%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL838_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 : n014.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 11:56:49 AM UTC 2026
% Result : Theorem 3.17s 1.32s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 12 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 4 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 21 con; 0-5 aty)
% Number of variables : 25 ( 0 sgn 23 !; 2 ?; 25 :)
% 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(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,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(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: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_12,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_13,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_14,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_15,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_16,type,
suc: nat > nat ).
tff(func_def_17,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_18,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_23,type,
t1: type ).
tff(func_def_24,type,
t_a: type ).
tff(func_def_25,type,
t: type ).
tff(func_def_26,type,
a: dB ).
tff(func_def_27,type,
as: list(dB) ).
tff(func_def_28,type,
e: fun(nat,type) ).
tff(func_def_29,type,
ea: fun(nat,type) ).
tff(func_def_30,type,
i: nat ).
tff(func_def_31,type,
ia: nat ).
tff(func_def_32,type,
r: dB ).
tff(func_def_33,type,
t2: dB ).
tff(func_def_34,type,
u: dB ).
tff(func_def_35,type,
ua: dB ).
tff(func_def_36,type,
sK1: ( dB * fun(nat,type) ) > type ).
tff(func_def_37,type,
sK2: ( dB * fun(nat,type) ) > type ).
tff(func_def_38,type,
sK3: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_39,type,
sK4: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_40,type,
sK5: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_41,type,
sK6: ( dB * dB ) > dB ).
tff(func_def_42,type,
sK7: ( dB * dB * dB ) > dB ).
tff(func_def_43,type,
sK8: ( dB * dB * dB ) > dB ).
tff(func_def_44,type,
sK9: ( dB * dB * dB ) > dB ).
tff(func_def_45,type,
sK10: nat > nat ).
tff(func_def_46,type,
sK11: fun(nat,bool) > nat ).
tff(func_def_47,type,
sK12: fun(nat,bool) > nat ).
tff(func_def_48,type,
sK13: nat > nat ).
tff(func_def_49,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_50,type,
sK15: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK16: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_52,type,
sK17: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK18: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_54,type,
sK19: dB > dB ).
tff(func_def_55,type,
sK20: dB > dB ).
tff(func_def_56,type,
sK21: dB > list(dB) ).
tff(func_def_57,type,
sK22: dB > list(dB) ).
tff(func_def_58,type,
sK23: dB > nat ).
tff(func_def_59,type,
sK24: 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] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
typing: ( fun(nat,type) * dB * type ) > $o ).
tff(pred_def_5,type,
typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_8,type,
sP0: dB > $o ).
tff(pred_def_9,type,
sQ25_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f4,axiom,
typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_T) ).
tff(f75,axiom,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( typing(X3,foldl(dB,dB,app,X2,X1),X0)
=> ? [X4: list(type)] :
( typing(X3,X2,foldr(type,type,fun1,X4,X0))
& typings(X3,X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_list__app__typeD) ).
tff(f109,axiom,
! [X0: type] :
( typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f110,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f111,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f110]) ).
tff(f114,plain,
~ thesis,
inference(flattening,[],[f111]) ).
tff(f163,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typing(X3,X2,foldr(type,type,fun1,X4,X0))
& typings(X3,X1,X4) )
| ~ typing(X3,foldl(dB,dB,app,X2,X1),X0) ),
inference(ennf_transformation,[],[f75]) ).
tff(f175,plain,
! [X0: type] :
( thesis
| ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0) ),
inference(ennf_transformation,[],[f109]) ).
tff(f201,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( typing(X3,X2,foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))
& typings(X3,X1,sK15(X0,X1,X2,X3)) )
| ~ typing(X3,foldl(dB,dB,app,X2,X1),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X4,sK15(X0,X1,X2,X3))],[f163]) ).
tff(f218,plain,
typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t1),
inference(cnf_transformation,[],[f4]) ).
tff(f314,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( typing(X3,X2,foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))
| ~ typing(X3,foldl(dB,dB,app,X2,X1),X0) ),
inference(cnf_transformation,[],[f201]) ).
tff(f364,plain,
! [X0: type] :
( thesis
| ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0) ),
inference(cnf_transformation,[],[f175]) ).
tff(f365,plain,
~ thesis,
inference(cnf_transformation,[],[f114]) ).
tff(f467,definition,
( spl26_1
<=> ! [X0: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
tff(f468,plain,
( ! [X0: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f467]) ).
tff(f470,definition,
( spl26_2
<=> thesis ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
tff(f471,plain,
( thesis
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f470]) ).
tff(f472,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f364,f470,f467]) ).
