%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL813_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 : n019.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 11:56:42 AM UTC 2026
% Result : Theorem 2.83s 1.43s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 66 ( 66 usr; 26 con; 0-5 aty)
% Number of variables : 47 ( 47 !; 0 ?; 47 :)
% 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,
type: $tType ).
tff(type_def_10,type,
fun1: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,X1),fun1(fun1(X2,X0),fun1(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * X1 ) > fun1(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun1(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * fun1(X0,X1) ) > fun1(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun1(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun1(dB,fun1(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun1(dB,fun1(nat,dB)) ).
tff(func_def_11,type,
subst: fun1(dB,fun1(dB,fun1(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun1(X1,fun1(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_17,type,
shift:
!>[X0: $tType] : ( ( fun1(nat,X0) * nat * X0 ) > fun1(nat,X0) ) ).
tff(func_def_18,type,
fun: fun1(type,fun1(type,type)) ).
tff(func_def_19,type,
typing: fun1(nat,type) > fun1(dB,fun1(type,bool)) ).
tff(func_def_20,type,
typings: ( fun1(nat,type) * list(dB) ) > fun1(list(type),bool) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fEx:
!>[X0: $tType] : fun1(fun1(X0,bool),bool) ).
tff(func_def_23,type,
fFalse: bool ).
tff(func_def_24,type,
fTrue: bool ).
tff(func_def_25,type,
fconj: fun1(bool,fun1(bool,bool)) ).
tff(func_def_26,type,
t2: type ).
tff(func_def_27,type,
t: type ).
tff(func_def_28,type,
t_a: type ).
tff(func_def_29,type,
t1: type ).
tff(func_def_30,type,
ts: list(type) ).
tff(func_def_31,type,
a: dB ).
tff(func_def_32,type,
as: list(dB) ).
tff(func_def_33,type,
e: fun1(nat,type) ).
tff(func_def_34,type,
ea: fun1(nat,type) ).
tff(func_def_35,type,
i: nat ).
tff(func_def_36,type,
ia: nat ).
tff(func_def_37,type,
n: nat ).
tff(func_def_38,type,
rs: list(dB) ).
tff(func_def_39,type,
t3: dB ).
tff(func_def_40,type,
u: dB ).
tff(func_def_41,type,
ua: dB ).
tff(func_def_42,type,
sK1: ( dB * fun1(nat,type) ) > type ).
tff(func_def_43,type,
sK2: ( dB * fun1(nat,type) ) > type ).
tff(func_def_44,type,
sK3: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_45,type,
sK4: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_46,type,
sK5: ( type * dB * dB * fun1(nat,type) ) > type ).
tff(func_def_47,type,
sK6: type ).
tff(func_def_48,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( fun1(X1,X0) * fun1(X1,X0) ) > X1 ) ).
tff(func_def_49,type,
sK8: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_50,type,
sK9: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK10: ( type * type * list(dB) * fun1(nat,type) ) > list(type) ).
tff(func_def_52,type,
sK11: ( type * list(dB) * nat * fun1(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK12: list(type) ).
tff(func_def_54,type,
sK13: dB > dB ).
tff(func_def_55,type,
sK14: dB > dB ).
tff(func_def_56,type,
sK15: dB > list(dB) ).
tff(func_def_57,type,
sK16: dB > list(dB) ).
tff(func_def_58,type,
sK17: dB > nat ).
tff(func_def_59,type,
sK18: dB > dB ).
tff(func_def_60,type,
sK19: ( dB * dB * dB ) > dB ).
tff(func_def_61,type,
sK20: ( dB * dB * dB ) > dB ).
tff(func_def_62,type,
sK21: ( dB * dB * dB ) > dB ).
tff(func_def_63,type,
sK22: ( dB * dB ) > dB ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun1(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sP0: dB > $o ).
tff(f2,axiom,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_typing_OVar) ).
