%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL778_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:00:34 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 70 ( 70 usr; 9 con; 0-5 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% 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,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
it: fun(dB,bool) ).
tff(func_def_2,type,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_3,type,
abs: dB > dB ).
tff(func_def_4,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_5,type,
var: nat > dB ).
tff(func_def_6,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_7,type,
dB_size: dB > nat ).
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,
append:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
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_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_18,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_19,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_20,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fFalse: bool ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
i: nat ).
tff(func_def_25,type,
r: dB ).
tff(func_def_26,type,
s: dB ).
tff(func_def_27,type,
ss: list(dB) ).
tff(func_def_28,type,
sK2: dB > dB ).
tff(func_def_29,type,
sK3: dB > dB ).
tff(func_def_30,type,
sK4: dB > list(dB) ).
tff(func_def_31,type,
sK5: dB > list(dB) ).
tff(func_def_32,type,
sK6: dB > nat ).
tff(func_def_33,type,
sK7: dB > dB ).
tff(func_def_34,type,
sK8: dB > dB ).
tff(func_def_35,type,
sK9: dB > dB ).
tff(func_def_36,type,
sK10: dB > dB ).
tff(func_def_37,type,
sK11: dB > nat ).
tff(func_def_38,type,
sK12: dB > list(dB) ).
tff(func_def_39,type,
sK13: dB > dB ).
tff(func_def_40,type,
sK14: dB > nat ).
tff(func_def_41,type,
sK15: dB > dB ).
tff(func_def_42,type,
sK16: ( dB * dB ) > dB ).
tff(func_def_43,type,
sK17: ( dB * dB * dB ) > dB ).
tff(func_def_44,type,
sK18: ( dB * dB * dB ) > dB ).
tff(func_def_45,type,
sK19: ( dB * dB * dB ) > dB ).
tff(func_def_46,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_47,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_48,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_49,type,
sK23: ( dB * list(dB) * nat ) > list(dB) ).
tff(func_def_50,type,
sK24: ( dB * list(dB) * dB ) > dB ).
tff(func_def_51,type,
sK25: ( dB * list(dB) * dB ) > dB ).
tff(func_def_52,type,
sK26: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_53,type,
sK27: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_54,type,
sK28: ( dB * list(dB) * dB ) > dB ).
tff(func_def_55,type,
sK29:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_56,type,
sK30:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).
tff(func_def_57,type,
sK31:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_58,type,
sK32:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_59,type,
sK33:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_60,type,
sK34:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_61,type,
sK35:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > list(X0) ) ).
tff(func_def_62,type,
sK36:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > X0 ) ).
tff(func_def_63,type,
sK37:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_64,type,
sK38: ( list(dB) * dB * dB * dB ) > list(dB) ).
tff(func_def_65,type,
sK39:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_66,type,
sK40:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_67,type,
sK41:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(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,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $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(f104,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f107,conjecture,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f108,negated_conjecture,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f112,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(flattening,[],[f108]) ).
tff(f427,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(cnf_transformation,[],[f104]) ).
tff(f430,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(cnf_transformation,[],[f112]) ).
tff(f497,plain,
$false,
inference(global_subsumption,[],[f427,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL778_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % 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 16:51:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (3058046)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (3058053)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=228371285:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (3058053) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3058046-3058053"...
% 0.11/0.45 % (3058053)...printing done.
% 0.11/0.45 % (3058052)% WARNING: option uhcvi not known.
% 0.11/0.45 % (3058051)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2057124662_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (3058053)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3058053)------------------------------
% 0.11/0.45 % (3058053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3058053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3058053)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3058053)Termination reason: Refutation
% 0.11/0.45 % (3058053)Time elapsed: 0.004 s
% 0.11/0.45 % (3058053)Peak memory usage: 11 MB
% 0.11/0.45 % (3058053)Instructions burned: 14 (million)
% 0.11/0.45 % (3058046)Success in time 0.035 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------