TSTP Solution File: LCL775_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL775_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:49:15 EDT 2024
% Result : Theorem 0.18s 0.57s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 101
% Syntax : Number of formulae : 151 ( 40 unt; 86 typ; 0 def)
% Number of atoms : 181 ( 62 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 175 ( 59 ~; 56 |; 52 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 154 ( 71 >; 83 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-6 aty)
% Number of functors : 67 ( 67 usr; 9 con; 0-5 aty)
% Number of variables : 217 ( 128 !; 39 ?; 217 :)
% ( 50 !>; 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_size: dB > nat ).
tff(func_def_7,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_8,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_9,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_10,type,
append:
!>[X0: $tType] : ( ( list(X0) * 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,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_14,type,
nil:
!>[X0: $tType] : 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,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_17,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_18,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_19,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
i: nat ).
tff(func_def_24,type,
r: dB ).
tff(func_def_25,type,
s: dB ).
tff(func_def_26,type,
ss: list(dB) ).
tff(func_def_27,type,
sK10: dB > dB ).
tff(func_def_28,type,
sK11: dB > list(dB) ).
tff(func_def_29,type,
sK12: dB > nat ).
tff(func_def_30,type,
sK13: dB > dB ).
tff(func_def_31,type,
sK14: dB > dB ).
tff(func_def_32,type,
sK15: dB > list(dB) ).
tff(func_def_33,type,
sK16:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_34,type,
sK17:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_35,type,
sK18:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_36,type,
sK19:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_37,type,
sK20:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_38,type,
sK21:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_39,type,
sK22: ( dB * dB ) > dB ).
tff(func_def_40,type,
sK23:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_41,type,
sK24:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_42,type,
sK25:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_43,type,
sK26:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_44,type,
sK27: ( dB * list(dB) * dB ) > dB ).
tff(func_def_45,type,
sK28: ( dB * list(dB) * dB ) > dB ).
tff(func_def_46,type,
sK29: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_47,type,
sK30: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_48,type,
sK31: ( dB * list(dB) * dB ) > dB ).
tff(func_def_49,type,
sK32: ( dB * list(dB) * nat ) > list(dB) ).
tff(func_def_50,type,
sK33: ( dB * dB * dB ) > dB ).
tff(func_def_51,type,
sK34: ( dB * dB * dB ) > dB ).
tff(func_def_52,type,
sK35: ( dB * dB * dB ) > dB ).
tff(func_def_53,type,
sK36:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > X0 ) ).
tff(func_def_54,type,
sK37:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_55,type,
sK38:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_56,type,
sK39: ( dB * dB * list(dB) * dB ) > list(dB) ).
tff(func_def_57,type,
sK40:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > list(X0) ) ).
tff(func_def_58,type,
sK41:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool)) ) > X0 ) ).
tff(func_def_59,type,
sK42:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_60,type,
sK43:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_61,type,
sK44:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_62,type,
sK45:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_63,type,
sK46:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_64,type,
sK47:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > 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 > $o ).
tff(pred_def_9,type,
sP2: ( dB * list(dB) * dB ) > $o ).
tff(pred_def_10,type,
sP3: ( dB * dB * dB ) > $o ).
tff(pred_def_11,type,
sP4:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_12,type,
sP5: ( dB * dB * list(dB) * dB ) > $o ).
tff(pred_def_13,type,
sP6:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > $o ) ).
tff(pred_def_14,type,
sP7:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > $o ) ).
tff(pred_def_15,type,
sP8:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_16,type,
sP9:
!>[X0: $tType] : ( ( list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0 ) > $o ) ).
tff(f4420,plain,
$false,
inference(subsumption_resolution,[],[f4419,f1128]) ).
tff(f1128,plain,
~ sP0(foldl(dB,dB,app,abs(r),rotate1(dB,cons(dB,var(i),cons(dB,s,ss))))),
inference(backward_demodulation,[],[f724,f1126]) ).
tff(f1126,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: X0] : ( rotate1(X0,cons(X0,X3,cons(X0,X1,X2))) = cons(X0,X1,rotate1(X0,cons(X0,X3,X2))) ),
inference(forward_demodulation,[],[f1091,f683]) ).
tff(f683,plain,
! [X1: $tType,X2: list(X1),X3: X1] : ( rotate1(X1,cons(X1,X3,X2)) = append(X1,X2,insert(X1,X3,nil(X1))) ),
inference(forward_demodulation,[],[f519,f421]) ).
