%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL768_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:56:31 AM UTC 2026
% Result : Theorem 2.72s 1.29s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 21 unt; 0 typ; 4 def)
% Number of atoms : 145 ( 19 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 151 ( 59 ~; 57 |; 28 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 9 con; 0-5 aty)
% Number of variables : 79 ( 0 sgn 71 !; 8 ?; 79 :)
% 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,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(X1,fun(X0,X2)) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
it: fun(dB,bool) ).
tff(func_def_5,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_6,type,
var: nat > dB ).
tff(func_def_7,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_8,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_9,type,
append:
!>[X0: $tType] : fun(list(X0),fun(list(X0),list(X0))) ).
tff(func_def_10,type,
butlast:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_11,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_12,type,
hd:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_13,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_14,type,
last:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_15,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_16,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_17,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_18,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_19,type,
rev:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_20,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_21,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_22,type,
tl:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fNot: fun(bool,bool) ).
tff(func_def_26,type,
fTrue: bool ).
tff(func_def_27,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_28,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_30,type,
i: nat ).
tff(func_def_31,type,
rs: list(dB) ).
tff(func_def_32,type,
sK0:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_33,type,
sK1:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_34,type,
sK2:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_35,type,
sK3:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_36,type,
sK4:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).
tff(func_def_37,type,
sK5:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_38,type,
sK6:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_39,type,
sK7:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_40,type,
sK8:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_41,type,
sK9:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_42,type,
sK10:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_43,type,
sK11:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_44,type,
sK12:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_45,type,
sK13:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_46,type,
sK14:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_47,type,
sK15:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_48,type,
sK16:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_49,type,
sK17:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_50,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_51,type,
sK19:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_52,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_53,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(pred_def_1,type,
list_all:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_2,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sQ22_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f1,axiom,
! [X4: nat] : pp(aa(dB,bool,it,var(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Var__IT) ).
tff(f3,axiom,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: fun(X0,bool)] :
( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
<=> ( listsp(X0,X3,X2)
& listsp(X0,X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_append__in__listsp__conv) ).
tff(f4,axiom,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_listsp_ONil) ).
tff(f12,axiom,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
<=> ( listsp(X0,X2,X3)
& listsp(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_listsp__conj__eq) ).
tff(f29,axiom,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( listsp(X0,X2,X1)
<=> ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_listsp_Osimps) ).
tff(f117,axiom,
listsp(dB,combs(dB,bool,bool,combb(bool,fun(bool,bool),dB,fconj,it),combb(dB,bool,dB,it,aa(dB,fun(dB,dB),combc(dB,dB,dB,app),var(i)))),rs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f118,conjecture,
listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f119,negated_conjecture,
~ listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
inference(negated_conjecture,[status(cth)],[f118]) ).
tff(f120,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f1]) ).
tff(f122,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
inference(flattening,[],[f119]) ).
tff(f155,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: fun(X0,bool)] :
( ( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
| ~ listsp(X0,X3,X2)
| ~ listsp(X0,X3,X1) )
& ( ( listsp(X0,X3,X2)
& listsp(X0,X3,X1) )
| ~ listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f156,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: fun(X0,bool)] :
( ( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
| ~ listsp(X0,X3,X2)
| ~ listsp(X0,X3,X1) )
& ( ( listsp(X0,X3,X2)
& listsp(X0,X3,X1) )
| ~ listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) ) ),
inference(flattening,[],[f155]) ).
tff(f165,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
| ~ listsp(X0,X2,X3)
| ~ listsp(X0,X1,X3) )
& ( ( listsp(X0,X2,X3)
& listsp(X0,X1,X3) )
| ~ listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) ) ),
inference(nnf_transformation,[],[f12]) ).
tff(f166,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
| ~ listsp(X0,X2,X3)
| ~ listsp(X0,X1,X3) )
& ( ( listsp(X0,X2,X3)
& listsp(X0,X1,X3) )
| ~ listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) ) ),
inference(flattening,[],[f165]) ).
