%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL817_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 : n015.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 11:56:43 AM UTC 2026
% Result : Theorem 1.16s 1.20s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 52 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 103 ( 50 ~; 39 |; 7 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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; 0-3 aty)
% Number of functors : 61 ( 61 usr; 26 con; 0-5 aty)
% Number of variables : 153 ( 152 !; 1 ?; 153 :)
% 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
listset:
!>[X0: $tType] : ( list(fun(X0,bool)) > fun(list(X0),bool) ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
set_Cons:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(list(X0),bool) ) > fun(list(X0),bool) ) ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_20,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_21,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_22,type,
typing: fun(nat,type) > fun(dB,fun(type,bool)) ).
tff(func_def_23,type,
typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fFalse: bool ).
tff(func_def_27,type,
fTrue: bool ).
tff(func_def_28,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_31,type,
t: type ).
tff(func_def_32,type,
t2: type ).
tff(func_def_33,type,
t_a: type ).
tff(func_def_34,type,
t1: type ).
tff(func_def_35,type,
ts: list(type) ).
tff(func_def_36,type,
a: dB ).
tff(func_def_37,type,
as: list(dB) ).
tff(func_def_38,type,
e: fun(nat,type) ).
tff(func_def_39,type,
ea: fun(nat,type) ).
tff(func_def_40,type,
i: nat ).
tff(func_def_41,type,
ia: nat ).
tff(func_def_42,type,
n: nat ).
tff(func_def_43,type,
rs: list(dB) ).
tff(func_def_44,type,
t3: dB ).
tff(func_def_45,type,
u: dB ).
tff(func_def_46,type,
ua: dB ).
tff(func_def_47,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_48,type,
sK1: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_49,type,
sK2: list(type) ).
tff(func_def_50,type,
sK3: type ).
tff(func_def_51,type,
sK4: ( dB * fun(nat,type) ) > type ).
tff(func_def_52,type,
sK5: ( dB * fun(nat,type) ) > type ).
tff(func_def_53,type,
sK6: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_54,type,
sK7: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_55,type,
sK8: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_56,type,
sK9: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_57,type,
sK10: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(func_def_58,type,
sK11: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(f1,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uT) ).
tff(f2,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_True) ).
tff(f8,axiom,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
=> ( ( X6 = shift(type,X3,X0,X1) )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_subst__lemma) ).
tff(f17,axiom,
~ ! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__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(f19,axiom,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
<=> ( ( X3 = X1 )
& ( X2 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_type_Osimps_I2_J) ).
tff(f20,axiom,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_typing__elims_I1_J) ).
tff(f24,axiom,
t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_T) ).
tff(f33,axiom,
! [X0: $tType,X1: X0,X2: fun(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_32_shift__eq) ).
tff(f105,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f115,conjecture,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f116,negated_conjecture,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
inference(negated_conjecture,[status(cth)],[f115]) ).
tff(f117,plain,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
inference(flattening,[],[f116]) ).
tff(f118,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(ennf_transformation,[],[f8]) ).
tff(f119,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(flattening,[],[f118]) ).
tff(f122,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f20]) ).
tff(f123,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f33]) ).
tff(f132,plain,
? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2)))) ),
inference(ennf_transformation,[],[f17]) ).
tff(f160,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X3 = X1 )
& ( X2 = X0 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f19]) ).
tff(f161,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X1 != X3 )
| ( X0 != X2 ) )
& ( ( ( X3 = X1 )
& ( X2 = X0 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(flattening,[],[f160]) ).
tff(f163,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK3),foldr(type,type,fun1,ts,t2)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f132]) ).
tff(f176,plain,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
inference(cnf_transformation,[],[f117]) ).
tff(f179,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(cnf_transformation,[],[f119]) ).
tff(f180,plain,
t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)),
inference(cnf_transformation,[],[f24]) ).
tff(f187,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)),
inference(cnf_transformation,[],[f1]) ).
tff(f194,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) = X0 ) ),
inference(cnf_transformation,[],[f122]) ).
tff(f198,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f123]) ).
tff(f203,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f161]) ).
tff(f216,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK3),foldr(type,type,fun1,ts,t2)))),
inference(cnf_transformation,[],[f163]) ).
tff(f217,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK3)),
inference(cnf_transformation,[],[f163]) ).
tff(f218,plain,
n = i,
inference(cnf_transformation,[],[f2]) ).
tff(f233,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f105]) ).
tff(f268,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK3),foldr(type,type,fun1,ts,t2)))),
inference(definition_unfolding,[],[f216,f218]) ).
tff(f269,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(equality_resolution,[],[f179]) ).
tff(f274,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f198]) ).
tff(f294,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X3,fun(X0,fun(X1,X2))),X5: X3] : ( aa(X3,X2,combc(X3,X1,X2,combc(X3,X0,fun(X1,X2),X4,X6),X7),X5) = aa(X1,X2,aa(X0,fun(X1,X2),aa(X3,fun(X0,fun(X1,X2)),X4,X5),X6),X7) ),
inference(superposition,[],[f233,f233]) ).
tff(f297,plain,
t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),t),
inference(superposition,[],[f233,f180]) ).
tff(f299,plain,
pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u)),
inference(superposition,[],[f187,f233]) ).
tff(f301,plain,
pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK3),a)),
inference(superposition,[],[f217,f233]) ).
