TSTP Solution File: SWW485_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW485_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 : n010.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 17:35:22 EDT 2024
% Result : Theorem 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 267
% Syntax : Number of formulae : 693 ( 184 unt; 49 typ; 0 def)
% Number of atoms : 1704 ( 192 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1668 ( 608 ~; 592 |; 115 &)
% ( 161 <=>; 192 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 43 ( 28 >; 15 *; 0 +; 0 <<)
% Number of predicates : 135 ( 133 usr; 119 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 5 con; 0-4 aty)
% Number of variables : 1075 (1004 !; 24 ?;1075 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
poly1: $tType > $tType ).
tff(type_def_9,type,
real: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
order1:
!>[X0: $tType] : ( ( X0 * poly1(X0) ) > nat ) ).
tff(func_def_2,type,
poly:
!>[X0: $tType] : ( poly1(X0) > fun(X0,X0) ) ).
tff(func_def_3,type,
norm_norm:
!>[X0: $tType] : ( X0 > real ) ).
tff(func_def_4,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_5,type,
fFalse: bool ).
tff(func_def_6,type,
fTrue: bool ).
tff(func_def_7,type,
cs: poly1(complex) ).
tff(func_def_8,type,
r: real ).
tff(func_def_9,type,
sK1: real > complex ).
tff(func_def_10,type,
sK2:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_11,type,
sK3:
!>[X0: $tType] : ( ( X0 * X0 * X0 ) > X0 ) ).
tff(func_def_12,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_13,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_14,type,
sK6: ( real * real ) > real ).
tff(func_def_15,type,
sK7: ( nat * fun(nat,bool) ) > nat ).
tff(func_def_16,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_17,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_18,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_19,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_20,type,
sK12:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_21,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_22,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_23,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_24,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_25,type,
sK17:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_26,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_27,type,
sK19: real ).
tff(pred_def_1,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
dense_linorder:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(pred_def_16,type,
sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).
tff(f1614,plain,
$false,
inference(avatar_sat_refutation,[],[f698,f703,f708,f713,f718,f723,f728,f733,f738,f743,f748,f753,f758,f763,f768,f773,f778,f783,f788,f793,f798,f803,f808,f813,f818,f823,f828,f833,f838,f842,f846,f850,f854,f858,f862,f866,f870,f874,f878,f882,f886,f890,f894,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f947,f951,f957,f961,f965,f969,f973,f980,f996,f1000,f1004,f1008,f1012,f1016,f1020,f1024,f1028,f1032,f1088,f1095,f1099,f1103,f1107,f1164,f1168,f1181,f1185,f1189,f1193,f1197,f1201,f1206,f1210,f1214,f1317,f1321,f1327,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1360,f1364,f1460,f1464,f1468,f1484,f1488,f1506,f1510,f1514,f1518,f1554,f1558,f1563,f1570,f1574,f1600,f1607,f1613]) ).
tff(f1613,plain,
( ~ spl20_53
| spl20_113 ),
inference(avatar_contradiction_clause,[],[f1610]) ).
tff(f1610,plain,
( $false
| ~ spl20_53
| spl20_113 ),
inference(resolution,[],[f1562,f934]) ).
tff(f934,plain,
( ! [X0: real] : ord_less_eq(real,norm_norm(complex,sK1(X0)),r)
| ~ spl20_53 ),
inference(avatar_component_clause,[],[f933]) ).
tff(f933,plain,
( spl20_53
<=> ! [X0: real] : ord_less_eq(real,norm_norm(complex,sK1(X0)),r) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_53])]) ).
tff(f1562,plain,
( ~ ord_less_eq(real,norm_norm(complex,sK1(sK19)),r)
| spl20_113 ),
inference(avatar_component_clause,[],[f1560]) ).
tff(f1560,plain,
( spl20_113
<=> ord_less_eq(real,norm_norm(complex,sK1(sK19)),r) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_113])]) ).
tff(f1607,plain,
spl20_117,
inference(avatar_split_clause,[],[f647,f1605]) ).
tff(f1605,plain,
( spl20_117
<=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ord_less(nat,X1,X2)
| ( X1 = X2 )
| sP0(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_117])]) ).
tff(f647,plain,
! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ord_less(nat,X1,X2)
| ( X1 = X2 )
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f383]) ).
tff(f383,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| sP0(X2,X1,X0) ),
inference(definition_folding,[],[f379,f382]) ).
tff(f382,plain,
! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) )
| ~ sP0(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f379,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) ) ),
inference(flattening,[],[f378]) ).
tff(f378,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) ) ),
inference(ennf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( ( ord_less(nat,X2,X1)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> ( ( ( X1 = X2 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> ( ( ord_less(nat,X1,X2)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) ) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X16: fun(nat,fun(nat,bool)),X28: nat,X29: nat] :
( ( ord_less(nat,X29,X28)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X16,X28),X29)) )
=> ( ( ( X28 = X29 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X16,X28),X29)) )
=> ( ( ord_less(nat,X28,X29)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X16,X28),X29)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X16,X28),X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_nat__less__cases) ).
tff(f1600,plain,
spl20_116,
inference(avatar_split_clause,[],[f619,f1598]) ).
tff(f1598,plain,
( spl20_116
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,sK7(X0,X1)))
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_116])]) ).
tff(f619,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,sK7(X0,X1)))
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(cnf_transformation,[],[f429]) ).
tff(f429,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ( pp(aa(nat,bool,X1,sK7(X0,X1)))
& ! [X3: nat] :
( ~ pp(aa(nat,bool,X1,X3))
| ~ ord_less(nat,X3,sK7(X0,X1)) )
& ord_less_eq(nat,sK7(X0,X1),X0) )
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f364,f428]) ).
tff(f428,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ? [X2: nat] :
( pp(aa(nat,bool,X1,X2))
& ! [X3: nat] :
( ~ pp(aa(nat,bool,X1,X3))
| ~ ord_less(nat,X3,X2) )
& ord_less_eq(nat,X2,X0) )
=> ( pp(aa(nat,bool,X1,sK7(X0,X1)))
& ! [X3: nat] :
( ~ pp(aa(nat,bool,X1,X3))
| ~ ord_less(nat,X3,sK7(X0,X1)) )
& ord_less_eq(nat,sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f364,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ? [X2: nat] :
( pp(aa(nat,bool,X1,X2))
& ! [X3: nat] :
( ~ pp(aa(nat,bool,X1,X3))
| ~ ord_less(nat,X3,X2) )
& ord_less_eq(nat,X2,X0) )
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(flattening,[],[f363]) ).
tff(f363,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ? [X2: nat] :
( pp(aa(nat,bool,X1,X2))
& ! [X3: nat] :
( ~ pp(aa(nat,bool,X1,X3))
| ~ ord_less(nat,X3,X2) )
& ord_less_eq(nat,X2,X0) )
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(ennf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,zero_zero(nat)))
=> ( pp(aa(nat,bool,X1,X0))
=> ? [X2: nat] :
( pp(aa(nat,bool,X1,X2))
& ! [X3: nat] :
( ord_less(nat,X3,X2)
=> ~ pp(aa(nat,bool,X1,X3)) )
& ord_less_eq(nat,X2,X0) ) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X28: nat,X16: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X16,zero_zero(nat)))
=> ( pp(aa(nat,bool,X16,X28))
=> ? [X36: nat] :
( pp(aa(nat,bool,X16,X36))
& ! [X37: nat] :
( ord_less(nat,X37,X36)
=> ~ pp(aa(nat,bool,X16,X37)) )
& ord_less_eq(nat,X36,X28) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ex__least__nat__le) ).
tff(f1574,plain,
spl20_115,
inference(avatar_split_clause,[],[f601,f1572]) ).
tff(f1572,plain,
( spl20_115
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ord_less(fun(X1,X0),X3,X2)
| ord_less_eq(fun(X1,X0),X2,X3)
| ~ ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_115])]) ).
