%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL794_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 : n001.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 11:56:37 AM UTC 2026
% Result : Theorem 2.66s 1.05s
% Output : Refutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 41 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 80 ( 38 ~; 27 |; 7 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 60 ( 60 usr; 26 con; 0-5 aty)
% Number of variables : 100 ( 99 !; 1 ?; 100 :)
% 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,
fun1: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,X1),fun1(fun1(X2,X0),fun1(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * X1 ) > fun1(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun1(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * fun1(X0,X1) ) > fun1(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun1(dB,bool) ).
tff(func_def_6,type,
beta: fun1(dB,fun1(dB,bool)) ).
tff(func_def_7,type,
abs: dB > dB ).
tff(func_def_8,type,
app: fun1(dB,fun1(dB,dB)) ).
tff(func_def_9,type,
var: nat > dB ).
tff(func_def_10,type,
dB_size: dB > nat ).
tff(func_def_11,type,
lift: fun1(dB,fun1(nat,dB)) ).
tff(func_def_12,type,
subst: fun1(dB,fun1(dB,fun1(nat,dB))) ).
tff(func_def_13,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_14,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_15,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_16,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun1(X1,fun1(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_19,type,
shift:
!>[X0: $tType] : ( ( fun1(nat,X0) * nat * X0 ) > fun1(nat,X0) ) ).
tff(func_def_20,type,
fun: fun1(type,fun1(type,type)) ).
tff(func_def_21,type,
type_case:
!>[X0: $tType] : ( ( fun1(nat,X0) * fun1(type,fun1(type,X0)) * type ) > X0 ) ).
tff(func_def_22,type,
typing: ( fun1(nat,type) * dB ) > fun1(type,bool) ).
tff(func_def_23,type,
typings: ( fun1(nat,type) * list(dB) ) > fun1(list(type),bool) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fFalse: bool ).
tff(func_def_26,type,
fTrue: bool ).
tff(func_def_27,type,
fconj: fun1(bool,fun1(bool,bool)) ).
tff(func_def_28,type,
t1: type ).
tff(func_def_29,type,
t: type ).
tff(func_def_30,type,
t_a: type ).
tff(func_def_31,type,
t2: type ).
tff(func_def_32,type,
ts: list(type) ).
tff(func_def_33,type,
a: dB ).
tff(func_def_34,type,
as: list(dB) ).
tff(func_def_35,type,
e: fun1(nat,type) ).
tff(func_def_36,type,
ea: fun1(nat,type) ).
tff(func_def_37,type,
i: nat ).
tff(func_def_38,type,
ia: nat ).
tff(func_def_39,type,
n: nat ).
tff(func_def_40,type,
rs: list(dB) ).
tff(func_def_41,type,
t3: dB ).
tff(func_def_42,type,
u: dB ).
tff(func_def_43,type,
ua: dB ).
tff(func_def_44,type,
sK0: ( dB * fun1(nat,type) ) > type ).
tff(func_def_45,type,
sK1: ( dB * fun1(nat,type) ) > type ).
tff(func_def_46,type,
sK2: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_47,type,
sK3: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_48,type,
sK4: ( type * dB * dB * fun1(nat,type) ) > type ).
tff(func_def_49,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun1(X1,X0) * fun1(X1,X0) ) > X1 ) ).
tff(func_def_50,type,
sK6: ( dB * dB * dB ) > dB ).
tff(func_def_51,type,
sK7: ( dB * dB * dB ) > dB ).
tff(func_def_52,type,
sK8: ( dB * dB * dB ) > dB ).
tff(func_def_53,type,
sK9: ( dB * dB ) > dB ).
tff(func_def_54,type,
sK10: type ).
tff(func_def_55,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun1(X0,fun1(X1,X0)) > X1 ) ).
tff(func_def_56,type,
sK12:
!>[X0: $tType,X1: $tType] : ( fun1(X0,fun1(X1,X0)) > X1 ) ).
tff(func_def_57,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun1(X0,fun1(X1,X0)) > X0 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
step1:
!>[X0: $tType] : ( ( fun1(X0,fun1(X0,bool)) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun1(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(f4,axiom,
pp(aa(type,bool,typing(e,u),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uT) ).
tff(f5,axiom,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(X4,X3),X2))
=> pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_lift__type) ).
tff(f7,axiom,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1)))
=> ( pp(aa(type,bool,typing(X4,X0),X2))
=> pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_App) ).
tff(f8,axiom,
t2 = aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_T) ).
tff(f11,axiom,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,typing(X2,var(X1)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_typing_OVar) ).
tff(f12,axiom,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,typing(X2,var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_typing__elims_I1_J) ).
tff(f13,axiom,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) = aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
<=> ( ( X3 = X1 )
& ( X2 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_type_Osimps_I2_J) ).
tff(f18,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_True) ).
tff(f24,axiom,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( X4 = X3 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_shift__eq) ).