tff(f304,plain,
! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),var(X2)))
| ( aa(nat,type,X0,X2) = X1 ) ),
inference(superposition,[],[f194,f233]) ).
tff(f313,plain,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,u),a),i)),t)),
inference(superposition,[],[f176,f233]) ).
tff(f316,plain,
~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,u),a),i))),
inference(forward_demodulation,[],[f313,f233]) ).
tff(f320,plain,
~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a))),
inference(forward_demodulation,[],[f316,f233]) ).
tff(f342,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,combc(type,type,type,fun1,X0),X1) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f203,f233]) ).
tff(f343,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,combc(type,type,type,fun1,X0),X1) != aa(type,type,combc(type,type,type,fun1,X2),X3) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f342,f233]) ).
tff(f344,plain,
! [X0: type,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X0),X1) )
| ( t = X1 ) ),
inference(superposition,[],[f343,f297]) ).
tff(f408,plain,
pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,aa(type,fun(type,type),fun1,sK3),foldr(type,type,fun1,ts,t2))),var(i))),
inference(forward_demodulation,[],[f268,f233]) ).
tff(f409,plain,
pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK3)),var(i))),
inference(forward_demodulation,[],[f408,f233]) ).
tff(f410,plain,
aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK3) = aa(nat,type,shift(type,e,i,t1),i),
inference(resolution,[],[f409,f304]) ).
tff(f411,plain,
t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK3),
inference(forward_demodulation,[],[f410,f274]) ).
tff(f419,plain,
( ( t1 != t1 )
| ( t = sK3 ) ),
inference(superposition,[],[f344,f411]) ).
tff(f422,plain,
t = sK3,
inference(trivial_inequality_removal,[],[f419]) ).
tff(f592,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X2,X7: X0,X4: fun(X3,fun(X0,fun(X2,X1))),X5: X3] : ( aa(X0,X1,combc(X0,X2,X1,aa(X3,fun(X0,fun(X2,X1)),X4,X5),X6),X7) = aa(X3,X1,combc(X3,X2,X1,combc(X3,X0,fun(X2,X1),X4,X7),X6),X5) ),
inference(superposition,[],[f294,f233]) ).
tff(f790,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f269,f233]) ).
tff(f791,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f790,f233]) ).
tff(f792,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X0),X5)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f791,f592]) ).
tff(f793,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X0),X5)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f792,f233]) ).
tff(f794,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X0),X5)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5)) ),
inference(forward_demodulation,[],[f793,f233]) ).
tff(f805,plain,
! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),X0),u))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,X0)),t),a)) ),
inference(resolution,[],[f794,f320]) ).
tff(f811,plain,
! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,X0)),sK3),a))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),X0),u)) ),
inference(forward_demodulation,[],[f805,f422]) ).
tff(f812,plain,
~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u)),
inference(resolution,[],[f811,f301]) ).
tff(f813,plain,
$false,
inference(forward_subsumption_resolution,[],[f812,f299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL817_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 16:58:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 1.16/1.20 % (1853950)Detected formulas, will run a generic FOF schedule.
% 1.16/1.20 % (1853959)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3295508583:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.16/1.20 % (1853959)First to succeed.
% 1.16/1.20 % (1853959)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1853950"
% 1.16/1.20 % (1853961)dis-21_1_sil=8000:lcm=predicate:random_seed=1954441427: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)
% 1.16/1.20 % (1853960)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3742325918:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.16/1.20 % (1853957)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=743563560:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.16/1.20 % (1853956)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=788633365:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.16/1.20 % (1853955)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=1565240494:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.16/1.20 % (1853958)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3026494474:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.16/1.20 % (1853958)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.16/1.20 % (1853958)Also succeeded, but the first one will report.
% 1.16/1.20 % (1853957)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.16/1.20 % (1853961)Also succeeded, but the first one will report.
% 1.16/1.20 % (1853960)Instruction limit reached!
% 1.16/1.20 % (1853960)------------------------------
% 1.16/1.20 % (1853960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.16/1.20 % (1853960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/1.20 % (1853960)CaDiCaL version: 2.1.3
% 1.16/1.20 % (1853960)Termination reason: Instruction limit
% 1.16/1.20 % (1853960)Termination phase: Saturation
% 1.16/1.20 % (1853960)Time elapsed: 0.083 s
% 1.16/1.20 % (1853960)Peak memory usage: 89 MB
% 1.16/1.20 % (1853960)Instructions burned: 140 (million)
% 1.16/1.20 % (1853959)Refutation found. Thanks to Tanya!
% 1.16/1.20 % SZS status Theorem for theBenchmark
% 1.16/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.40 % (1853959)------------------------------
% 0.17/1.40 % (1853959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (1853959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (1853959)CaDiCaL version: 2.1.3
% 0.17/1.40 % (1853959)Termination reason: Refutation
% 0.17/1.40 % (1853959)Time elapsed: 0.029 s
% 0.17/1.40 % (1853959)Peak memory usage: 89 MB
% 0.17/1.40 % (1853959)Instructions burned: 83 (million)
% 0.17/1.40 % (1853959)------------------------------
% 0.17/1.40 % (1853959)------------------------------
% 0.17/1.40 % (1853950)Success in time 0.346 s
% 0.17/1.40 % Vampire exiting
%------------------------------------------------------------------------------