tff(f601,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ord_less(fun(X1,X0),X3,X2)
| ord_less_eq(fun(X1,X0),X2,X3)
| ~ ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord(X0) ),
inference(cnf_transformation,[],[f425]) ).
tff(f425,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( ord_less(fun(X1,X0),X3,X2)
| ord_less_eq(fun(X1,X0),X2,X3)
| ~ ord_less_eq(fun(X1,X0),X3,X2) )
& ( ( ~ ord_less_eq(fun(X1,X0),X2,X3)
& ord_less_eq(fun(X1,X0),X3,X2) )
| ~ ord_less(fun(X1,X0),X3,X2) ) )
| ~ ord(X0) ),
inference(flattening,[],[f424]) ).
tff(f424,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( ord_less(fun(X1,X0),X3,X2)
| ord_less_eq(fun(X1,X0),X2,X3)
| ~ ord_less_eq(fun(X1,X0),X3,X2) )
& ( ( ~ ord_less_eq(fun(X1,X0),X2,X3)
& ord_less_eq(fun(X1,X0),X3,X2) )
| ~ ord_less(fun(X1,X0),X3,X2) ) )
| ~ ord(X0) ),
inference(nnf_transformation,[],[f345]) ).
tff(f345,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ord_less(fun(X1,X0),X3,X2)
<=> ( ~ ord_less_eq(fun(X1,X0),X2,X3)
& ord_less_eq(fun(X1,X0),X3,X2) ) )
| ~ ord(X0) ),
inference(ennf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType,X1: $tType] :
( ord(X0)
=> ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ord_less(fun(X1,X0),X3,X2)
<=> ( ~ ord_less_eq(fun(X1,X0),X2,X3)
& ord_less_eq(fun(X1,X0),X3,X2) ) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X1: $tType,X0: $tType] :
( ord(X1)
=> ! [X8: fun(X0,X1),X9: fun(X0,X1)] :
( ord_less(fun(X0,X1),X9,X8)
<=> ( ~ ord_less_eq(fun(X0,X1),X8,X9)
& ord_less_eq(fun(X0,X1),X9,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__fun__def) ).
tff(f1570,plain,
spl20_114,
inference(avatar_split_clause,[],[f597,f1568]) ).
tff(f1568,plain,
( spl20_114
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X5: X1,X2: fun(X1,X0)] :
( ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
| ~ ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_114])]) ).
tff(f597,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: X1] :
( ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
| ~ ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord(X0) ),
inference(cnf_transformation,[],[f423]) ).
tff(f423,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord_less_eq(X0,aa(X1,X0,X3,sK5(X0,X1,X2,X3)),aa(X1,X0,X2,sK5(X0,X1,X2,X3))) )
& ( ! [X5: X1] : ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
| ~ ord_less_eq(fun(X1,X0),X3,X2) ) )
| ~ ord(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f421,f422]) ).
tff(f422,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ~ ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4))
=> ~ ord_less_eq(X0,aa(X1,X0,X3,sK5(X0,X1,X2,X3)),aa(X1,X0,X2,sK5(X0,X1,X2,X3))) ),
introduced(choice_axiom,[]) ).
tff(f421,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( ord_less_eq(fun(X1,X0),X3,X2)
| ? [X4: X1] : ~ ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
& ( ! [X5: X1] : ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
| ~ ord_less_eq(fun(X1,X0),X3,X2) ) )
| ~ ord(X0) ),
inference(rectify,[],[f420]) ).
tff(f420,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( ord_less_eq(fun(X1,X0),X3,X2)
| ? [X4: X1] : ~ ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
& ( ! [X4: X1] : ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4))
| ~ ord_less_eq(fun(X1,X0),X3,X2) ) )
| ~ ord(X0) ),
inference(nnf_transformation,[],[f344]) ).
tff(f344,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ord_less_eq(fun(X1,X0),X3,X2)
<=> ! [X4: X1] : ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
| ~ ord(X0) ),
inference(ennf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType,X1: $tType] :
( ord(X0)
=> ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ord_less_eq(fun(X1,X0),X3,X2)
<=> ! [X4: X1] : ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X1: $tType,X0: $tType] :
( ord(X1)
=> ! [X8: fun(X0,X1),X9: fun(X0,X1)] :
( ord_less_eq(fun(X0,X1),X9,X8)
<=> ! [X10: X0] : ord_less_eq(X1,aa(X0,X1,X9,X10),aa(X0,X1,X8,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_le__fun__def) ).
tff(f1563,plain,
( ~ spl20_113
| ~ spl20_91
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f1540,f1516,f1319,f1560]) ).
tff(f1319,plain,
( spl20_91
<=> ! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK1(X0))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_91])]) ).
tff(f1516,plain,
( spl20_110
<=> ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK19)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_110])]) ).
tff(f1540,plain,
( ~ ord_less_eq(real,norm_norm(complex,sK1(sK19)),r)
| ~ spl20_91
| ~ spl20_110 ),
inference(resolution,[],[f1517,f1320]) ).
tff(f1320,plain,
( ! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK1(X0))),X0)
| ~ spl20_91 ),
inference(avatar_component_clause,[],[f1319]) ).
tff(f1517,plain,
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK19)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
| ~ spl20_110 ),
inference(avatar_component_clause,[],[f1516]) ).
tff(f1558,plain,
spl20_112,
inference(avatar_split_clause,[],[f617,f1556]) ).
tff(f1556,plain,
( spl20_112
<=> ! [X0: nat,X1: fun(nat,bool)] :
( ord_less_eq(nat,sK7(X0,X1),X0)
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_112])]) ).
tff(f617,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ord_less_eq(nat,sK7(X0,X1),X0)
| ~ pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(cnf_transformation,[],[f429]) ).
tff(f1554,plain,
spl20_111,
inference(avatar_split_clause,[],[f516,f1552]) ).
tff(f1552,plain,
( spl20_111
<=> ! [X0: $tType,X2: poly1(X0),X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
| ( zero_zero(nat) = order1(X0,X1,X2) )
| ~ idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_111])]) ).
tff(f516,plain,
! [X0: $tType,X2: poly1(X0),X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
| ( zero_zero(nat) = order1(X0,X1,X2) )
| ~ idom(X0) ),
inference(cnf_transformation,[],[f394]) ).
tff(f394,plain,
! [X0: $tType] :
( ! [X1: X0,X2: poly1(X0)] :
( ( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
| ( ( zero_zero(nat) = order1(X0,X1,X2) )
& ( zero_zero(poly1(X0)) != X2 ) ) )
& ( ( zero_zero(nat) != order1(X0,X1,X2) )
| ( zero_zero(poly1(X0)) = X2 )
| ( zero_zero(X0) != aa(X0,X0,poly(X0,X2),X1) ) ) )
| ~ idom(X0) ),
inference(flattening,[],[f393]) ).
tff(f393,plain,
! [X0: $tType] :
( ! [X1: X0,X2: poly1(X0)] :
( ( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
| ( ( zero_zero(nat) = order1(X0,X1,X2) )
& ( zero_zero(poly1(X0)) != X2 ) ) )
& ( ( zero_zero(nat) != order1(X0,X1,X2) )
| ( zero_zero(poly1(X0)) = X2 )
| ( zero_zero(X0) != aa(X0,X0,poly(X0,X2),X1) ) ) )
| ~ idom(X0) ),
inference(nnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0,X2: poly1(X0)] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
<=> ( ( zero_zero(nat) != order1(X0,X1,X2) )
| ( zero_zero(poly1(X0)) = X2 ) ) )
| ~ idom(X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType] :
( idom(X0)
=> ! [X1: X0,X2: poly1(X0)] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
<=> ( ( zero_zero(nat) != order1(X0,X1,X2) )
| ( zero_zero(poly1(X0)) = X2 ) ) ) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X0: $tType] :
( idom(X0)
=> ! [X21: X0,X6: poly1(X0)] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,X6),X21) )
<=> ( ( order1(X0,X21,X6) != zero_zero(nat) )
| ( zero_zero(poly1(X0)) = X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_order__root) ).
