%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL784_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 : n001.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 11:56:35 AM UTC 2026
% Result : Theorem 2.82s 1.37s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 75 ( 75 usr; 18 con; 0-5 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% 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,
fun: ( $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,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
it: fun(dB,bool) ).
tff(func_def_4,type,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_5,type,
abs: dB > dB ).
tff(func_def_6,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_7,type,
var: nat > dB ).
tff(func_def_8,type,
dB_size: dB > nat ).
tff(func_def_9,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_10,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_11,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_15,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_16,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_17,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_18,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_19,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_20,type,
atom: nat > type ).
tff(func_def_21,type,
fun1: ( type * type ) > type ).
tff(func_def_22,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_23,type,
type_size: type > nat ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fFalse: bool ).
tff(func_def_26,type,
fTrue: bool ).
tff(func_def_27,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_28,type,
t1: type ).
tff(func_def_29,type,
t_a: type ).
tff(func_def_30,type,
t: type ).
tff(func_def_31,type,
e: fun(nat,type) ).
tff(func_def_32,type,
ea: fun(nat,type) ).
tff(func_def_33,type,
i: nat ).
tff(func_def_34,type,
ia: nat ).
tff(func_def_35,type,
n: nat ).
tff(func_def_36,type,
rs: list(dB) ).
tff(func_def_37,type,
t2: dB ).
tff(func_def_38,type,
u: dB ).
tff(func_def_39,type,
ua: dB ).
tff(func_def_40,type,
sK2: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_41,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_42,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_43,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_44,type,
sK6: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_45,type,
sK7: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_46,type,
sK8: dB > dB ).
tff(func_def_47,type,
sK9: dB > dB ).
tff(func_def_48,type,
sK10: dB > list(dB) ).
tff(func_def_49,type,
sK11: dB > list(dB) ).
tff(func_def_50,type,
sK12: dB > nat ).
tff(func_def_51,type,
sK13: dB > dB ).
tff(func_def_52,type,
sK14: ( dB * fun(nat,type) ) > type ).
tff(func_def_53,type,
sK15: ( dB * fun(nat,type) ) > type ).
tff(func_def_54,type,
sK16: ( dB * dB ) > dB ).
tff(func_def_55,type,
sK17: ( dB * dB * dB ) > dB ).
tff(func_def_56,type,
sK18: ( dB * dB * dB ) > dB ).
tff(func_def_57,type,
sK19: ( dB * dB * dB ) > dB ).
tff(func_def_58,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_59,type,
sK21: ( dB * list(dB) * nat ) > list(dB) ).
tff(func_def_60,type,
sK22: ( dB * list(dB) * dB ) > dB ).
tff(func_def_61,type,
sK23: ( dB * list(dB) * dB ) > dB ).
tff(func_def_62,type,
sK24: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_63,type,
sK25: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_64,type,
sK26: ( dB * list(dB) * dB ) > dB ).
tff(func_def_65,type,
sK27:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_66,type,
sK28:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).
tff(func_def_67,type,
sK29:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_68,type,
sK30:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_69,type,
sK31:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_70,type,
sK32:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_71,type,
sK33:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > list(X0) ) ).
tff(func_def_72,type,
sK34:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > X0 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
step1:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_5,type,
typing: ( fun(nat,type) * dB * type ) > $o ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_7,type,
sP0: dB > $o ).
tff(pred_def_8,type,
sP1: ( dB * list(dB) * dB ) > $o ).
tff(f3,axiom,
rs = nil(dB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Nil) ).
tff(f4,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT) ).
tff(f5,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_True) ).
tff(f15,axiom,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__eq) ).
tff(f28,axiom,
! [X0: $tType,X1: $tType,X2: X1,X3: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X3,X2,nil(X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_foldl__Nil) ).
tff(f108,conjecture,
pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f109,negated_conjecture,
~ pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i))),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f112,plain,
~ pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i))),
inference(flattening,[],[f109]) ).
tff(f219,plain,
rs = nil(dB),
inference(cnf_transformation,[],[f3]) ).