tff(f473,plain,
( $false
| ~ spl26_2 ),
inference(resolution,[],[f471,f365]) ).
tff(f474,plain,
~ spl26_2,
inference(avatar_contradiction_clause,[],[f473]) ).
tff(f685,plain,
( ! [X0: list(dB),X1: type] : ~ typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),X1)
| ~ spl26_1 ),
inference(resolution,[],[f314,f468]) ).
tff(f1165,plain,
( $false
| ~ spl26_1 ),
inference(resolution,[],[f218,f685]) ).
tff(f1166,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f1165]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f472]) ).
cnf(s2,plain,
~ spl26_2,
inference(sat_conversion,[],[f474]) ).
cnf(s3,plain,
~ spl26_1,
inference(sat_conversion,[],[f1166]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f1167,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL838_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 16:58:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.17/1.32 % (1012879)Detected formulas, will run a generic FOF schedule.
% 3.17/1.32 % (1012886)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=3447377837:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.17/1.32 % (1012886)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.17/1.32 % (1012888)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2703758705:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.17/1.32 % (1012885)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=294026119:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.17/1.32 % (1012890)dis-21_1_sil=8000:lcm=predicate:random_seed=3780504185: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)
% 3.17/1.32 % (1012887)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2124748054:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.17/1.32 % (1012884)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=3317244819:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.17/1.32 % (1012889)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=139997212:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.17/1.32 % (1012887)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.17/1.32 % (1012887)Refutation not found, incomplete strategy
% 3.17/1.32 % (1012887)------------------------------
% 3.17/1.32 % (1012887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (1012887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (1012887)CaDiCaL version: 2.1.3
% 3.17/1.32 % (1012887)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.32 % (1012887)Time elapsed: 0.003 s
% 3.17/1.32 % (1012887)Peak memory usage: 88 MB
% 3.17/1.32 % (1012887)Instructions burned: 3 (million)
% 3.17/1.32 % (1012890)First to succeed.
% 3.17/1.32 % (1012890)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1012879"
% 3.17/1.32 % (1012888)Instruction limit reached!
% 3.17/1.32 % (1012888)------------------------------
% 3.17/1.32 % (1012888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (1012888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (1012888)CaDiCaL version: 2.1.3
% 3.17/1.32 % (1012888)Termination reason: Instruction limit
% 3.17/1.32 % (1012888)Termination phase: Saturation
% 3.17/1.32 % (1012888)Time elapsed: 0.075 s
% 3.17/1.32 % (1012888)Peak memory usage: 88 MB
% 3.17/1.32 % (1012888)Instructions burned: 120 (million)
% 3.17/1.32 % (1012889)Also succeeded, but the first one will report.
% 3.17/1.32 % Exception at run slice level
% 3.17/1.32 User error: GNN currently only supports monomorphic FOL.
% 3.17/1.32 % (1012898)lrs+10_1_sil=8000:sp=occurrence:random_seed=957053778:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.17/1.32 % (1012898)Also succeeded, but the first one will report.
% 3.17/1.32 % (1012887)------------------------------
% 3.17/1.32 % (1012887)------------------------------
% 3.17/1.32 % (1012899)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1756504581:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.17/1.32 % (1012899)Refutation not found, incomplete strategy
% 3.17/1.32 % (1012899)------------------------------
% 3.17/1.32 % (1012899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (1012899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (1012899)CaDiCaL version: 2.1.3
% 3.17/1.32 % (1012899)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.32 % (1012899)Time elapsed: 0.001 s
% 3.17/1.32 % (1012899)Peak memory usage: 87 MB
% 3.17/1.32 % (1012899)Instructions burned: 2 (million)
% 3.17/1.32 % (1012890)Refutation found. Thanks to Tanya!
% 3.17/1.32 % SZS status Theorem for theBenchmark
% 3.17/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.52 % (1012890)------------------------------
% 3.92/1.52 % (1012890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.52 % (1012890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.52 % (1012890)CaDiCaL version: 2.1.3
% 3.92/1.52 % (1012890)Termination reason: Refutation
% 3.92/1.52 % (1012890)Time elapsed: 0.061 s
% 3.92/1.52 % (1012890)Peak memory usage: 90 MB
% 3.92/1.52 % (1012890)Instructions burned: 119 (million)
% 3.92/1.52 % (1012890)------------------------------
% 3.92/1.52 % (1012890)------------------------------
% 3.92/1.52 % (1012879)Success in time 0.473 s
% 3.92/1.52 % Vampire exiting
%------------------------------------------------------------------------------