tff(f11,axiom,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( X4 = X3 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_shift__eq) ).
tff(f105,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f113,conjecture,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(flattening,[],[f114]) ).
tff(f124,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f125,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f201,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(cnf_transformation,[],[f115]) ).
tff(f212,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f124]) ).
tff(f213,plain,
! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f125]) ).
tff(f269,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f105]) ).
tff(f326,plain,
! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f212]) ).
tff(f327,plain,
! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f213]) ).
tff(f573,plain,
~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),foldr(type,type,fun,ts,t)),var(zero_zero(nat)))),
inference(superposition,[],[f201,f269]) ).
tff(f574,plain,
! [X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1)),var(X1))),
inference(superposition,[],[f326,f269]) ).
tff(f667,plain,
! [X2: nat,X0: type,X1: fun1(nat,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X1,X2,X0)),X0),var(X2))),
inference(superposition,[],[f574,f327]) ).
tff(f669,plain,
$false,
inference(resolution,[],[f667,f573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL813_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 16:54:33 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.48 Running first-order theorem proving
% 0.24/0.48 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
% 2.83/1.43 % (3262794)Detected formulas, will run a generic FOF schedule.
% 2.83/1.43 % (3262803)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2519095807:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.83/1.43 % (3262803)First to succeed.
% 2.83/1.43 % (3262803)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3262794"
% 2.83/1.43 % (3262802)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1657028884:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.83/1.43 % (3262800)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=1496166632:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.83/1.43 % (3262799)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=1495521811:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.83/1.43 % (3262801)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=2141904050:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.83/1.43 % (3262802)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.83/1.43 % (3262802)Refutation not found, incomplete strategy
% 2.83/1.43 % (3262802)------------------------------
% 2.83/1.43 % (3262802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.43 % (3262802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.43 % (3262802)CaDiCaL version: 2.1.3
% 2.83/1.43 % (3262802)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.43 % (3262802)Time elapsed: 0.004 s
% 2.83/1.43 % (3262802)Peak memory usage: 88 MB
% 2.83/1.43 % (3262802)Instructions burned: 4 (million)
% 2.83/1.43 % (3262801)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.83/1.43 % (3262804)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2318336999:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.83/1.43 % (3262805)dis-21_1_sil=8000:lcm=predicate:random_seed=3135336338: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)
% 2.83/1.43 % (3262805)Instruction limit reached!
% 2.83/1.43 % (3262805)------------------------------
% 2.83/1.43 % (3262805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.43 % (3262805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.43 % (3262805)CaDiCaL version: 2.1.3
% 2.83/1.43 % (3262805)Termination reason: Instruction limit
% 2.83/1.43 % (3262805)Termination phase: Saturation
% 2.83/1.43 % (3262805)Time elapsed: 0.074 s
% 2.83/1.43 % (3262805)Peak memory usage: 89 MB
% 2.83/1.43 % (3262805)Instructions burned: 130 (million)
% 2.83/1.43 % (3262804)Also succeeded, but the first one will report.
% 2.83/1.43 % (3262803)Refutation found. Thanks to Tanya!
% 2.83/1.43 % SZS status Theorem for theBenchmark
% 2.83/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.43 % (3262803)------------------------------
% 2.83/1.43 % (3262803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.43 % (3262803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.43 % (3262803)CaDiCaL version: 2.1.3
% 2.83/1.43 % (3262803)Termination reason: Refutation
% 2.83/1.43 % (3262803)Time elapsed: 0.012 s
% 2.83/1.43 % (3262803)Peak memory usage: 88 MB
% 2.83/1.43 % (3262803)Instructions burned: 32 (million)
% 2.83/1.43 % (3262803)------------------------------
% 2.83/1.43 % (3262803)------------------------------
% 2.83/1.43 % (3262794)Success in time 0.308 s
% 2.83/1.43 % Vampire exiting
%------------------------------------------------------------------------------