tff(f182,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) )
| ~ listsp(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
tff(f183,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) )
| ~ listsp(X0,X2,X1) ) ),
inference(flattening,[],[f182]) ).
tff(f184,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ? [X5: X0,X6: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) = X1 )
& pp(aa(X0,bool,X2,X5))
& listsp(X0,X2,X6) )
| ~ listsp(X0,X2,X1) ) ),
inference(rectify,[],[f183]) ).
tff(f185,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK3(X0,X1,X2)),sK4(X0,X1,X2)) = X1 )
& pp(aa(X0,bool,X2,sK3(X0,X1,X2)))
& listsp(X0,X2,sK4(X0,X1,X2)) )
| ~ listsp(X0,X2,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X5,sK3(X0,X1,X2)),skolemize(X6,sK4(X0,X1,X2))],[f184]) ).
tff(f217,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f120]) ).
tff(f223,plain,
! [X0: $tType,X2: list(X0),X3: fun(X0,bool),X1: list(X0)] :
( listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))
| ~ listsp(X0,X3,X2)
| ~ listsp(X0,X3,X1) ),
inference(cnf_transformation,[],[f156]) ).
tff(f224,plain,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f4]) ).
tff(f241,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( ~ listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)
| listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f166]) ).
tff(f281,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0),X4: list(X0)] :
( listsp(X0,X2,X1)
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ),
inference(cnf_transformation,[],[f185]) ).
tff(f404,plain,
listsp(dB,combs(dB,bool,bool,combb(bool,fun(bool,bool),dB,fconj,it),combb(dB,bool,dB,it,aa(dB,fun(dB,dB),combc(dB,dB,dB,app),var(i)))),rs),
inference(cnf_transformation,[],[f117]) ).
tff(f405,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
inference(cnf_transformation,[],[f122]) ).
tff(f466,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X4: list(X0)] :
( listsp(X0,X2,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4))
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ),
inference(equality_resolution,[],[f281]) ).
tff(f707,plain,
( ~ listsp(dB,it,rs)
| ~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))) ),
inference(resolution,[],[f223,f405]) ).
tff(f713,definition,
( spl23_1
<=> listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
tff(f714,plain,
( ~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))
| spl23_1 ),
inference(avatar_component_clause,[],[f713]) ).
tff(f716,definition,
( spl23_2
<=> listsp(dB,it,rs) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
tff(f717,plain,
( ~ listsp(dB,it,rs)
| spl23_2 ),
inference(avatar_component_clause,[],[f716]) ).
tff(f718,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(avatar_split_clause,[],[f707,f716,f713]) ).
tff(f757,plain,
( ~ pp(aa(dB,bool,it,var(i)))
| ~ listsp(dB,it,nil(dB))
| spl23_1 ),
inference(resolution,[],[f466,f714]) ).
tff(f761,definition,
( spl23_3
<=> listsp(dB,it,nil(dB)) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
tff(f762,plain,
( ~ listsp(dB,it,nil(dB))
| spl23_3 ),
inference(avatar_component_clause,[],[f761]) ).
tff(f764,definition,
( spl23_4
<=> pp(aa(dB,bool,it,var(i))) ),
introduced(definition,[new_symbols(definition,[spl23_4])],[avatar_definition]) ).
tff(f765,plain,
( ~ pp(aa(dB,bool,it,var(i)))
| spl23_4 ),
inference(avatar_component_clause,[],[f764]) ).
tff(f766,plain,
( ~ spl23_3
| ~ spl23_4
| spl23_1 ),
inference(avatar_split_clause,[],[f757,f713,f764,f761]) ).
tff(f770,plain,
( $false
| spl23_3 ),
inference(resolution,[],[f762,f224]) ).
tff(f771,plain,
spl23_3,
inference(avatar_contradiction_clause,[],[f770]) ).
tff(f772,plain,
( $false
| spl23_4 ),
inference(resolution,[],[f765,f217]) ).
tff(f773,plain,
spl23_4,
inference(avatar_contradiction_clause,[],[f772]) ).
tff(f778,plain,
listsp(dB,it,rs),
inference(resolution,[],[f404,f241]) ).