tff(f1518,plain,
spl20_110,
inference(avatar_split_clause,[],[f653,f1516]) ).
tff(f653,plain,
! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK19)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) ),
inference(cnf_transformation,[],[f453]) ).
tff(f453,plain,
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK19)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f381,f452]) ).
tff(f452,plain,
( ? [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),X0) )
=> ( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK19)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),sK19) ) ),
introduced(choice_axiom,[]) ).
tff(f381,plain,
? [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) )
& ord_less(real,zero_zero(real),X0) ),
inference(ennf_transformation,[],[f254]) ).
tff(f254,plain,
? [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,X1),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
& ord_less(real,zero_zero(real),X0) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
? [X2: real] :
( ! [X3: complex] :
( ord_less_eq(real,norm_norm(complex,X3),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X3)),X2) )
& ord_less(real,zero_zero(real),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_pCons) ).
tff(f1514,plain,
spl20_109,
inference(avatar_split_clause,[],[f497,f1512]) ).
tff(f1512,plain,
( spl20_109
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,sK3(X0,X1,X2,X3),X1)
| ~ ord_less(X0,X3,X2)
| ~ dense_linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_109])]) ).
tff(f497,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,sK3(X0,X1,X2,X3),X1)
| ~ ord_less(X0,X3,X2)
| ~ dense_linorder(X0) ),
inference(cnf_transformation,[],[f389]) ).
tff(f389,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X2,X1)
| ( ~ ord_less_eq(X0,sK3(X0,X1,X2,X3),X1)
& ord_less(X0,sK3(X0,X1,X2,X3),X2)
& ord_less(X0,X3,sK3(X0,X1,X2,X3)) )
| ~ ord_less(X0,X3,X2) )
| ~ dense_linorder(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f258,f388]) ).
tff(f388,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0] :
( ? [X4: X0] :
( ~ ord_less_eq(X0,X4,X1)
& ord_less(X0,X4,X2)
& ord_less(X0,X3,X4) )
=> ( ~ ord_less_eq(X0,sK3(X0,X1,X2,X3),X1)
& ord_less(X0,sK3(X0,X1,X2,X3),X2)
& ord_less(X0,X3,sK3(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X2,X1)
| ? [X4: X0] :
( ~ ord_less_eq(X0,X4,X1)
& ord_less(X0,X4,X2)
& ord_less(X0,X3,X4) )
| ~ ord_less(X0,X3,X2) )
| ~ dense_linorder(X0) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X2,X1)
| ? [X4: X0] :
( ~ ord_less_eq(X0,X4,X1)
& ord_less(X0,X4,X2)
& ord_less(X0,X3,X4) )
| ~ ord_less(X0,X3,X2) )
| ~ dense_linorder(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( dense_linorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X2)
=> ( ! [X4: X0] :
( ord_less(X0,X3,X4)
=> ( ord_less(X0,X4,X2)
=> ord_less_eq(X0,X4,X1) ) )
=> ord_less_eq(X0,X2,X1) ) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType] :
( dense_linorder(X0)
=> ! [X17: X0,X11: X0,X4: X0] :
( ord_less(X0,X4,X11)
=> ( ! [X23: X0] :
( ord_less(X0,X4,X23)
=> ( ord_less(X0,X23,X11)
=> ord_less_eq(X0,X23,X17) ) )
=> ord_less_eq(X0,X11,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dense__le__bounded) ).
tff(f1510,plain,
spl20_108,
inference(avatar_split_clause,[],[f496,f1508]) ).
tff(f1508,plain,
( spl20_108
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less(X0,sK3(X0,X1,X2,X3),X2)
| ~ ord_less(X0,X3,X2)
| ~ dense_linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_108])]) ).
tff(f496,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less(X0,sK3(X0,X1,X2,X3),X2)
| ~ ord_less(X0,X3,X2)
| ~ dense_linorder(X0) ),
inference(cnf_transformation,[],[f389]) ).
tff(f1506,plain,
spl20_107,
inference(avatar_split_clause,[],[f495,f1504]) ).
tff(f1504,plain,
( spl20_107
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less(X0,X3,sK3(X0,X1,X2,X3))
| ~ ord_less(X0,X3,X2)
| ~ dense_linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_107])]) ).
tff(f495,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less(X0,X3,sK3(X0,X1,X2,X3))
| ~ ord_less(X0,X3,X2)
| ~ dense_linorder(X0) ),
inference(cnf_transformation,[],[f389]) ).
tff(f1488,plain,
spl20_106,
inference(avatar_split_clause,[],[f614,f1486]) ).
tff(f1486,plain,
( spl20_106
<=> ! [X0: real,X1: real] :
( ord_less(real,zero_zero(real),sK6(X0,X1))
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_106])]) ).
tff(f614,plain,
! [X0: real,X1: real] :
( ord_less(real,zero_zero(real),sK6(X0,X1))
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ),
inference(cnf_transformation,[],[f427]) ).
tff(f427,plain,
! [X0: real,X1: real] :
( ( ord_less(real,sK6(X0,X1),X0)
& ord_less(real,sK6(X0,X1),X1)
& ord_less(real,zero_zero(real),sK6(X0,X1)) )
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f362,f426]) ).
tff(f426,plain,
! [X0: real,X1: real] :
( ? [X2: real] :
( ord_less(real,X2,X0)
& ord_less(real,X2,X1)
& ord_less(real,zero_zero(real),X2) )
=> ( ord_less(real,sK6(X0,X1),X0)
& ord_less(real,sK6(X0,X1),X1)
& ord_less(real,zero_zero(real),sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f362,plain,
! [X0: real,X1: real] :
( ? [X2: real] :
( ord_less(real,X2,X0)
& ord_less(real,X2,X1)
& ord_less(real,zero_zero(real),X2) )
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ),
inference(flattening,[],[f361]) ).
tff(f361,plain,
! [X0: real,X1: real] :
( ? [X2: real] :
( ord_less(real,X2,X0)
& ord_less(real,X2,X1)
& ord_less(real,zero_zero(real),X2) )
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ),
inference(ennf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: real,X1: real] :
( ord_less(real,zero_zero(real),X1)
=> ( ord_less(real,zero_zero(real),X0)
=> ? [X2: real] :
( ord_less(real,X2,X0)
& ord_less(real,X2,X1)
& ord_less(real,zero_zero(real),X2) ) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X24: real,X25: real] :
( ord_less(real,zero_zero(real),X25)
=> ( ord_less(real,zero_zero(real),X24)
=> ? [X26: real] :
( ord_less(real,X26,X24)
& ord_less(real,X26,X25)
& ord_less(real,zero_zero(real),X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_real__lbound__gt__zero) ).
tff(f1484,plain,
spl20_105,
inference(avatar_split_clause,[],[f588,f1482]) ).
tff(f1482,plain,
( spl20_105
<=> ! [X0: $tType,X2: poly1(X0),X1: poly1(X0)] :
( ( X1 = X2 )
| ( poly(X0,X2) != poly(X0,X1) )
| ~ idom(X0)
| ~ ring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_105])]) ).
tff(f588,plain,
! [X0: $tType,X2: poly1(X0),X1: poly1(X0)] :
( ( X1 = X2 )
| ( poly(X0,X2) != poly(X0,X1) )
| ~ idom(X0)
| ~ ring_char_0(X0) ),
inference(cnf_transformation,[],[f415]) ).
tff(f415,plain,
! [X0: $tType] :
( ! [X1: poly1(X0),X2: poly1(X0)] :
( ( ( poly(X0,X2) = poly(X0,X1) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( poly(X0,X2) != poly(X0,X1) ) ) )
| ~ idom(X0)
| ~ ring_char_0(X0) ),
inference(nnf_transformation,[],[f341]) ).
tff(f341,plain,
! [X0: $tType] :
( ! [X1: poly1(X0),X2: poly1(X0)] :
( ( poly(X0,X2) = poly(X0,X1) )
<=> ( X1 = X2 ) )
| ~ idom(X0)
| ~ ring_char_0(X0) ),
inference(flattening,[],[f340]) ).
