%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL777_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 : n020.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 12:00:33 PM UTC 2026
% Result : Theorem 0.36s 0.51s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 66 ( 66 usr; 9 con; 0-5 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% 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_size: dB > nat ).
tff(func_def_7,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_8,type,
append:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_10,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_11,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_13,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_14,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_15,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(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,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
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,
i: nat ).
tff(func_def_23,type,
r: dB ).
tff(func_def_24,type,
s: dB ).
tff(func_def_25,type,
ss: list(dB) ).
tff(func_def_26,type,
sK0: ( list(dB) * dB * dB * dB ) > list(dB) ).
tff(func_def_27,type,
sK1:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_28,type,
sK2:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_29,type,
sK3:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_30,type,
sK4:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_31,type,
sK5:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_32,type,
sK6:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_33,type,
sK7:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_34,type,
sK8:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_35,type,
sK9:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_36,type,
sK10:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_37,type,
sK11:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_38,type,
sK12:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_39,type,
sK13:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_40,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_41,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_42,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_43,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_44,type,
sK18: ( dB * dB ) > dB ).
tff(func_def_45,type,
sK19:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_46,type,
sK20:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).
tff(func_def_47,type,
sK21: dB > dB ).
tff(func_def_48,type,
sK22: dB > dB ).
tff(func_def_49,type,
sK23: dB > list(dB) ).
tff(func_def_50,type,
sK24: dB > dB ).
tff(func_def_51,type,
sK25: dB > list(dB) ).
tff(func_def_52,type,
sK26: dB > nat ).
tff(func_def_53,type,
sK27: ( dB * dB * dB ) > dB ).
tff(func_def_54,type,
sK28: ( dB * dB * dB ) > dB ).
tff(func_def_55,type,
sK29: ( dB * dB * dB ) > dB ).
tff(func_def_56,type,
sK30: ( dB * list(dB) * dB ) > dB ).
tff(func_def_57,type,
sK31: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_58,type,
sK32: ( dB * list(dB) * dB ) > dB ).
tff(func_def_59,type,
sK33: ( dB * list(dB) * dB ) > dB ).
tff(func_def_60,type,
sK34: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_61,type,
sK35: ( dB * list(dB) * nat ) > list(dB) ).
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] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > 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,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_5,type,
pp: bool > $o ).
tff(f7,axiom,
! [X0: dB,X1: list(dB),X2: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,append(dB,X1,cons(dB,X0,nil(dB)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_app__last) ).
tff(f52,axiom,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1] :
( ( rotate1(X0,nil(X0)) = nil(X0) )
& ( rotate1(X1,cons(X1,X3,X2)) = append(X1,X2,cons(X1,X3,nil(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rotate__simps) ).
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,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f108,negated_conjecture,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f112,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
inference(flattening,[],[f108]) ).
tff(f167,plain,
! [X2: dB,X0: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,append(dB,X1,cons(dB,X0,nil(dB)))) ),
inference(cnf_transformation,[],[f7]) ).
tff(f245,plain,
! [X1: $tType,X2: list(X1),X3: X1] : ( rotate1(X1,cons(X1,X3,X2)) = append(X1,X2,cons(X1,X3,nil(X1))) ),
inference(cnf_transformation,[],[f52]) ).
tff(f359,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(f362,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
inference(cnf_transformation,[],[f112]) ).
tff(f550,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),rotate1(dB,cons(dB,var(i),ss))))),
inference(superposition,[],[f362,f245]) ).
tff(f979,plain,
! [X2: dB,X0: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,rotate1(dB,cons(dB,X0,X1))) ),
inference(forward_demodulation,[],[f167,f245]) ).
tff(f983,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),rotate1(dB,cons(dB,var(i),ss))))),
inference(superposition,[],[f359,f979]) ).
tff(f994,plain,
$false,
inference(forward_subsumption_resolution,[],[f983,f550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL777_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 16:48:34 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.36/0.51 % (3600932)Will run a generic schedule for satisfiability detection.
% 0.36/0.51 % (3600941)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2314629532:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.51 % (3600938)% WARNING: option uhcvi not known.
% 0.36/0.51 % (3600939)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4031499810:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.51 % (3600937)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4160347305_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.51 % (3600942)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3297863207:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.51 % (3600940)dis+10_1_sil=32000:sp=arity:random_seed=169895119:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.51 % (3600943)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4047434565:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.51 % (3600938)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=81785485:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.51 % Exception at run slice level
% 0.36/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.36/0.51 % (3600951)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1853181142:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.36/0.51 % (3600941)Instruction limit reached!
% 0.36/0.51 % (3600941)------------------------------
% 0.36/0.51 % (3600941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.51 % (3600941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.51 % (3600941)CaDiCaL version: 2.1.3
% 0.36/0.51 % (3600941)Termination reason: Instruction limit
% 0.36/0.51 % (3600941)Termination phase: Saturation
% 0.36/0.51 % (3600941)Time elapsed: 0.036 s
% 0.36/0.51 % (3600941)Peak memory usage: 12 MB
% 0.36/0.51 % (3600941)Instructions burned: 117 (million)
% 0.36/0.51 % Exception at run slice level
% 0.36/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.36/0.51 % (3600953)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=62638669:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.51 % (3600938) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3600932-3600938"...
% 0.36/0.51 % (3600938)...printing done.
% 0.36/0.51 % (3600938)Refutation found. Thanks to Tanya!
% 0.36/0.51 % SZS status Theorem for theBenchmark
% 0.36/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.52 % (3600938)------------------------------
% 0.36/0.52 % (3600938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.52 % (3600938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.52 % (3600938)CaDiCaL version: 2.1.3
% 0.36/0.52 % (3600938)Termination reason: Refutation
% 0.36/0.52 % (3600938)Time elapsed: 0.045 s
% 0.36/0.52 % (3600938)Peak memory usage: 13 MB
% 0.36/0.52 % (3600938)Instructions burned: 72 (million)
% 0.36/0.52 % (3600932)Success in time 0.086 s
% 0.36/0.52 % Vampire exiting
%------------------------------------------------------------------------------