tff(f421,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType,X63: X0] : ( insert(X0,X63,nil(X0)) = cons(X0,X63,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_insert__Nil) ).
tff(f519,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,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1] :
( ( rotate1(X1,cons(X1,X3,X2)) = append(X1,X2,cons(X1,X3,nil(X1))) )
& ( nil(X0) = rotate1(X0,nil(X0)) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: $tType,X1: $tType,X62: list(X1),X63: X1] :
( ( rotate1(X1,cons(X1,X63,X62)) = append(X1,X62,cons(X1,X63,nil(X1))) )
& ( nil(X0) = rotate1(X0,nil(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_rotate__simps) ).
tff(f1091,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: X0] : ( cons(X0,X1,append(X0,X2,insert(X0,X3,nil(X0)))) = rotate1(X0,cons(X0,X3,cons(X0,X1,X2))) ),
inference(superposition,[],[f683,f512]) ).
tff(f512,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: list(X0)] : ( append(X0,cons(X0,X3,X2),X1) = cons(X0,X3,append(X0,X2,X1)) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: X0] : ( append(X0,cons(X0,X3,X2),X1) = cons(X0,X3,append(X0,X2,X1)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X76: list(X0),X62: list(X0),X63: X0] : ( append(X0,cons(X0,X63,X62),X76) = cons(X0,X63,append(X0,X62,X76)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_append__Cons) ).
tff(f724,plain,
~ sP0(foldl(dB,dB,app,abs(r),cons(dB,s,rotate1(dB,cons(dB,var(i),ss))))),
inference(resolution,[],[f722,f404]) ).
tff(f404,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK10(X0)))
& ( abs(sK10(X0)) = X0 ) )
| ( listsp(dB,it,sK11(X0))
& ( foldl(dB,dB,app,var(sK12(X0)),sK11(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f269,f271,f270]) ).
tff(f270,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK10(X0)))
& ( abs(sK10(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f271,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK11(X0))
& ( foldl(dB,dB,app,var(sK12(X0)),sK11(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f269,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f268]) ).
tff(f268,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f267]) ).
tff(f267,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f722,plain,
~ sP1(foldl(dB,dB,app,abs(r),cons(dB,s,rotate1(dB,cons(dB,var(i),ss))))),
inference(resolution,[],[f410,f703]) ).
tff(f703,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,abs(r),cons(dB,s,rotate1(dB,cons(dB,var(i),ss)))))),
inference(backward_demodulation,[],[f687,f583]) ).
tff(f583,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType,X1: $tType,X44: list(X1),X27: X1,X34: X0,X43: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X43,X34,cons(X1,X27,X44)) = foldl(X0,X1,X43,aa(X1,X0,aa(X0,fun(X1,X0),X43,X34),X27),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_foldl__Cons) ).
tff(f687,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),rotate1(dB,cons(dB,var(i),ss))))),
inference(backward_demodulation,[],[f675,f683]) ).
tff(f675,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),append(dB,ss,insert(dB,var(i),nil(dB)))))),
inference(backward_demodulation,[],[f384,f674]) ).
tff(f674,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,insert(dB,X0,nil(dB)))) ),
inference(forward_demodulation,[],[f448,f421]) ).
tff(f448,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,[],[f150]) ).
tff(f150,plain,
! [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)))) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X84: dB,X17: list(dB),X18: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X18,X17)),X84) = foldl(dB,dB,app,X18,append(dB,X17,cons(dB,X84,nil(dB)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_app__last) ).
tff(f384,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),ss)),var(i)))),
inference(cnf_transformation,[],[f109]) ).
tff(f109,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),ss)),var(i)))),
inference(flattening,[],[f108]) ).
tff(f108,negated_conjecture,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),ss)),var(i)))),
inference(negated_conjecture,[],[f107]) ).
tff(f107,conjecture,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),ss)),var(i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f410,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f115,f248,f247]) ).
tff(f247,plain,
! [X0: dB] :
( sP0(X0)
<=> ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f115,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X34: dB] :
( pp(aa(dB,bool,it,X34))
<=> ( ? [X37: dB,X38: dB,X39: list(dB)] :
( pp(aa(dB,bool,it,X38))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X37,X38,zero_zero(nat)),X39)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X37)),X38),X39) = X34 ) )
| ? [X37: dB] :
( pp(aa(dB,bool,it,X37))
& ( abs(X37) = X34 ) )
| ? [X35: list(dB),X36: nat] :
( listsp(dB,it,X35)
& ( foldl(dB,dB,app,var(X36),X35) = X34 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_IT_Osimps) ).