tff(f340,plain,
! [X0: $tType] :
( ! [X1: poly1(X0),X2: poly1(X0)] :
( ( poly(X0,X2) = poly(X0,X1) )
<=> ( X1 = X2 ) )
| ~ idom(X0)
| ~ ring_char_0(X0) ),
inference(ennf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ( idom(X0)
& ring_char_0(X0) )
=> ! [X1: poly1(X0),X2: poly1(X0)] :
( ( poly(X0,X2) = poly(X0,X1) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType] :
( ( idom(X0)
& ring_char_0(X0) )
=> ! [X5: poly1(X0),X6: poly1(X0)] :
( ( poly(X0,X6) = poly(X0,X5) )
<=> ( X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_poly__eq__iff) ).
tff(f1468,plain,
spl20_104,
inference(avatar_split_clause,[],[f646,f1466]) ).
tff(f1466,plain,
( spl20_104
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_104])]) ).
tff(f646,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f449]) ).
tff(f449,plain,
! [X0: nat,X1: nat,X2: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
& ord_less(nat,X0,X1) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f448]) ).
tff(f448,plain,
! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) )
| ~ sP0(X2,X1,X0) ),
inference(nnf_transformation,[],[f382]) ).
tff(f1464,plain,
spl20_103,
inference(avatar_split_clause,[],[f616,f1462]) ).
tff(f1462,plain,
( spl20_103
<=> ! [X0: real,X1: real] :
( ord_less(real,sK6(X0,X1),X0)
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_103])]) ).
tff(f616,plain,
! [X0: real,X1: real] :
( ord_less(real,sK6(X0,X1),X0)
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ),
inference(cnf_transformation,[],[f427]) ).
tff(f1460,plain,
spl20_102,
inference(avatar_split_clause,[],[f615,f1458]) ).
tff(f1458,plain,
( spl20_102
<=> ! [X0: real,X1: real] :
( ord_less(real,sK6(X0,X1),X1)
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_102])]) ).
tff(f615,plain,
! [X0: real,X1: real] :
( ord_less(real,sK6(X0,X1),X1)
| ~ ord_less(real,zero_zero(real),X0)
| ~ ord_less(real,zero_zero(real),X1) ),
inference(cnf_transformation,[],[f427]) ).
tff(f1364,plain,
spl20_101,
inference(avatar_split_clause,[],[f657,f1362]) ).
tff(f1362,plain,
( spl20_101
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_101])]) ).
tff(f657,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ idom(X0) ),
inference(equality_resolution,[],[f515]) ).
tff(f515,plain,
! [X0: $tType,X2: poly1(X0),X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,X2),X1) )
| ( zero_zero(poly1(X0)) != X2 )
| ~ idom(X0) ),
inference(cnf_transformation,[],[f394]) ).
tff(f1360,plain,
( ~ spl20_25
| ~ spl20_100
| ~ spl20_44
| ~ spl20_68 ),
inference(avatar_split_clause,[],[f1063,f1010,f896,f1357,f815]) ).
tff(f815,plain,
( spl20_25
<=> preorder(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_25])]) ).
tff(f1357,plain,
( spl20_100
<=> ord_less(real,sK19,zero_zero(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_100])]) ).
tff(f896,plain,
( spl20_44
<=> ord_less(real,zero_zero(real),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_44])]) ).
tff(f1010,plain,
( spl20_68
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_68])]) ).
tff(f1063,plain,
( ~ ord_less(real,sK19,zero_zero(real))
| ~ preorder(real)
| ~ spl20_44
| ~ spl20_68 ),
inference(resolution,[],[f1011,f898]) ).
tff(f898,plain,
( ord_less(real,zero_zero(real),sK19)
| ~ spl20_44 ),
inference(avatar_component_clause,[],[f896]) ).
tff(f1011,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X1,X2)
| ~ preorder(X0) )
| ~ spl20_68 ),
inference(avatar_component_clause,[],[f1010]) ).
tff(f1355,plain,
spl20_99,
inference(avatar_split_clause,[],[f600,f1353]) ).
tff(f1353,plain,
( spl20_99
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ~ ord_less_eq(fun(X1,X0),X2,X3)
| ~ ord_less(fun(X1,X0),X3,X2)
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_99])]) ).
tff(f600,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ~ ord_less_eq(fun(X1,X0),X2,X3)
| ~ ord_less(fun(X1,X0),X3,X2)
| ~ ord(X0) ),
inference(cnf_transformation,[],[f425]) ).
tff(f1351,plain,
spl20_98,
inference(avatar_split_clause,[],[f599,f1349]) ).
tff(f1349,plain,
( spl20_98
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord_less(fun(X1,X0),X3,X2)
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_98])]) ).
tff(f599,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ord_less_eq(fun(X1,X0),X3,X2)
| ~ ord_less(fun(X1,X0),X3,X2)
| ~ ord(X0) ),
inference(cnf_transformation,[],[f425]) ).
tff(f1347,plain,
spl20_97,
inference(avatar_split_clause,[],[f566,f1345]) ).
tff(f1345,plain,
( spl20_97
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_97])]) ).
tff(f566,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2) )
| ~ preorder(X0) ),
inference(flattening,[],[f320]) ).
tff(f320,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X2)
=> ( ord_less(X0,X2,X1)
=> ord_less(X0,X3,X1) ) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X17: X0,X11: X0,X4: X0] :
( ord_less(X0,X4,X11)
=> ( ord_less(X0,X11,X17)
=> ord_less(X0,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_order__less__trans) ).
tff(f1343,plain,
spl20_96,
inference(avatar_split_clause,[],[f564,f1341]) ).
tff(f1341,plain,
( spl20_96
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X3,X2)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_96])]) ).
tff(f564,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X3,X2)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X3,X2) )
| ~ preorder(X0) ),
inference(flattening,[],[f316]) ).
tff(f316,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X3,X2) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X2)
=> ( ord_less_eq(X0,X2,X1)
=> ord_less(X0,X3,X1) ) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X17: X0,X11: X0,X4: X0] :
( ord_less(X0,X4,X11)
=> ( ord_less_eq(X0,X11,X17)
=> ord_less(X0,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_order__less__le__trans) ).
tff(f1339,plain,
spl20_95,
inference(avatar_split_clause,[],[f563,f1337]) ).
tff(f1337,plain,
( spl20_95
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_95])]) ).
tff(f563,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2) )
| ~ preorder(X0) ),
inference(flattening,[],[f314]) ).
tff(f314,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X3,X2)
=> ( ord_less(X0,X2,X1)
=> ord_less(X0,X3,X1) ) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X17: X0,X11: X0,X4: X0] :
( ord_less_eq(X0,X4,X11)
=> ( ord_less(X0,X11,X17)
=> ord_less(X0,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_order__le__less__trans) ).
tff(f1335,plain,
spl20_94,
inference(avatar_split_clause,[],[f562,f1333]) ).
tff(f1333,plain,
( spl20_94
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_94])]) ).
tff(f562,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2) )
| ~ preorder(X0) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X3,X1)
| ~ ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,X3,X2) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less_eq(X0,X3,X2)
=> ( ord_less_eq(X0,X2,X1)
=> ord_less_eq(X0,X3,X1) ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X17: X0,X11: X0,X4: X0] :
( ord_less_eq(X0,X4,X11)
=> ( ord_less_eq(X0,X11,X17)
=> ord_less_eq(X0,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_order__trans) ).
tff(f1331,plain,
spl20_93,
inference(avatar_split_clause,[],[f561,f1329]) ).
tff(f1329,plain,
( spl20_93
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_93])]) ).
tff(f561,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f406]) ).
tff(f406,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less(X0,X2,X1)
| ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
& ( ( ~ ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) )
| ~ ord_less(X0,X2,X1) ) )
| ~ preorder(X0) ),
inference(flattening,[],[f405]) ).
