%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 11:56:41 AM UTC 2026
% Result : Theorem 2.24s 1.05s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 15 con; 0-5 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
char1: $tType ).
tff(type_def_10,type,
literal: $tType ).
tff(type_def_11,type,
nibble: $tType ).
tff(type_def_12,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(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,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
bool_size: bool > nat ).
tff(func_def_8,type,
it: fun(dB,bool) ).
tff(func_def_9,type,
abs: dB > dB ).
tff(func_def_10,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_11,type,
var: nat > dB ).
tff(func_def_12,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_13,type,
dB_size: dB > nat ).
tff(func_def_14,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_15,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_16,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_17,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_18,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_19,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_20,type,
monoid_add_listsum:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_21,type,
suc: nat > nat ).
tff(func_def_22,type,
nat_size: nat > nat ).
tff(func_def_23,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_24,type,
char: ( nibble * nibble ) > char1 ).
tff(func_def_25,type,
char_case:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char1 ) > X0 ) ).
tff(func_def_26,type,
char_rec:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char1 ) > X0 ) ).
tff(func_def_27,type,
char_size: char1 > nat ).
tff(func_def_28,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_29,type,
fFalse: bool ).
tff(func_def_30,type,
fTrue: bool ).
tff(func_def_31,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_32,type,
a: dB ).
tff(func_def_33,type,
b: dB ).
tff(func_def_34,type,
bs: list(dB) ).
tff(func_def_35,type,
i: nat ).
tff(func_def_36,type,
n: nat ).
tff(func_def_37,type,
t: dB ).
tff(func_def_38,type,
u: dB ).
tff(func_def_39,type,
ua: dB ).
tff(func_def_40,type,
sK1: char1 > nibble ).
tff(func_def_41,type,
sK2: char1 > nibble ).
tff(func_def_42,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_43,type,
sK4: dB > dB ).
tff(func_def_44,type,
sK5: dB > dB ).
tff(func_def_45,type,
sK6: dB > list(dB) ).
tff(func_def_46,type,
sK7: dB > list(dB) ).
tff(func_def_47,type,
sK8: dB > nat ).
tff(func_def_48,type,
sK9: dB > dB ).
tff(func_def_49,type,
sK10: nat > nat ).
tff(func_def_50,type,
sK11: fun(nat,bool) > nat ).
tff(func_def_51,type,
sK12: nat > nat ).
tff(func_def_52,type,
sK13: fun(nat,bool) > nat ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_7,type,
sP0: dB > $o ).
tff(pred_def_8,type,
sQ14_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f4,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096IT_A_Ib_091u_Pi_093_J_096) ).
tff(f5,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_True) ).
tff(f6,axiom,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_lift__IT) ).
tff(f116,conjecture,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f117,negated_conjecture,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(negated_conjecture,[status(cth)],[f116]) ).
tff(f119,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(flattening,[],[f117]) ).
tff(f121,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f181,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i))),
inference(cnf_transformation,[],[f4]) ).
tff(f182,plain,
i = n,
inference(cnf_transformation,[],[f5]) ).
tff(f183,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f121]) ).
tff(f325,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f119]) ).
tff(f326,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))),
inference(definition_unfolding,[],[f181,f182]) ).
tff(f333,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)),zero_zero(nat)))),
inference(definition_unfolding,[],[f325,f182]) ).
tff(f559,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))),
inference(resolution,[],[f183,f333]) ).
tff(f564,plain,
$false,
inference(resolution,[],[f326,f559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n004.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 16:53:37 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.24/1.05 % (3739536)Detected formulas, will run a generic FOF schedule.
% 2.24/1.05 % (3739547)dis-21_1_sil=8000:lcm=predicate:random_seed=2204123729: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)
% 2.24/1.05 % (3739547)First to succeed.
% 2.24/1.05 % (3739547)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3739536"
% 2.24/1.05 % (3739546)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4128315707:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.24/1.05 % (3739543)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=690595203:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.24/1.05 % (3739542)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=2425555214:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.24/1.05 % (3739541)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=2764815507:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.24/1.05 % (3739545)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3958549634:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.24/1.05 % (3739544)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2253273649:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.24/1.05 % (3739544)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.24/1.05 % (3739544)Also succeeded, but the first one will report.
% 2.24/1.05 % (3739545)Also succeeded, but the first one will report.
% 2.24/1.05 % (3739543)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.24/1.05 % (3739546)Also succeeded, but the first one will report.
% 2.24/1.05 % (3739547)Refutation found. Thanks to Tanya!
% 2.24/1.05 % SZS status Theorem for theBenchmark
% 2.24/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.24/1.05 % (3739547)------------------------------
% 2.24/1.05 % (3739547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.05 % (3739547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.05 % (3739547)CaDiCaL version: 2.1.3
% 2.24/1.05 % (3739547)Termination reason: Refutation
% 2.24/1.05 % (3739547)Time elapsed: 0.006 s
% 2.24/1.05 % (3739547)Peak memory usage: 89 MB
% 2.24/1.05 % (3739547)Instructions burned: 16 (million)
% 2.24/1.05 % (3739547)------------------------------
% 2.24/1.05 % (3739547)------------------------------
% 2.24/1.05 % (3739536)Success in time 0.261 s
% 2.24/1.05 % Vampire exiting
%------------------------------------------------------------------------------