%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM080_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 : n003.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 09:39:31 AM UTC 2026
% Result : Theorem 4.58s 1.44s
% Output : Refutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 5 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-5 aty)
% Number of functors : 47 ( 47 usr; 12 con; 0-5 aty)
% Number of variables : 19 ( 18 !; 1 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
fm: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
atom: $tType ).
tff(type_def_11,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_12,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_1,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_4,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_5,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_8,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_9,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_10,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_11,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_13,type,
list_conj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_14,type,
list_disj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_15,type,
map_fm:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fm(X0) ) > fm(X1) ) ).
tff(func_def_16,type,
neg:
!>[X0: $tType] : ( fm(X0) > fm(X0) ) ).
tff(func_def_17,type,
suc: nat > nat ).
tff(func_def_18,type,
i_Z: fun(atom,fun(list(int),bool)) ).
tff(func_def_19,type,
asubst: ( int * list(int) ) > fun(atom,atom) ).
tff(func_def_20,type,
divisor: atom > int ).
tff(func_def_21,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_22,type,
qEpres896714165pres_1: list(atom) > fm(atom) ).
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,
fTrue: bool ).
tff(func_def_26,type,
as: list(atom) ).
tff(func_def_27,type,
il: int ).
tff(func_def_28,type,
ksl: list(int) ).
tff(func_def_29,type,
m: int ).
tff(func_def_30,type,
xs: list(int) ).
tff(func_def_31,type,
sK0: atom ).
tff(func_def_32,type,
sK1:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_33,type,
sK2:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_34,type,
sK3:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_35,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_36,type,
sK5: int ).
tff(func_def_37,type,
sK6: list(int) ).
tff(func_def_38,type,
sK7: int ).
tff(func_def_39,type,
sK8:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_40,type,
sK9:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_41,type,
sK10:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_42,type,
sK11:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(pred_def_1,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_13,type,
interpret:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(list(X1),bool)) * fm(X0) * list(X1) ) > $o ) ).
tff(pred_def_14,type,
qfree:
!>[X0: $tType] : ( fm(X0) > $o ) ).
tff(pred_def_15,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f1,axiom,
! [X4: atom] :
( member(atom,X4,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X4)),xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096) ).
tff(f5,axiom,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_IZ__asubst) ).
tff(f123,conjecture,
! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f124,negated_conjecture,
~ ! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
inference(negated_conjecture,[status(cth)],[f123]) ).
tff(f126,plain,
! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs)) ),
inference(rectify,[],[f1]) ).
tff(f127,plain,
? [X0: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f124]) ).
tff(f133,plain,
! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f126]) ).
tff(f136,plain,
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,sK0,set(atom,as)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f127]) ).
tff(f148,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) )
& ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f149,plain,
member(atom,sK0,set(atom,as)),
inference(cnf_transformation,[],[f136]) ).
tff(f150,plain,
~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))),
inference(cnf_transformation,[],[f136]) ).
tff(f163,plain,
! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ),
inference(cnf_transformation,[],[f133]) ).
tff(f170,plain,
! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f148]) ).
tff(f270,plain,
~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs)),
inference(resolution,[],[f170,f150]) ).
tff(f272,plain,
~ member(atom,sK0,set(atom,as)),
inference(resolution,[],[f270,f163]) ).
tff(f274,plain,
$false,
inference(forward_subsumption_resolution,[],[f272,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM080_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n003.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 21:54:42 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running first-order theorem proving
% 0.24/0.29 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
% 4.58/1.44 % (2071488)Detected formulas, will run a generic FOF schedule.
% 4.58/1.44 % (2071499)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=350382767:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.58/1.44 % (2071499)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.58/1.44 % (2071498)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=3922259612:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.58/1.44 % (2071500)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2481617038:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.58/1.44 % (2071500)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.58/1.44 % (2071500)Refutation not found, incomplete strategy
% 4.58/1.44 % (2071500)------------------------------
% 4.58/1.44 % (2071500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.44 % (2071500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.44 % (2071500)CaDiCaL version: 2.1.3
% 4.58/1.44 % (2071500)Termination reason: Refutation not found, incomplete strategy
% 4.58/1.44 % (2071500)Time elapsed: 0.004 s
% 4.58/1.44 % (2071500)Peak memory usage: 88 MB
% 4.58/1.44 % (2071500)Instructions burned: 2 (million)
% 4.58/1.44 % (2071503)dis-21_1_sil=8000:lcm=predicate:random_seed=50157071: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)
% 4.58/1.44 % (2071502)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2191122163:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.58/1.44 % (2071501)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4048065991:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.58/1.44 % (2071497)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=1121293495:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.58/1.44 % (2071501)First to succeed.
% 4.58/1.44 % (2071501)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2071488"
% 4.58/1.44 % (2071503)Instruction limit reached!
% 4.58/1.44 % (2071503)------------------------------
% 4.58/1.44 % (2071503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.44 % (2071503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.44 % (2071503)CaDiCaL version: 2.1.3
% 4.58/1.44 % (2071503)Termination reason: Instruction limit
% 4.58/1.44 % (2071503)Termination phase: Saturation
% 4.58/1.44 % (2071503)Time elapsed: 0.119 s
% 4.58/1.44 % (2071503)Peak memory usage: 89 MB
% 4.58/1.44 % (2071503)Instructions burned: 129 (million)
% 4.58/1.44 % (2071502)Instruction limit reached!
% 4.58/1.44 % (2071502)------------------------------
% 4.58/1.44 % (2071502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.44 % (2071502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.44 % (2071502)CaDiCaL version: 2.1.3
% 4.58/1.44 % (2071502)Termination reason: Instruction limit
% 4.58/1.44 % (2071502)Termination phase: Saturation
% 4.58/1.44 % (2071502)Time elapsed: 0.145 s
% 4.58/1.44 % (2071502)Peak memory usage: 89 MB
% 4.58/1.44 % (2071502)Instructions burned: 139 (million)
% 4.58/1.44 % Exception at run slice level
% 4.58/1.44 User error: GNN currently only supports monomorphic FOL.
% 4.58/1.44 % (2071500)------------------------------
% 4.58/1.44 % (2071500)------------------------------
% 4.58/1.44 % (2071514)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1562402925:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 4.58/1.44 % (2071513)lrs+10_1_sil=8000:sp=occurrence:random_seed=753786608:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 4.58/1.44 % (2071514)Also succeeded, but the first one will report.
% 4.58/1.44 % (2071501)Refutation found. Thanks to Tanya!
% 4.58/1.44 % SZS status Theorem for theBenchmark
% 4.58/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 5.69/1.64 % (2071501)------------------------------
% 5.69/1.64 % (2071501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.69/1.64 % (2071501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.69/1.64 % (2071501)CaDiCaL version: 2.1.3
% 5.69/1.64 % (2071501)Termination reason: Refutation
% 5.69/1.64 % (2071501)Time elapsed: 0.013 s
% 5.69/1.64 % (2071501)Peak memory usage: 88 MB
% 5.69/1.64 % (2071501)Instructions burned: 11 (million)
% 5.69/1.64 % (2071501)------------------------------
% 5.69/1.64 % (2071501)------------------------------
% 5.69/1.64 % (2071488)Success in time 0.707 s
% 5.69/1.64 % Vampire exiting
%------------------------------------------------------------------------------