tff(f405,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less(X0,X2,X1)
| ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
& ( ( ~ ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) )
| ~ ord_less(X0,X2,X1) ) )
| ~ preorder(X0) ),
inference(nnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
<=> ( ~ ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) ) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
<=> ( ~ ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) ) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X12: X0,X7: X0] :
( ord_less(X0,X7,X12)
<=> ( ~ ord_less_eq(X0,X12,X7)
& ord_less_eq(X0,X7,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__le__not__le) ).
tff(f1327,plain,
spl20_92,
inference(avatar_split_clause,[],[f519,f1325]) ).
tff(f1325,plain,
( spl20_92
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ comm_semiring_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_92])]) ).
tff(f519,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X1: X0] : ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X4: X0] : ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_poly__0) ).
tff(f1321,plain,
( spl20_91
| spl20_1 ),
inference(avatar_split_clause,[],[f456,f695,f1319]) ).
tff(f695,plain,
( spl20_1
<=> thesis ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
tff(f456,plain,
! [X0: real] :
( thesis
| ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK1(X0))),X0) ),
inference(cnf_transformation,[],[f385]) ).
tff(f385,plain,
! [X0: real] :
( thesis
| ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK1(X0))),X0)
& ord_less_eq(real,norm_norm(complex,sK1(X0)),r) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f255,f384]) ).
tff(f384,plain,
! [X0: real] :
( ? [X1: complex] :
( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
& ord_less_eq(real,norm_norm(complex,X1),r) )
=> ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK1(X0))),X0)
& ord_less_eq(real,norm_norm(complex,sK1(X0)),r) ) ),
introduced(choice_axiom,[]) ).
tff(f255,plain,
! [X0: real] :
( thesis
| ? [X1: complex] :
( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
& ord_less_eq(real,norm_norm(complex,X1),r) ) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,X1),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
=> thesis ),
inference(rectify,[],[f140]) ).
tff(f140,axiom,
! [X40: real] :
( ! [X41: complex] :
( ord_less_eq(real,norm_norm(complex,X41),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X41)),X40) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f1317,plain,
( spl20_90
| ~ spl20_6
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f975,f955,f720,f1314]) ).
tff(f1314,plain,
( spl20_90
<=> ( zero_zero(real) = norm_norm(real,zero_zero(real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_90])]) ).
tff(f720,plain,
( spl20_6
<=> real_normed_vector(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_6])]) ).
tff(f955,plain,
( spl20_58
<=> ! [X0: $tType] :
( ( zero_zero(real) = norm_norm(X0,zero_zero(X0)) )
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_58])]) ).
tff(f975,plain,
( ( zero_zero(real) = norm_norm(real,zero_zero(real)) )
| ~ spl20_6
| ~ spl20_58 ),
inference(resolution,[],[f956,f722]) ).
tff(f722,plain,
( real_normed_vector(real)
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f720]) ).
tff(f956,plain,
( ! [X0: $tType] :
( ~ real_normed_vector(X0)
| ( zero_zero(real) = norm_norm(X0,zero_zero(X0)) ) )
| ~ spl20_58 ),
inference(avatar_component_clause,[],[f955]) ).
tff(f1214,plain,
spl20_89,
inference(avatar_split_clause,[],[f570,f1212]) ).
tff(f1212,plain,
( spl20_89
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_89])]) ).
tff(f570,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1)
| ~ order(X0) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
| ~ order(X0) ),
inference(flattening,[],[f328]) ).
tff(f328,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
=> ( ord_less_eq(X0,X1,X2)
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X11: X0,X4: X0] :
( ord_less_eq(X0,X4,X11)
=> ( ord_less_eq(X0,X11,X4)
=> ( X4 = X11 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_order__antisym) ).
tff(f1210,plain,
spl20_88,
inference(avatar_split_clause,[],[f567,f1208]) ).
tff(f1208,plain,
( spl20_88
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X2,X1)
| ( X1 = X2 )
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_88])]) ).
tff(f567,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X2,X1)
| ( X1 = X2 )
| ~ order(X0) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X2,X1)
| ( X1 = X2 ) )
| ~ order(X0) ),
inference(flattening,[],[f322]) ).
tff(f322,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X2,X1)
| ( X1 = X2 ) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 != X2 )
=> ( ord_less_eq(X0,X2,X1)
=> ord_less(X0,X2,X1) ) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X14: X0,X15: X0] :
( ( X14 != X15 )
=> ( ord_less_eq(X0,X15,X14)
=> ord_less(X0,X15,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_order__neq__le__trans) ).
tff(f1206,plain,
( spl20_87
| ~ spl20_4
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f974,f955,f710,f1203]) ).
tff(f1203,plain,
( spl20_87
<=> ( zero_zero(real) = norm_norm(complex,zero_zero(complex)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_87])]) ).
tff(f710,plain,
( spl20_4
<=> real_normed_vector(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_4])]) ).
tff(f974,plain,
( ( zero_zero(real) = norm_norm(complex,zero_zero(complex)) )
| ~ spl20_4
| ~ spl20_58 ),
inference(resolution,[],[f956,f712]) ).
tff(f712,plain,
( real_normed_vector(complex)
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f1201,plain,
spl20_86,
inference(avatar_split_clause,[],[f532,f1199]) ).
tff(f1199,plain,
( spl20_86
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,X2,X1)
| ord_less(X0,X2,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_86])]) ).
tff(f532,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,X2,X1)
| ord_less(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f397]) ).
tff(f397,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( ord_less_eq(X0,X2,X1)
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ ord_less_eq(X0,X2,X1) ) )
| ord_less(X0,X2,X1) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less_eq(X0,X2,X1)
<=> ( X1 = X2 ) )
| ord_less(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
=> ( ord_less_eq(X0,X2,X1)
<=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X12: X0,X7: X0] :
( ~ ord_less(X0,X7,X12)
=> ( ord_less_eq(X0,X7,X12)
<=> ( X7 = X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_linorder__antisym__conv1) ).
tff(f1197,plain,
spl20_85,
inference(avatar_split_clause,[],[f524,f1195]) ).
tff(f1195,plain,
( spl20_85
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_85])]) ).
tff(f524,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X11: X0,X4: X0] :
( ord_less(X0,X11,X4)
| ( X4 = X11 )
| ord_less(X0,X4,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_linorder__less__linear) ).
tff(f1193,plain,
spl20_84,
inference(avatar_split_clause,[],[f512,f1191]) ).
tff(f1191,plain,
( spl20_84
<=> ! [X0: $tType,X1: X0] :
( ord_less(real,zero_zero(real),norm_norm(X0,X1))
| ( zero_zero(X0) = X1 )
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_84])]) ).
tff(f512,plain,
! [X0: $tType,X1: X0] :
( ord_less(real,zero_zero(real),norm_norm(X0,X1))
| ( zero_zero(X0) = X1 )
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f392]) ).
tff(f392,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(real,zero_zero(real),norm_norm(X0,X1))
| ( zero_zero(X0) = X1 ) )
& ( ( zero_zero(X0) != X1 )
| ~ ord_less(real,zero_zero(real),norm_norm(X0,X1)) ) )
| ~ real_normed_vector(X0) ),
inference(nnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(real,zero_zero(real),norm_norm(X0,X1))
<=> ( zero_zero(X0) != X1 ) )
| ~ real_normed_vector(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X1: X0] :
( ord_less(real,zero_zero(real),norm_norm(X0,X1))
<=> ( zero_zero(X0) != X1 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X7: X0] :
( ord_less(real,zero_zero(real),norm_norm(X0,X7))
<=> ( zero_zero(X0) != X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__less__norm__iff) ).
tff(f1189,plain,
spl20_83,
inference(avatar_split_clause,[],[f509,f1187]) ).
tff(f1187,plain,
( spl20_83
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ ord_less_eq(real,norm_norm(X0,X1),zero_zero(real))
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_83])]) ).
