%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL800_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:00:39 PM UTC 2026
% Result : Theorem 0.17s 0.53s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 10 con; 0-5 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
app: ( dB * dB ) > dB ).
tff(func_def_3,type,
var: nat > dB ).
tff(func_def_4,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_5,type,
dB_rec:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,fun(X0,fun(X0,X0)))) * fun(dB,fun(X0,X0)) * dB ) > X0 ) ).
tff(func_def_6,type,
dB_size: dB > nat ).
tff(func_def_7,type,
lift: ( dB * nat ) > dB ).
tff(func_def_8,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_9,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_10,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_11,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_15,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_17,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_18,type,
suc: nat > nat ).
tff(func_def_19,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
a: dB ).
tff(func_def_24,type,
as: list(dB) ).
tff(func_def_25,type,
i: nat ).
tff(func_def_26,type,
n: nat ).
tff(func_def_27,type,
rs: list(dB) ).
tff(func_def_28,type,
t: dB ).
tff(func_def_29,type,
u: dB ).
tff(func_def_30,type,
ua: dB ).
tff(func_def_31,type,
sK0:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_32,type,
sK1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_33,type,
sK2:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_34,type,
sK3:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_35,type,
sK4: nat > nat ).
tff(func_def_36,type,
sK5: fun(nat,bool) > nat ).
tff(func_def_37,type,
sK6: fun(nat,bool) > nat ).
tff(func_def_38,type,
sK7: nat > nat ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
equal_equal:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_8,type,
it: dB > $o ).
tff(pred_def_9,type,
listMem:
!>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).
tff(pred_def_10,type,
member1:
!>[X0: $tType] : ( ( list(X0) * X0 ) > $o ) ).
tff(pred_def_11,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_12,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f5,axiom,
it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,i),zero_zero(nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f7,axiom,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( subst(app(X3,X2),X1,X0) = app(subst(X3,X1,X0),subst(X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subst__App) ).
tff(f14,axiom,
! [X0: dB,X1: nat,X2: dB] : ( subst(lift(X2,X1),X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__lift) ).
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(f106,conjecture,
it(app(u,subst(a,u,i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f107,negated_conjecture,
~ it(app(u,subst(a,u,i))),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f108,plain,
~ it(app(u,subst(a,u,i))),
inference(flattening,[],[f107]) ).
tff(f168,plain,
it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,i),zero_zero(nat))),
inference(cnf_transformation,[],[f5]) ).
tff(f170,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( subst(app(X3,X2),X1,X0) = app(subst(X3,X1,X0),subst(X2,X1,X0)) ),
inference(cnf_transformation,[],[f7]) ).
tff(f179,plain,
! [X2: dB,X0: dB,X1: nat] : ( subst(lift(X2,X1),X0,X1) = X2 ),
inference(cnf_transformation,[],[f14]) ).
tff(f180,plain,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
inference(cnf_transformation,[],[f15]) ).
tff(f302,plain,
~ it(app(u,subst(a,u,i))),
inference(cnf_transformation,[],[f108]) ).
tff(f812,plain,
! [X2: dB,X3: dB,X0: dB,X1: nat] : ( subst(app(lift(X0,X1),X2),X3,X1) = app(X0,subst(X2,X3,X1)) ),
inference(superposition,[],[f170,f179]) ).
tff(f830,plain,
it(app(u,subst(var(zero_zero(nat)),subst(a,u,i),zero_zero(nat)))),
inference(backward_demodulation,[],[f168,f812]) ).
tff(f831,plain,
it(app(u,subst(a,u,i))),
inference(forward_demodulation,[],[f830,f180]) ).
tff(f835,plain,
$false,
inference(forward_subsumption_resolution,[],[f831,f302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL800_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 16:54:27 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.53 % (776974)Will run a generic schedule for satisfiability detection.
% 0.17/0.53 % (776982)dis+10_1_sil=32000:sp=arity:random_seed=1665726541:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.53 % (776980)% WARNING: option uhcvi not known.
% 0.17/0.53 % (776979)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=550552782_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.53 % (776980)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3326698080:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.53 % (776984)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4186360113:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.53 % (776981)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2403168299:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.53 % (776983)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2150216812:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.53 % (776985)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3307066606:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.53 % Exception at run slice level
% 0.17/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.53 % (776993)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2535705827:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.53 % (776982)Instruction limit reached!
% 0.17/0.53 % (776982)------------------------------
% 0.17/0.53 % (776982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.53 % (776982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.53 % (776982)CaDiCaL version: 2.1.3
% 0.17/0.53 % (776982)Termination reason: Instruction limit
% 0.17/0.53 % (776982)Termination phase: Saturation
% 0.17/0.53 % (776982)Time elapsed: 0.033 s
% 0.17/0.53 % Exception at run slice level% (776982)Peak memory usage: 12 MB
% 0.17/0.53
% 0.17/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.53 % (776982)Instructions burned: 105 (million)
% 0.17/0.53 % (776995)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2270138686:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.53 % (776996)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1275894732:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.17/0.53 % (776996) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-776974-776996"...
% 0.17/0.53 % (776995) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-776974-776995"...
% 0.17/0.53 % (776995)...printing done.
% 0.17/0.53 % (776996)...printing done.
% 0.17/0.53 % (776995)Refutation found. Thanks to Tanya!
% 0.17/0.53 % SZS status Theorem for theBenchmark
% 0.17/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.53 % (776995)------------------------------
% 0.17/0.53 % (776995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.53 % (776995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.53 % (776995)CaDiCaL version: 2.1.3
% 0.17/0.53 % (776995)Termination reason: Refutation
% 0.17/0.53 % (776995)Time elapsed: 0.018 s
% 0.17/0.53 % (776995)Peak memory usage: 12 MB
% 0.17/0.53 % (776995)Instructions burned: 50 (million)
% 0.17/0.53 % (776974)Success in time 0.097 s
% 0.17/0.53 % Vampire exiting
%------------------------------------------------------------------------------