TSTP Solution File: SWW521_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW521_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 : n016.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 : Sun May 5 11:41:15 EDT 2024
% Result : Theorem 1.99s 0.70s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 73
% Syntax : Number of formulae : 125 ( 10 unt; 61 typ; 0 def)
% Number of atoms : 163 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 165 ( 66 ~; 59 |; 19 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 62 ( 41 >; 21 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 4 prp; 0-6 aty)
% Number of functors : 43 ( 43 usr; 8 con; 0-5 aty)
% Number of variables : 169 ( 97 !; 12 ?; 169 :)
% ( 60 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
hoare_28830079triple: $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)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_3,type,
suc: nat > nat ).
tff(func_def_4,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_5,type,
powp:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(X0,bool),bool) ) ).
tff(func_def_6,type,
ord_atLeast:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_7,type,
ord_atMost:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_8,type,
ord_greaterThan:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_9,type,
ord_lessThan:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_10,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_11,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_12,type,
fFalse: bool ).
tff(func_def_13,type,
fNot: fun(bool,bool) ).
tff(func_def_14,type,
fTrue: bool ).
tff(func_def_15,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_16,type,
ga: fun(hoare_28830079triple(a),bool) ).
tff(func_def_17,type,
ts: fun(hoare_28830079triple(a),bool) ).
tff(func_def_18,type,
tsa: fun(hoare_28830079triple(a),bool) ).
tff(func_def_19,type,
sK0: nat ).
tff(func_def_20,type,
sK1: hoare_28830079triple(a) ).
tff(func_def_21,type,
sK2: nat > hoare_28830079triple(a) ).
tff(func_def_22,type,
sK3:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_23,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_24,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_25,type,
sK6: nat > nat ).
tff(func_def_26,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_27,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_28,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_29,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_30,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_31,type,
sK12:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_32,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_33,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_34,type,
sK15: fun(nat,bool) > nat ).
tff(func_def_35,type,
sK16: ( fun(nat,bool) * nat ) > nat ).
tff(func_def_36,type,
sK17:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_37,type,
sK18:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_38,type,
sK19:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_39,type,
sK20:
!>[X0: $tType] : ( ( nat * fun(hoare_28830079triple(X0),bool) ) > hoare_28830079triple(X0) ) ).
tff(func_def_40,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
boolean_algebra:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
hoare_992312373derivs:
!>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).
tff(pred_def_10,type,
hoare_592965047valids:
!>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).
tff(pred_def_11,type,
hoare_1633586161_valid:
!>[X0: $tType] : ( ( nat * hoare_28830079triple(X0) ) > $o ) ).
tff(pred_def_12,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
order_strict_mono:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > $o ) ).
tff(pred_def_14,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(f4860,plain,
$false,
inference(avatar_sat_refutation,[],[f3588,f4035,f4764,f4858]) ).
tff(f4858,plain,
( ~ spl22_38
| spl22_48 ),
inference(avatar_contradiction_clause,[],[f4857]) ).
tff(f4857,plain,
( $false
| ~ spl22_38
| spl22_48 ),
inference(subsumption_resolution,[],[f4850,f3283]) ).
tff(f3283,plain,
( pp(aa(hoare_28830079triple(a),bool,tsa,sK1))
| ~ spl22_38 ),
inference(avatar_component_clause,[],[f3282]) ).
tff(f3282,plain,
( spl22_38
<=> pp(aa(hoare_28830079triple(a),bool,tsa,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_38])]) ).
tff(f4850,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,tsa,sK1))
| spl22_48 ),
inference(resolution,[],[f4846,f407]) ).
tff(f407,plain,
ord_less_eq(fun(hoare_28830079triple(a),bool),tsa,ts),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
ord_less_eq(fun(hoare_28830079triple(a),bool),tsa,ts),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f4846,plain,
( ! [X0: fun(hoare_28830079triple(a),bool)] :
( ~ ord_less_eq(fun(hoare_28830079triple(a),bool),X0,ts)
| ~ pp(aa(hoare_28830079triple(a),bool,X0,sK1)) )
| spl22_48 ),
inference(resolution,[],[f4767,f550]) ).
tff(f550,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(flattening,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(ennf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X3,X2))
=> ( ord_less_eq(fun(X0,bool),X3,X1)
=> pp(aa(X0,bool,X1,X2)) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X1: $tType,X16: fun(X1,bool),X15: X1,X17: fun(X1,bool)] :
( pp(aa(X1,bool,X17,X15))
=> ( ord_less_eq(fun(X1,bool),X17,X16)
=> pp(aa(X1,bool,X16,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rev__predicate1D) ).