tff(f27,axiom,
~ ! [X0: type] :
( pp(aa(type,bool,typing(shift(type,e,i,t2),var(n)),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t))))
=> ~ pp(aa(type,bool,typing(shift(type,e,i,t2),a),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f112,conjecture,
pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun,ts,t))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f113,negated_conjecture,
~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun,ts,t))),
inference(negated_conjecture,[status(cth)],[f112]) ).
tff(f114,plain,
~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun,ts,t))),
inference(flattening,[],[f113]) ).
tff(f119,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,typing(X2,var(X1)),X0)) ),
inference(ennf_transformation,[],[f12]) ).
tff(f120,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,typing(X2,var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f123,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,typing(X4,X3),X2)) ),
inference(ennf_transformation,[],[f5]) ).
tff(f124,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f24]) ).
tff(f126,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,typing(X4,X0),X2))
| ~ pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(ennf_transformation,[],[f7]) ).
tff(f127,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,typing(X4,X0),X2))
| ~ pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(flattening,[],[f126]) ).
tff(f150,plain,
? [X0: type] :
( pp(aa(type,bool,typing(shift(type,e,i,t2),a),X0))
& pp(aa(type,bool,typing(shift(type,e,i,t2),var(n)),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t)))) ),
inference(ennf_transformation,[],[f27]) ).
tff(f160,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) = aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X3 = X1 )
& ( X2 = X0 ) )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
tff(f161,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) = aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X3 = X1 )
& ( X2 = X0 ) )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ) ),
inference(flattening,[],[f160]) ).
tff(f169,plain,
( pp(aa(type,bool,typing(shift(type,e,i,t2),a),sK10))
& pp(aa(type,bool,typing(shift(type,e,i,t2),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK10),foldr(type,type,fun,ts,t)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f150]) ).
tff(f174,plain,
~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),foldr(type,type,fun,ts,t))),
inference(cnf_transformation,[],[f114]) ).
tff(f182,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(type,bool,typing(X2,var(X1)),X0))
| ( aa(nat,type,X2,X1) = X0 ) ),
inference(cnf_transformation,[],[f119]) ).
tff(f183,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,typing(X2,var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f120]) ).
tff(f192,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,typing(X4,X3),X2)) ),
inference(cnf_transformation,[],[f123]) ).
tff(f193,plain,
! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f124]) ).
tff(f197,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f161]) ).
tff(f199,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,typing(X4,X0),X2))
| ~ pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(cnf_transformation,[],[f127]) ).
tff(f202,plain,
aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t)) = t2,
inference(cnf_transformation,[],[f8]) ).
tff(f206,plain,
pp(aa(type,bool,typing(e,u),t2)),
inference(cnf_transformation,[],[f4]) ).
tff(f248,plain,
pp(aa(type,bool,typing(shift(type,e,i,t2),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK10),foldr(type,type,fun,ts,t)))),
inference(cnf_transformation,[],[f169]) ).
tff(f251,plain,
i = n,
inference(cnf_transformation,[],[f18]) ).
tff(f262,plain,
pp(aa(type,bool,typing(shift(type,e,n,t2),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK10),foldr(type,type,fun,ts,t)))),
inference(definition_unfolding,[],[f248,f251]) ).
tff(f266,plain,
! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f183]) ).
tff(f268,plain,
! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f193]) ).
tff(f280,plain,
! [X2: nat,X0: type,X1: fun1(nat,type)] : pp(aa(type,bool,typing(shift(type,X1,X2,X0),var(X2)),X0)),
inference(superposition,[],[f266,f268]) ).
tff(f296,plain,
! [X0: type,X1: type] :
( ( t2 != aa(type,type,aa(type,fun1(type,type),fun,X0),X1) )
| ( t1 = X0 ) ),
inference(superposition,[],[f197,f202]) ).
tff(f325,plain,
aa(type,type,aa(type,fun1(type,type),fun,sK10),foldr(type,type,fun,ts,t)) = aa(nat,type,shift(type,e,n,t2),n),
inference(resolution,[],[f262,f182]) ).
tff(f326,plain,
t2 = aa(type,type,aa(type,fun1(type,type),fun,sK10),foldr(type,type,fun,ts,t)),
inference(forward_demodulation,[],[f325,f268]) ).
tff(f328,plain,
( ( t2 != t2 )
| ( t1 = sK10 ) ),
inference(superposition,[],[f296,f326]) ).
tff(f333,plain,
t1 = sK10,
inference(trivial_inequality_removal,[],[f328]) ).
tff(f403,plain,
! [X0: type] :
( ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),var(zero_zero(nat))),X0))
| ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t)))) ),
inference(resolution,[],[f199,f174]) ).
tff(f406,plain,
! [X0: type] :
( ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),sK10),var(zero_zero(nat))),X0))
| ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),t1),aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t)))) ),
inference(forward_demodulation,[],[f403,f333]) ).
tff(f407,plain,
! [X0: type] :
( ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),sK10),aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t))))
| ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),sK10),var(zero_zero(nat))),X0)) ),
inference(forward_demodulation,[],[f406,f333]) ).