tff(f509,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ ord_less_eq(real,norm_norm(X0,X1),zero_zero(real))
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f391]) ).
tff(f391,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less_eq(real,norm_norm(X0,X1),zero_zero(real))
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ~ ord_less_eq(real,norm_norm(X0,X1),zero_zero(real)) ) )
| ~ real_normed_vector(X0) ),
inference(nnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less_eq(real,norm_norm(X0,X1),zero_zero(real))
<=> ( zero_zero(X0) = X1 ) )
| ~ real_normed_vector(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X1: X0] :
( ord_less_eq(real,norm_norm(X0,X1),zero_zero(real))
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X7: X0] :
( ord_less_eq(real,norm_norm(X0,X7),zero_zero(real))
<=> ( zero_zero(X0) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_norm__le__zero__iff) ).
tff(f1185,plain,
spl20_82,
inference(avatar_split_clause,[],[f494,f1183]) ).
tff(f1183,plain,
( spl20_82
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,sK2(X0,X1,X2),X1)
| ~ dense_linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_82])]) ).
tff(f494,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,sK2(X0,X1,X2),X1)
| ~ dense_linorder(X0) ),
inference(cnf_transformation,[],[f387]) ).
tff(f387,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
| ( ~ ord_less_eq(X0,sK2(X0,X1,X2),X1)
& ord_less(X0,sK2(X0,X1,X2),X2) ) )
| ~ dense_linorder(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f256,f386]) ).
tff(f386,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ? [X3: X0] :
( ~ ord_less_eq(X0,X3,X1)
& ord_less(X0,X3,X2) )
=> ( ~ ord_less_eq(X0,sK2(X0,X1,X2),X1)
& ord_less(X0,sK2(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
tff(f256,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
| ? [X3: X0] :
( ~ ord_less_eq(X0,X3,X1)
& ord_less(X0,X3,X2) ) )
| ~ dense_linorder(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( dense_linorder(X0)
=> ! [X1: X0,X2: X0] :
( ! [X3: X0] :
( ord_less(X0,X3,X2)
=> ord_less_eq(X0,X3,X1) )
=> ord_less_eq(X0,X2,X1) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( dense_linorder(X0)
=> ! [X17: X0,X11: X0] :
( ! [X18: X0] :
( ord_less(X0,X18,X11)
=> ord_less_eq(X0,X18,X17) )
=> ord_less_eq(X0,X11,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_dense__le) ).
tff(f1181,plain,
spl20_81,
inference(avatar_split_clause,[],[f493,f1179]) ).
tff(f1179,plain,
( spl20_81
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less(X0,sK2(X0,X1,X2),X2)
| ~ dense_linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_81])]) ).
tff(f493,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less(X0,sK2(X0,X1,X2),X2)
| ~ dense_linorder(X0) ),
inference(cnf_transformation,[],[f387]) ).
tff(f1168,plain,
spl20_80,
inference(avatar_split_clause,[],[f644,f1166]) ).
tff(f1166,plain,
( spl20_80
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less_eq(nat,X2,X0)
| ~ ord_less_eq(nat,X1,X0)
| ~ ord_less_eq(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_80])]) ).
tff(f644,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less_eq(nat,X2,X0)
| ~ ord_less_eq(nat,X1,X0)
| ~ ord_less_eq(nat,X2,X1) ),
inference(cnf_transformation,[],[f377]) ).
tff(f377,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less_eq(nat,X2,X0)
| ~ ord_less_eq(nat,X1,X0)
| ~ ord_less_eq(nat,X2,X1) ),
inference(flattening,[],[f376]) ).
tff(f376,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less_eq(nat,X2,X0)
| ~ ord_less_eq(nat,X1,X0)
| ~ ord_less_eq(nat,X2,X1) ),
inference(ennf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less_eq(nat,X2,X1)
=> ( ord_less_eq(nat,X1,X0)
=> ord_less_eq(nat,X2,X0) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X33: nat,X34: nat,X35: nat] :
( ord_less_eq(nat,X35,X34)
=> ( ord_less_eq(nat,X34,X33)
=> ord_less_eq(nat,X35,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_le__trans) ).
tff(f1164,plain,
spl20_79,
inference(avatar_split_clause,[],[f507,f1162]) ).
tff(f1162,plain,
( spl20_79
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(real) != norm_norm(X0,X1) )
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_79])]) ).
tff(f507,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(real) != norm_norm(X0,X1) )
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f390]) ).
tff(f390,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(real) = norm_norm(X0,X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(real) != norm_norm(X0,X1) ) ) )
| ~ real_normed_vector(X0) ),
inference(nnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(real) = norm_norm(X0,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ real_normed_vector(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X1: X0] :
( ( zero_zero(real) = norm_norm(X0,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X7: X0] :
( ( zero_zero(real) = norm_norm(X0,X7) )
<=> ( zero_zero(X0) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_norm__eq__zero) ).
tff(f1107,plain,
spl20_78,
inference(avatar_split_clause,[],[f635,f1105]) ).
tff(f1105,plain,
( spl20_78
<=> ! [X0: real,X1: real] :
( ( X0 = X1 )
| ord_less(real,X1,X0)
| ~ ord_less_eq(real,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_78])]) ).
tff(f635,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ord_less(real,X1,X0)
| ~ ord_less_eq(real,X1,X0) ),
inference(cnf_transformation,[],[f443]) ).
tff(f443,plain,
! [X0: real,X1: real] :
( ( ord_less_eq(real,X1,X0)
| ( ( X0 != X1 )
& ~ ord_less(real,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(real,X1,X0)
| ~ ord_less_eq(real,X1,X0) ) ),
inference(flattening,[],[f442]) ).
tff(f442,plain,
! [X0: real,X1: real] :
( ( ord_less_eq(real,X1,X0)
| ( ( X0 != X1 )
& ~ ord_less(real,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(real,X1,X0)
| ~ ord_less_eq(real,X1,X0) ) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: real,X1: real] :
( ord_less_eq(real,X1,X0)
<=> ( ( X0 = X1 )
| ord_less(real,X1,X0) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X12: real,X7: real] :
( ord_less_eq(real,X7,X12)
<=> ( ( X7 = X12 )
| ord_less(real,X7,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__eq__real__def) ).
tff(f1103,plain,
spl20_77,
inference(avatar_split_clause,[],[f609,f1101]) ).
tff(f1101,plain,
( spl20_77
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ ord_less_eq(nat,X0,X1)
| ~ ord_less_eq(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_77])]) ).
tff(f609,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ ord_less_eq(nat,X0,X1)
| ~ ord_less_eq(nat,X1,X0) ),
inference(cnf_transformation,[],[f356]) ).
tff(f356,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ ord_less_eq(nat,X0,X1)
| ~ ord_less_eq(nat,X1,X0) ),
inference(flattening,[],[f355]) ).
tff(f355,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ~ ord_less_eq(nat,X0,X1)
| ~ ord_less_eq(nat,X1,X0) ),
inference(ennf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
=> ( ord_less_eq(nat,X0,X1)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X27: nat,X30: nat] :
( ord_less_eq(nat,X30,X27)
=> ( ord_less_eq(nat,X27,X30)
=> ( X27 = X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_le__antisym) ).
tff(f1099,plain,
spl20_76,
inference(avatar_split_clause,[],[f608,f1097]) ).
tff(f1097,plain,
( spl20_76
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_76])]) ).
tff(f608,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(nat,X1,X0) ),
inference(cnf_transformation,[],[f354]) ).
tff(f354,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(nat,X1,X0) ),
inference(flattening,[],[f353]) ).
tff(f353,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(nat,X1,X0) ),
inference(ennf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
=> ( ( X0 != X1 )
=> ord_less(nat,X1,X0) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X27: nat,X30: nat] :
( ord_less_eq(nat,X30,X27)
=> ( ( X27 != X30 )
=> ord_less(nat,X30,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_le__neq__implies__less) ).
tff(f1095,plain,
spl20_75,
inference(avatar_split_clause,[],[f606,f1093]) ).