tff(f220,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f4]) ).
tff(f221,plain,
n = i,
inference(cnf_transformation,[],[f5]) ).
tff(f239,plain,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
inference(cnf_transformation,[],[f15]) ).
tff(f252,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X3,X2,nil(X0)) = X2 ),
inference(cnf_transformation,[],[f28]) ).
tff(f386,plain,
~ pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i))),
inference(cnf_transformation,[],[f112]) ).
tff(f420,plain,
~ pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,n))),
inference(superposition,[],[f386,f221]) ).
tff(f425,plain,
! [X0: $tType,X2: X0,X1: fun(X0,fun(dB,X0))] : ( foldl(X0,dB,X1,X2,rs) = X2 ),
inference(superposition,[],[f252,f219]) ).
tff(f433,plain,
~ pp(aa(dB,bool,it,subst(var(n),u,n))),
inference(superposition,[],[f420,f425]) ).
tff(f438,plain,
~ pp(aa(dB,bool,it,u)),
inference(forward_demodulation,[],[f433,f239]) ).
tff(f440,plain,
$false,
inference(forward_subsumption_resolution,[],[f438,f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 16:55:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.82/1.37 % (3788335)Detected formulas, will run a generic FOF schedule.
% 2.82/1.37 % (3788345)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2653899128:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.82/1.37 % (3788345)First to succeed.
% 2.82/1.37 % (3788345)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3788335"
% 2.82/1.37 % (3788340)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=2138710339:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.82/1.37 % (3788344)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4180453629:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.82/1.37 % (3788346)dis-21_1_sil=8000:lcm=predicate:random_seed=3025509871: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)
% 2.82/1.37 % (3788342)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=683112040:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.82/1.37 % (3788343)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2752199520:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.82/1.37 % (3788341)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=2793131242:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.82/1.37 % (3788343)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.82/1.37 % (3788343)Refutation not found, incomplete strategy
% 2.82/1.37 % (3788343)------------------------------
% 2.82/1.37 % (3788343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.37 % (3788343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.37 % (3788343)CaDiCaL version: 2.1.3
% 2.82/1.37 % (3788343)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.37 % (3788343)Time elapsed: 0.003 s
% 2.82/1.37 % (3788343)Peak memory usage: 88 MB
% 2.82/1.37 % (3788343)Instructions burned: 3 (million)
% 2.82/1.37 % (3788344)Also succeeded, but the first one will report.
% 2.82/1.37 % (3788342)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.82/1.37 % (3788346)Instruction limit reached!
% 2.82/1.37 % (3788346)------------------------------
% 2.82/1.37 % (3788346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.37 % (3788346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.37 % (3788346)CaDiCaL version: 2.1.3
% 2.82/1.37 % (3788346)Termination reason: Instruction limit
% 2.82/1.37 % (3788346)Termination phase: Saturation
% 2.82/1.37 % (3788346)Time elapsed: 0.077 s
% 2.82/1.37 % (3788346)Peak memory usage: 89 MB
% 2.82/1.37 % (3788346)Instructions burned: 130 (million)
% 2.82/1.37 % (3788345)Refutation found. Thanks to Tanya!
% 2.82/1.37 % SZS status Theorem for theBenchmark
% 2.82/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.37 % (3788345)------------------------------
% 2.82/1.37 % (3788345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.37 % (3788345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.37 % (3788345)CaDiCaL version: 2.1.3
% 2.82/1.37 % (3788345)Termination reason: Refutation
% 2.82/1.37 % (3788345)Time elapsed: 0.007 s
% 2.82/1.37 % (3788345)Peak memory usage: 89 MB
% 2.82/1.37 % (3788345)Instructions burned: 17 (million)
% 2.82/1.37 % (3788345)------------------------------
% 2.82/1.37 % (3788345)------------------------------
% 2.82/1.37 % (3788335)Success in time 0.321 s
% 2.82/1.37 % Vampire exiting
%------------------------------------------------------------------------------