tff(f4767,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,ts,sK1))
| spl22_48 ),
inference(resolution,[],[f4034,f597]) ).
tff(f597,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(backward_demodulation,[],[f544,f559]) ).
tff(f559,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,[],[f230]) ).
tff(f230,plain,
! [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) ),
inference(rectify,[],[f118]) ).
tff(f118,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X53: X0,X54: X1,X52: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X52,X54),X53) = aa(X1,X2,aa(X0,fun(X1,X2),X52,X53),X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f544,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f399]) ).
tff(f399,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X9: fun(X1,bool),X15: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X15),X9))
<=> pp(aa(X1,bool,X9,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mem__def) ).
tff(f4034,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),sK1))
| spl22_48 ),
inference(avatar_component_clause,[],[f4032]) ).
tff(f4032,plain,
( spl22_48
<=> pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_48])]) ).
tff(f4764,plain,
( ~ spl22_48
| spl22_47 ),
inference(avatar_split_clause,[],[f4762,f4028,f4032]) ).
tff(f4028,plain,
( spl22_47
<=> hoare_1633586161_valid(a,sK0,sK2(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_47])]) ).
tff(f4762,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),sK1))
| spl22_47 ),
inference(resolution,[],[f4758,f405]) ).
tff(f405,plain,
~ hoare_1633586161_valid(a,sK0,sK1),
inference(cnf_transformation,[],[f340]) ).
tff(f340,plain,
( ~ hoare_1633586161_valid(a,sK0,sK1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),sK1),tsa))
& ! [X2: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,sK0,X2)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f236,f339,f338]) ).
tff(f338,plain,
( ? [X0: nat] :
( ? [X1: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),tsa)) )
& ! [X2: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X2)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ) )
=> ( ? [X1: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,sK0,X1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),tsa)) )
& ! [X2: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,sK0,X2)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f339,plain,
( ? [X1: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,sK0,X1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),tsa)) )
=> ( ~ hoare_1633586161_valid(a,sK0,sK1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),sK1),tsa)) ) ),
introduced(choice_axiom,[]) ).
tff(f236,plain,
? [X0: nat] :
( ? [X1: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),tsa)) )
& ! [X2: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X2)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
~ ! [X0: nat] :
( ! [X1: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),tsa))
=> hoare_1633586161_valid(a,X0,X1) )
| ? [X2: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X2)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ) ),
inference(rectify,[],[f123]) ).
tff(f123,negated_conjecture,
~ ! [X42: nat] :
( ! [X25: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X25),tsa))
=> hoare_1633586161_valid(a,X42,X25) )
| ? [X31: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X42,X31)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X31),ga)) ) ),
inference(negated_conjecture,[],[f122]) ).
tff(f122,conjecture,
! [X42: nat] :
( ! [X25: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X25),tsa))
=> hoare_1633586161_valid(a,X42,X25) )
| ? [X31: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X42,X31)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X31),ga)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(f4758,plain,
( ! [X0: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,sK0,X0)
| ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),X0)) )
| spl22_47 ),
inference(resolution,[],[f606,f4040]) ).
tff(f4040,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ga),sK2(sK0)))
| spl22_47 ),
inference(resolution,[],[f4036,f596]) ).
tff(f596,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2)) ),
inference(backward_demodulation,[],[f543,f559]) ).
tff(f543,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(cnf_transformation,[],[f399]) ).
tff(f4036,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,ga,sK2(sK0)))
| spl22_47 ),
inference(resolution,[],[f4030,f3505]) ).
tff(f3505,plain,
! [X0: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,sK0,X0)
| ~ pp(aa(hoare_28830079triple(a),bool,ga,X0)) ),
inference(resolution,[],[f597,f590]) ).
tff(f590,plain,
! [X2: hoare_28830079triple(a)] :
( ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ga),X2))
| hoare_1633586161_valid(a,sK0,X2) ),
inference(backward_demodulation,[],[f403,f559]) ).
tff(f403,plain,
! [X2: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,sK0,X2)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ),
inference(cnf_transformation,[],[f340]) ).
tff(f4030,plain,
( ~ hoare_1633586161_valid(a,sK0,sK2(sK0))
| spl22_47 ),
inference(avatar_component_clause,[],[f4028]) ).
tff(f606,plain,
! [X0: nat,X1: hoare_28830079triple(a)] :
( pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ga),sK2(X0)))
| ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),X1))
| hoare_1633586161_valid(a,X0,X1) ),
inference(forward_demodulation,[],[f591,f559]) ).
tff(f591,plain,
! [X0: nat,X1: hoare_28830079triple(a)] :
( pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ga),sK2(X0)))
| hoare_1633586161_valid(a,X0,X1)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ts)) ),
inference(backward_demodulation,[],[f408,f559]) ).