tff(f4419,plain,
sP0(foldl(dB,dB,app,abs(r),rotate1(dB,cons(dB,var(i),cons(dB,s,ss))))),
inference(forward_demodulation,[],[f4418,f1126]) ).
tff(f4418,plain,
sP0(foldl(dB,dB,app,abs(r),cons(dB,s,rotate1(dB,cons(dB,var(i),ss))))),
inference(subsumption_resolution,[],[f4409,f385]) ).
tff(f385,plain,
pp(aa(dB,bool,it,s)),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
pp(aa(dB,bool,it,s)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f4409,plain,
( sP0(foldl(dB,dB,app,abs(r),cons(dB,s,rotate1(dB,cons(dB,var(i),ss)))))
| ~ pp(aa(dB,bool,it,s)) ),
inference(resolution,[],[f702,f686]) ).
tff(f686,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,substn(r,s,zero_zero(nat)),rotate1(dB,cons(dB,var(i),ss))))),
inference(backward_demodulation,[],[f676,f683]) ).
tff(f676,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,substn(r,s,zero_zero(nat)),append(dB,ss,insert(dB,var(i),nil(dB)))))),
inference(backward_demodulation,[],[f667,f674]) ).
tff(f667,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,substn(r,s,zero_zero(nat)),ss)),var(i)))),
inference(backward_demodulation,[],[f388,f420]) ).
tff(f420,plain,
! [X0: dB,X1: dB] : ( substn(X1,X0,zero_zero(nat)) = subst(X1,X0,zero_zero(nat)) ),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: dB,X1: dB] : ( substn(X1,X0,zero_zero(nat)) = subst(X1,X0,zero_zero(nat)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X14: dB,X16: dB] : ( substn(X16,X14,zero_zero(nat)) = subst(X16,X14,zero_zero(nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_substn__subst__0) ).
tff(f388,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(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(f702,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,substn(X1,X2,zero_zero(nat)),X3)))
| sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(backward_demodulation,[],[f669,f583]) ).
tff(f669,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,substn(X1,X2,zero_zero(nat)),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(backward_demodulation,[],[f605,f420]) ).
tff(f605,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f408]) ).
tff(f408,plain,
! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( sP0(X0)
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK14(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK13(X0),sK14(X0),zero_zero(nat)),sK15(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK13(X0))),sK14(X0)),sK15(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f274,f275]) ).
tff(f275,plain,
! [X0: dB] :
( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X4,X5,zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK14(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK13(X0),sK14(X0),zero_zero(nat)),sK15(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK13(X0))),sK14(X0)),sK15(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f274,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X4,X5,zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f273]) ).
tff(f273,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL775_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.32 % Computer : n020.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Apr 29 23:12:02 EDT 2024
% 0.14/0.33 % CPUTime :
% 0.14/0.33 % (30957)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.35 % (30964)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.36 % (30958)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (30964)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.36 % (30962)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.36 % (30960)WARNING: value z3 for option sas not known
% 0.14/0.36 % Exception at run slice level
% 0.14/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37 % (30959)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (30961)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (30960)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (30963)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % (30965)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (30966)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.18/0.40 % (30965)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.40 % Exception at run slice level
% 0.18/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.40 % (30966)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.41 % (30967)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.18/0.42 % (30968)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.18/0.57 % (30967)First to succeed.
% 0.18/0.57 % (30967)Refutation found. Thanks to Tanya!
% 0.18/0.57 % SZS status Theorem for theBenchmark
% 0.18/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.57 % (30967)------------------------------
% 0.18/0.57 % (30967)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.18/0.57 % (30967)Termination reason: Refutation
% 0.18/0.57
% 0.18/0.57 % (30967)Memory used [KB]: 2832
% 0.18/0.57 % (30967)Time elapsed: 0.164 s
% 0.18/0.57 % (30967)Instructions burned: 341 (million)
% 0.18/0.57 % (30967)------------------------------
% 0.18/0.57 % (30967)------------------------------
% 0.18/0.57 % (30957)Success in time 0.238 s
%------------------------------------------------------------------------------