tff(f412,plain,
( ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),sK10),aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),t2))
| ~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),sK10),var(zero_zero(nat))),sK10)) ),
inference(superposition,[],[f407,f326]) ).
tff(f413,plain,
~ pp(aa(type,bool,typing(shift(type,e,zero_zero(nat),sK10),aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),t2)),
inference(forward_subsumption_resolution,[],[f412,f280]) ).
tff(f419,plain,
~ pp(aa(type,bool,typing(e,u),t2)),
inference(resolution,[],[f413,f192]) ).
tff(f420,plain,
$false,
inference(forward_subsumption_resolution,[],[f419,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL794_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n001.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 16:58:01 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.66/1.04 % (3790110)Detected formulas, will run a generic FOF schedule.
% 2.66/1.04 % (3790121)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1431336096:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.04 % (3790116)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=4282857950:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.04 % (3790122)dis-21_1_sil=8000:lcm=predicate:random_seed=2758999027: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)
% 2.66/1.04 % (3790119)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1521340366:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.04 % (3790120)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3541108078:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.04 % (3790117)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=2042277615:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.05 % (3790118)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=346464057:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.05 % (3790119)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.66/1.05 % (3790119)Refutation not found, incomplete strategy
% 2.66/1.05 % (3790119)------------------------------
% 2.66/1.05 % (3790119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.05 % (3790119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.05 % (3790119)CaDiCaL version: 2.1.3
% 2.66/1.05 % (3790119)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.05 % (3790119)Time elapsed: 0.004 s
% 2.66/1.05 % (3790119)Peak memory usage: 88 MB
% 2.66/1.05 % (3790119)Instructions burned: 5 (million)
% 2.66/1.05 % (3790118)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.66/1.05 % (3790120)First to succeed.
% 2.66/1.05 % (3790120)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3790110"
% 2.66/1.05 % (3790121)Instruction limit reached!
% 2.66/1.05 % (3790121)------------------------------
% 2.66/1.05 % (3790121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.05 % (3790121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.05 % (3790121)CaDiCaL version: 2.1.3
% 2.66/1.05 % (3790121)Termination reason: Instruction limit
% 2.66/1.05 % (3790121)Termination phase: Saturation
% 2.66/1.05 % (3790121)Time elapsed: 0.042 s
% 2.66/1.05 % (3790121)Peak memory usage: 89 MB
% 2.66/1.05 % (3790121)Instructions burned: 139 (million)
% 2.66/1.05 % (3790122)Instruction limit reached!
% 2.66/1.05 % (3790122)------------------------------
% 2.66/1.05 % (3790122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.05 % (3790122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.05 % (3790122)CaDiCaL version: 2.1.3
% 2.66/1.05 % (3790122)Termination reason: Instruction limit
% 2.66/1.05 % (3790122)Termination phase: Saturation
% 2.66/1.05 % (3790122)Time elapsed: 0.074 s
% 2.66/1.05 % (3790122)Peak memory usage: 89 MB
% 2.66/1.05 % (3790122)Instructions burned: 129 (million)
% 2.66/1.05 % (3790130)lrs+10_1_sil=8000:sp=occurrence:random_seed=2741516793:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.66/1.05 % (3790131)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3776778350:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.66/1.05 % (3790130)Instruction limit reached!
% 2.66/1.05 % (3790130)------------------------------
% 2.66/1.05 % (3790130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.05 % (3790130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.05 % (3790130)CaDiCaL version: 2.1.3
% 2.66/1.05 % (3790130)Termination reason: Instruction limit
% 2.66/1.05 % (3790130)Termination phase: Saturation
% 2.66/1.05 % (3790130)Time elapsed: 0.094 s
% 2.66/1.05 % (3790130)Peak memory usage: 92 MB
% 2.66/1.05 % (3790130)Instructions burned: 288 (million)
% 2.66/1.05 % (3790131)Also succeeded, but the first one will report.
% 2.66/1.05 % (3790119)------------------------------
% 2.66/1.05 % (3790119)------------------------------
% 2.66/1.05 % (3790120)Refutation found. Thanks to Tanya!
% 2.66/1.05 % SZS status Theorem for theBenchmark
% 2.66/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.25/1.14 % (3790120)------------------------------
% 3.25/1.14 % (3790120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.14 % (3790120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.14 % (3790120)CaDiCaL version: 2.1.3
% 3.25/1.14 % (3790120)Termination reason: Refutation
% 3.25/1.14 % (3790120)Time elapsed: 0.018 s
% 3.25/1.14 % (3790120)Peak memory usage: 89 MB
% 3.25/1.14 % (3790120)Instructions burned: 30 (million)
% 3.25/1.14 % (3790120)------------------------------
% 3.25/1.14 % (3790120)------------------------------
% 3.25/1.14 % (3790110)Success in time 0.411 s
% 3.25/1.14 % Vampire exiting
%------------------------------------------------------------------------------