_31,type,
c: list(char) ).
tff(func_def_32,type,
e: fun(list(char),option(ty)) ).
tff(func_def_33,type,
fDTs: list(product_prod(product_prod(list(char),list(char)),ty)) ).
tff(func_def_34,type,
p: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) ).
tff(func_def_35,type,
t: ty ).
tff(func_def_36,type,
a: nat ).
tff(func_def_37,type,
h_a: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).
tff(func_def_38,type,
ha: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).
tff(func_def_39,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_40,type,
sK1:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(func_def_41,type,
sK2:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(func_def_42,type,
sK3:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(pred_def_1,type,
hconf:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > $o ) ).
tff(pred_def_2,type,
oconf:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))) ) > $o ) ).
tff(pred_def_3,type,
preallocated: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) > $o ).
tff(pred_def_4,type,
hext: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > $o ).
tff(pred_def_5,type,
is_none:
!>[X0: $tType] : ( option(X0) > $o ) ).
tff(pred_def_6,type,
fields:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * list(char) * list(product_prod(product_prod(list(char),list(char)),ty)) ) > $o ) ).
tff(pred_def_7,type,
wTrt: ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(list(char),option(ty)) * exp(list(char)) * ty ) > $o ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(f1,axiom,
new_Addr(ha) = aa(nat,option(nat),some(nat),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_RedNew_I1_J) ).
tff(f117,conjecture,
new_Addr(ha) = aa(nat,option(nat),some(nat),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f118,negated_conjecture,
( ( ~ new_Addr(ha) ) = aa(nat,option(nat),some(nat),a) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
tff(f119,plain,
new_Addr(ha) != aa(nat,option(nat),some(nat),a),
inference(flattening,[],[f118]) ).
tff(f132,plain,
new_Addr(ha) != aa(nat,option(nat),some(nat),a),
inference(cnf_transformation,[],[f119]) ).
tff(f134,plain,
new_Addr(ha) = aa(nat,option(nat),some(nat),a),
inference(cnf_transformation,[],[f1]) ).
tff(f148,plain,
$false,
inference(forward_subsumption_resolution,[],[f134,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW551_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 14:21:47 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 4.98/1.77 % (2656606)Detected formulas, will run a generic FOF schedule.
% 4.98/1.77 % (2656648)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1251448697:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.98/1.77 % (2656647)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1585054173:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.98/1.77 % (2656647)First to succeed.
% 4.98/1.77 % (2656647)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2656606"
% 4.98/1.77 % (2656648)Also succeeded, but the first one will report.
% 4.98/1.77 % (2656642)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3242478489:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.98/1.77 % (2656645)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=193094540:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.98/1.77 % (2656643)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3350958836:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.98/1.77 % (2656646)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3825969774:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.98/1.77 % (2656646)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.98/1.77 % (2656646)Also succeeded, but the first one will report.
% 4.98/1.77 % (2656645)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.98/1.77 % (2656649)dis-21_1_sil=8000:lcm=predicate:random_seed=400499886:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.98/1.77 % (2656649)Also succeeded, but the first one will report.
% 4.98/1.77 % (2656647)Refutation found. Thanks to Tanya!
% 4.98/1.77 % SZS status Theorem for theBenchmark
% 4.98/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 4.98/1.77 % (2656647)------------------------------
% 4.98/1.77 % (2656647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.77 % (2656647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.77 % (2656647)CaDiCaL version: 2.1.3
% 4.98/1.77 % (2656647)Termination reason: Refutation
% 4.98/1.77 % (2656647)Time elapsed: 0.003 s
% 4.98/1.77 % (2656647)Peak memory usage: 88 MB
% 4.98/1.77 % (2656647)Instructions burned: 3 (million)
% 4.98/1.77 % (2656647)------------------------------
% 4.98/1.77 % (2656647)------------------------------
% 4.98/1.77 % (2656606)Success in time 0.591 s
% 4.98/1.77 % Vampire exiting
%------------------------------------------------------------------------------