tff(f408,plain,
! [X0: nat,X1: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X1)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ts))
| pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),sK2(X0)),ga)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,plain,
! [X0: nat] :
( ! [X1: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X1)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ts)) )
| ( ~ hoare_1633586161_valid(a,X0,sK2(X0))
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),sK2(X0)),ga)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f341,f342]) ).
tff(f342,plain,
! [X0: nat] :
( ? [X2: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X2)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) )
=> ( ~ hoare_1633586161_valid(a,X0,sK2(X0))
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),sK2(X0)),ga)) ) ),
introduced(choice_axiom,[]) ).
tff(f341,plain,
! [X0: nat] :
( ! [X1: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X1)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ts)) )
| ? [X2: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X2)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ga)) ) ),
inference(rectify,[],[f237]) ).
tff(f237,plain,
! [X0: nat] :
( ! [X2: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X2)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ts)) )
| ? [X1: hoare_28830079triple(a)] :
( ~ hoare_1633586161_valid(a,X0,X1)
& pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ga)) ) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: nat] :
( ! [X1: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ga))
=> hoare_1633586161_valid(a,X0,X1) )
=> ! [X2: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X2),ts))
=> hoare_1633586161_valid(a,X0,X2) ) ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X55: nat] :
( ! [X25: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X25),ga))
=> hoare_1633586161_valid(a,X55,X25) )
=> ! [X31: hoare_28830079triple(a)] :
( pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X31),ts))
=> hoare_1633586161_valid(a,X55,X31) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f4035,plain,
( ~ spl22_47
| ~ spl22_48 ),
inference(avatar_split_clause,[],[f4025,f4032,f4028]) ).
tff(f4025,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),sK1))
| ~ hoare_1633586161_valid(a,sK0,sK2(sK0)) ),
inference(resolution,[],[f592,f405]) ).
tff(f592,plain,
! [X0: nat,X1: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X1)
| ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),ts),X1))
| ~ hoare_1633586161_valid(a,X0,sK2(X0)) ),
inference(backward_demodulation,[],[f409,f559]) ).
tff(f409,plain,
! [X0: nat,X1: hoare_28830079triple(a)] :
( hoare_1633586161_valid(a,X0,X1)
| ~ pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),X1),ts))
| ~ hoare_1633586161_valid(a,X0,sK2(X0)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f3588,plain,
spl22_38,
inference(avatar_contradiction_clause,[],[f3587]) ).
tff(f3587,plain,
( $false
| spl22_38 ),
inference(subsumption_resolution,[],[f3585,f589]) ).
tff(f589,plain,
pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),tsa),sK1)),
inference(backward_demodulation,[],[f404,f559]) ).
tff(f404,plain,
pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),bool),member(hoare_28830079triple(a)),sK1),tsa)),
inference(cnf_transformation,[],[f340]) ).
tff(f3585,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,combc(hoare_28830079triple(a),fun(hoare_28830079triple(a),bool),bool,member(hoare_28830079triple(a)),tsa),sK1))
| spl22_38 ),
inference(resolution,[],[f3284,f596]) ).
tff(f3284,plain,
( ~ pp(aa(hoare_28830079triple(a),bool,tsa,sK1))
| spl22_38 ),
inference(avatar_component_clause,[],[f3282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW521_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 19:30:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (26558)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (26561)WARNING: value z3 for option sas not known
% 0.15/0.38 % (26560)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (26561)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)
% 0.15/0.38 % (26562)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (26564)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)
% 0.15/0.38 % (26559)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (26563)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)
% 0.15/0.38 % (26565)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)
% 0.15/0.39 % (26565)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % (26566)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40 % (26567)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)
% 0.22/0.40 % (26568)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)
% 0.22/0.41 % (26566)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41 % (26567)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41 % Exception at run slice level
% 0.22/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (26569)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)
% 1.99/0.69 % (26568)First to succeed.
% 1.99/0.70 % (26568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26558"
% 1.99/0.70 % (26568)Refutation found. Thanks to Tanya!
% 1.99/0.70 % SZS status Theorem for theBenchmark
% 1.99/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 1.99/0.70 % (26568)------------------------------
% 1.99/0.70 % (26568)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.99/0.70 % (26568)Termination reason: Refutation
% 1.99/0.70
% 1.99/0.70 % (26568)Memory used [KB]: 2521
% 1.99/0.70 % (26568)Time elapsed: 0.293 s
% 1.99/0.70 % (26568)Instructions burned: 493 (million)
% 1.99/0.70 % (26558)Success in time 0.337 s
%------------------------------------------------------------------------------