tff(f780,plain,
( $false
| spl23_2 ),
inference(resolution,[],[f778,f717]) ).
tff(f781,plain,
spl23_2,
inference(avatar_contradiction_clause,[],[f780]) ).
cnf(s1,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f718]) ).
cnf(s2,plain,
( spl23_1
| ~ spl23_3
| ~ spl23_4 ),
inference(sat_conversion,[],[f766]) ).
cnf(s3,plain,
spl23_3,
inference(sat_conversion,[],[f771]) ).
cnf(s4,plain,
spl23_4,
inference(sat_conversion,[],[f773]) ).
cnf(s5,plain,
spl23_2,
inference(sat_conversion,[],[f781]) ).
cnf(s6,plain,
spl23_1,
inference(rat,[],[s2,s4,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s6]) ).
tff(f782,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL768_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 16:49:07 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.72/1.28 % (3731027)Detected formulas, will run a generic FOF schedule.
% 2.72/1.28 % (3731035)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1419282130:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.28 % (3731035)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.72/1.28 % (3731035)Refutation not found, incomplete strategy
% 2.72/1.28 % (3731035)------------------------------
% 2.72/1.28 % (3731035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (3731035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (3731035)CaDiCaL version: 2.1.3
% 2.72/1.28 % (3731035)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.28 % (3731035)Time elapsed: 0.005 s
% 2.72/1.28 % (3731035)Peak memory usage: 89 MB
% 2.72/1.28 % (3731035)Instructions burned: 15 (million)
% 2.72/1.28 % (3731036)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3937519242:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.28 % (3731032)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=1602381289:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.29 % (3731034)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=1477978123:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.29 % (3731033)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=117119572:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.29 % (3731034)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.72/1.29 % (3731037)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3952265741:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.29 % (3731038)dis-21_1_sil=8000:lcm=predicate:random_seed=3309984572: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)
% 2.72/1.29 % (3731038)First to succeed.
% 2.72/1.29 % (3731036)Also succeeded, but the first one will report.
% 2.72/1.29 % (3731038)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3731027"
% 2.72/1.29 % (3731037)Instruction limit reached!
% 2.72/1.29 % (3731037)------------------------------
% 2.72/1.29 % (3731037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.29 % (3731037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.29 % (3731037)CaDiCaL version: 2.1.3
% 2.72/1.29 % (3731037)Termination reason: Instruction limit
% 2.72/1.29 % (3731037)Termination phase: Saturation
% 2.72/1.29 % (3731037)Time elapsed: 0.090 s
% 2.72/1.29 % (3731037)Peak memory usage: 89 MB
% 2.72/1.29 % (3731037)Instructions burned: 140 (million)
% 2.72/1.29 % (3731035)------------------------------
% 2.72/1.29 % (3731035)------------------------------
% 2.72/1.29 % (3731047)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1820250014:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.72/1.29 % (3731047)Also succeeded, but the first one will report.
% 2.72/1.29 % (3731046)lrs+10_1_sil=8000:sp=occurrence:random_seed=1056747029:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.72/1.29 % (3731046)Also succeeded, but the first one will report.
% 2.72/1.29 % (3731038)Refutation found. Thanks to Tanya!
% 2.72/1.29 % SZS status Theorem for theBenchmark
% 2.72/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.48 % (3731038)------------------------------
% 3.65/1.48 % (3731038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.48 % (3731038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.48 % (3731038)CaDiCaL version: 2.1.3
% 3.65/1.48 % (3731038)Termination reason: Refutation
% 3.65/1.48 % (3731038)Time elapsed: 0.018 s
% 3.65/1.48 % (3731038)Peak memory usage: 89 MB
% 3.65/1.48 % (3731038)Instructions burned: 32 (million)
% 3.65/1.48 % (3731038)------------------------------
% 3.65/1.48 % (3731038)------------------------------
% 3.65/1.48 % (3731027)Success in time 0.449 s
% 3.65/1.48 % Vampire exiting
%------------------------------------------------------------------------------