tff(f1093,plain,
( spl20_75
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_75])]) ).
tff(f606,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f351]) ).
tff(f351,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(flattening,[],[f350]) ).
tff(f350,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ord_less(nat,X1,X0)
=> ord_less(nat,X0,X1) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X11: nat,X4: nat] :
( ( X4 != X11 )
=> ( ~ ord_less(nat,X4,X11)
=> ord_less(nat,X11,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_linorder__neqE__nat) ).
tff(f1088,plain,
( spl20_74
| ~ spl20_64 ),
inference(avatar_split_clause,[],[f1035,f994,f1086]) ).
tff(f1086,plain,
( spl20_74
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_74])]) ).
tff(f994,plain,
( spl20_64
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X1,X2)
| ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_64])]) ).
tff(f1035,plain,
( ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,X1)
| ~ linorder(X0) )
| ~ spl20_64 ),
inference(factoring,[],[f995]) ).
tff(f995,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ord_less_eq(X0,X1,X2)
| ~ linorder(X0) )
| ~ spl20_64 ),
inference(avatar_component_clause,[],[f994]) ).
tff(f1032,plain,
spl20_73,
inference(avatar_split_clause,[],[f656,f1030]) ).
tff(f1030,plain,
( spl20_73
<=> ! [X0: $tType] :
( ~ ord_less(real,zero_zero(real),norm_norm(X0,zero_zero(X0)))
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_73])]) ).
tff(f656,plain,
! [X0: $tType] :
( ~ ord_less(real,zero_zero(real),norm_norm(X0,zero_zero(X0)))
| ~ real_normed_vector(X0) ),
inference(equality_resolution,[],[f511]) ).
tff(f511,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != X1 )
| ~ ord_less(real,zero_zero(real),norm_norm(X0,X1))
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f392]) ).
tff(f1028,plain,
spl20_72,
inference(avatar_split_clause,[],[f655,f1026]) ).
tff(f1026,plain,
( spl20_72
<=> ! [X0: $tType] :
( ord_less_eq(real,norm_norm(X0,zero_zero(X0)),zero_zero(real))
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_72])]) ).
tff(f655,plain,
! [X0: $tType] :
( ord_less_eq(real,norm_norm(X0,zero_zero(X0)),zero_zero(real))
| ~ real_normed_vector(X0) ),
inference(equality_resolution,[],[f510]) ).
tff(f510,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(real,norm_norm(X0,X1),zero_zero(real))
| ( zero_zero(X0) != X1 )
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f391]) ).
tff(f1024,plain,
spl20_71,
inference(avatar_split_clause,[],[f580,f1022]) ).
tff(f1022,plain,
( spl20_71
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X2,X1)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_71])]) ).
tff(f580,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X2,X1)
| ~ order(X0) ),
inference(cnf_transformation,[],[f411]) ).
tff(f411,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less_eq(X0,X2,X1)
| ( ( X1 != X2 )
& ~ ord_less(X0,X2,X1) ) )
& ( ( X1 = X2 )
| ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X2,X1) ) )
| ~ order(X0) ),
inference(flattening,[],[f410]) ).
tff(f410,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less_eq(X0,X2,X1)
| ( ( X1 != X2 )
& ~ ord_less(X0,X2,X1) ) )
& ( ( X1 = X2 )
| ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X2,X1) ) )
| ~ order(X0) ),
inference(nnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
<=> ( ( X1 = X2 )
| ord_less(X0,X2,X1) ) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
<=> ( ( X1 = X2 )
| ord_less(X0,X2,X1) ) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X12: X0,X7: X0] :
( ord_less_eq(X0,X7,X12)
<=> ( ( X7 = X12 )
| ord_less(X0,X7,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_order__le__less) ).
tff(f1020,plain,
spl20_70,
inference(avatar_split_clause,[],[f560,f1018]) ).
tff(f1018,plain,
( spl20_70
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less_eq(X0,X1,X2)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_70])]) ).
tff(f560,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less_eq(X0,X1,X2)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f406]) ).
tff(f1016,plain,
spl20_69,
inference(avatar_split_clause,[],[f558,f1014]) ).
tff(f1014,plain,
( spl20_69
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_69])]) ).
tff(f558,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less(X0,X2,X1) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
=> ord_less_eq(X0,X2,X1) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X11: X0,X4: X0] :
( ord_less(X0,X4,X11)
=> ord_less_eq(X0,X4,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_order__less__imp__le) ).
tff(f1012,plain,
spl20_68,
inference(avatar_split_clause,[],[f554,f1010]) ).
tff(f554,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less(X0,X2,X1) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
=> ~ ord_less(X0,X1,X2) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X11: X0,X4: X0] :
( ord_less(X0,X4,X11)
=> ~ ord_less(X0,X11,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_order__less__asym) ).
tff(f1008,plain,
spl20_67,
inference(avatar_split_clause,[],[f545,f1006]) ).
tff(f1006,plain,
( spl20_67
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X1,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_67])]) ).
tff(f545,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X1,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f404]) ).
tff(f404,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ~ ord_less(X0,X2,X1)
| ( ( X1 != X2 )
& ~ ord_less(X0,X1,X2) ) )
& ( ( X1 = X2 )
| ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(flattening,[],[f403]) ).
tff(f403,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ~ ord_less(X0,X2,X1)
| ( ( X1 != X2 )
& ~ ord_less(X0,X1,X2) ) )
& ( ( X1 = X2 )
| ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
<=> ( ( X1 = X2 )
| ord_less(X0,X1,X2) ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
<=> ( ( X1 = X2 )
| ord_less(X0,X1,X2) ) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X12: X0,X7: X0] :
( ~ ord_less(X0,X7,X12)
<=> ( ( X7 = X12 )
| ord_less(X0,X12,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_not__less__iff__gr__or__eq) ).
tff(f1004,plain,
spl20_66,
inference(avatar_split_clause,[],[f534,f1002]) ).
tff(f1002,plain,
( spl20_66
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_66])]) ).
tff(f534,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
=> ~ ord_less(X0,X1,X2) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X4: X0,X11: X0] :
( ord_less_eq(X0,X11,X4)
=> ~ ord_less(X0,X4,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_leD) ).
tff(f1000,plain,
spl20_65,
inference(avatar_split_clause,[],[f523,f998]) ).
tff(f998,plain,
( spl20_65
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_65])]) ).
tff(f523,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less_eq(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less_eq(X0,X2,X1) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X11: X0,X4: X0] :
( ord_less(X0,X11,X4)
| ord_less_eq(X0,X4,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_linorder__le__less__linear) ).
tff(f996,plain,
spl20_64,
inference(avatar_split_clause,[],[f522,f994]) ).
tff(f522,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X1,X2)
| ord_less_eq(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X1,X2)
| ord_less_eq(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X1,X2)
| ord_less_eq(X0,X2,X1) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X11: X0,X4: X0] :
( ord_less_eq(X0,X11,X4)
| ord_less_eq(X0,X4,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_linorder__linear) ).
tff(f980,plain,
( spl20_63
| ~ spl20_44
| ~ spl20_56 ),
inference(avatar_split_clause,[],[f953,f945,f896,f977]) ).
tff(f977,plain,
( spl20_63
<=> ord_less_eq(real,zero_zero(real),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_63])]) ).
tff(f945,plain,
( spl20_56
<=> ! [X0: real,X1: real] :
( ord_less_eq(real,X1,X0)
| ~ ord_less(real,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_56])]) ).
tff(f953,plain,
( ord_less_eq(real,zero_zero(real),sK19)
| ~ spl20_44
| ~ spl20_56 ),
inference(resolution,[],[f946,f898]) ).
tff(f946,plain,
( ! [X0: real,X1: real] :
( ~ ord_less(real,X1,X0)
| ord_less_eq(real,X1,X0) )
| ~ spl20_56 ),
inference(avatar_component_clause,[],[f945]) ).
tff(f973,plain,
spl20_62,
inference(avatar_split_clause,[],[f592,f971]) ).
tff(f971,plain,
( spl20_62
<=> ! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_62])]) ).
tff(f592,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ~ ord_less_eq(nat,X0,zero_zero(nat)) ),
inference(cnf_transformation,[],[f417]) ).
tff(f417,plain,
! [X0: nat] :
( ( ord_less_eq(nat,X0,zero_zero(nat))
| ( zero_zero(nat) != X0 ) )
& ( ( zero_zero(nat) = X0 )
| ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
inference(nnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: nat] :
( ord_less_eq(nat,X0,zero_zero(nat))
<=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X28: nat] :
( ord_less_eq(nat,X28,zero_zero(nat))
<=> ( zero_zero(nat) = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_le__0__eq) ).
tff(f969,plain,
spl20_61,
inference(avatar_split_clause,[],[f585,f967]) ).
tff(f967,plain,
( spl20_61
<=> ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_61])]) ).
tff(f585,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f337]) ).
tff(f337,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X27: nat] :
( ( zero_zero(nat) != X27 )
=> ord_less(nat,zero_zero(nat),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_gr0I) ).
tff(f965,plain,
spl20_60,
inference(avatar_split_clause,[],[f506,f963]) ).
tff(f963,plain,
( spl20_60
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(real,zero_zero(real),norm_norm(X0,X1))
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_60])]) ).
tff(f506,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(real,zero_zero(real),norm_norm(X0,X1))
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(real,zero_zero(real),norm_norm(X0,X1))
| ~ real_normed_vector(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X1: X0] : ord_less_eq(real,zero_zero(real),norm_norm(X0,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X4: X0] : ord_less_eq(real,zero_zero(real),norm_norm(X0,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_norm__ge__zero) ).
tff(f961,plain,
spl20_59,
inference(avatar_split_clause,[],[f505,f959]) ).
tff(f959,plain,
( spl20_59
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(real,norm_norm(X0,X1),zero_zero(real))
| ~ real_normed_vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_59])]) ).
tff(f505,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(real,norm_norm(X0,X1),zero_zero(real))
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: X0] : ~ ord_less(real,norm_norm(X0,X1),zero_zero(real))
| ~ real_normed_vector(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X1: X0] : ~ ord_less(real,norm_norm(X0,X1),zero_zero(real)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType] :
( real_normed_vector(X0)
=> ! [X4: X0] : ~ ord_less(real,norm_norm(X0,X4),zero_zero(real)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_norm__not__less__zero) ).
tff(f957,plain,
spl20_58,
inference(avatar_split_clause,[],[f504,f955]) ).
tff(f504,plain,
! [X0: $tType] :
( ( zero_zero(real) = norm_norm(X0,zero_zero(X0)) )
| ~ real_normed_vector(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ( zero_zero(real) = norm_norm(X0,zero_zero(X0)) )
| ~ real_normed_vector(X0) ),
inference(ennf_transformation,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( real_normed_vector(X0)
=> ( zero_zero(real) = norm_norm(X0,zero_zero(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_norm__zero) ).
tff(f951,plain,
spl20_57,
inference(avatar_split_clause,[],[f645,f949]) ).
tff(f949,plain,
( spl20_57
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_57])]) ).
tff(f645,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f449]) ).
tff(f947,plain,
spl20_56,
inference(avatar_split_clause,[],[f636,f945]) ).
tff(f636,plain,
! [X0: real,X1: real] :
( ord_less_eq(real,X1,X0)
| ~ ord_less(real,X1,X0) ),
inference(cnf_transformation,[],[f443]) ).
tff(f943,plain,
spl20_55,
inference(avatar_split_clause,[],[f613,f941]) ).
tff(f941,plain,
( spl20_55
<=> ! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
| ~ ord_less(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_55])]) ).
tff(f613,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
| ~ ord_less(nat,X1,X0) ),
inference(cnf_transformation,[],[f360]) ).
tff(f360,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X1,X0)
| ~ ord_less(nat,X1,X0) ),
inference(ennf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
=> ord_less_eq(nat,X1,X0) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X27: nat,X30: nat] :
( ord_less(nat,X30,X27)
=> ord_less_eq(nat,X30,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__imp__le__nat) ).
tff(f939,plain,
spl20_54,
inference(avatar_split_clause,[],[f594,f937]) ).
tff(f937,plain,
( spl20_54
<=> ! [X0: nat,X1: nat] :
( ord_less_eq(nat,X0,X1)
| ord_less_eq(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_54])]) ).
tff(f594,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X0,X1)
| ord_less_eq(nat,X1,X0) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: nat,X1: nat] :
( ord_less_eq(nat,X0,X1)
| ord_less_eq(nat,X1,X0) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X27: nat,X30: nat] :
( ord_less_eq(nat,X27,X30)
| ord_less_eq(nat,X30,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_nat__le__linear) ).
tff(f935,plain,
( spl20_53
| spl20_1 ),
inference(avatar_split_clause,[],[f455,f695,f933]) ).
tff(f455,plain,
! [X0: real] :
( thesis
| ord_less_eq(real,norm_norm(complex,sK1(X0)),r) ),
inference(cnf_transformation,[],[f385]) ).
tff(f931,plain,
spl20_52,
inference(avatar_split_clause,[],[f675,f929]) ).
tff(f929,plain,
( spl20_52
<=> ! [X0: $tType,X2: X0] :
( ord_less_eq(X0,X2,X2)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_52])]) ).
tff(f675,plain,
! [X0: $tType,X2: X0] :
( ord_less_eq(X0,X2,X2)
| ~ order(X0) ),
inference(equality_resolution,[],[f577]) ).
tff(f577,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X1,X2)
| ( X1 != X2 )
| ~ order(X0) ),
inference(cnf_transformation,[],[f409]) ).
tff(f409,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
& ( ( ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) )
| ( X1 != X2 ) ) )
| ~ order(X0) ),
inference(flattening,[],[f408]) ).
tff(f408,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ ord_less_eq(X0,X1,X2)
| ~ ord_less_eq(X0,X2,X1) )
& ( ( ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) )
| ( X1 != X2 ) ) )
| ~ order(X0) ),
inference(nnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
<=> ( ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) ) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 = X2 )
<=> ( ord_less_eq(X0,X1,X2)
& ord_less_eq(X0,X2,X1) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X12: X0,X7: X0] :
( ( X7 = X12 )
<=> ( ord_less_eq(X0,X12,X7)
& ord_less_eq(X0,X7,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_order__eq__iff) ).
tff(f927,plain,
spl20_51,
inference(avatar_split_clause,[],[f672,f925]) ).
tff(f925,plain,
( spl20_51
<=> ! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_51])]) ).
tff(f672,plain,
! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ order(X0) ),
inference(equality_resolution,[],[f573]) ).
tff(f573,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 != X2 )
| ~ ord_less(X0,X2,X1)
| ~ order(X0) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 != X2 )
| ~ ord_less(X0,X2,X1) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
=> ( X1 != X2 ) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X11: X0,X4: X0] :
( ord_less(X0,X4,X11)
=> ( X4 != X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_order__less__imp__not__eq) ).
tff(f923,plain,
spl20_50,
inference(avatar_split_clause,[],[f663,f921]) ).
tff(f921,plain,
( spl20_50
<=> ! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_50])]) ).
tff(f663,plain,
! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ linorder(X0) ),
inference(equality_resolution,[],[f539]) ).
tff(f539,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 != X2 )
| ~ ord_less(X0,X1,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f400]) ).
tff(f400,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ~ ord_less(X0,X1,X2)
& ~ ord_less(X0,X2,X1) ) )
& ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) ) )
| ~ linorder(X0) ),
inference(flattening,[],[f399]) ).
tff(f399,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ~ ord_less(X0,X1,X2)
& ~ ord_less(X0,X2,X1) ) )
& ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 != X2 )
<=> ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 != X2 )
<=> ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X12: X0,X7: X0] :
( ( X7 != X12 )
<=> ( ord_less(X0,X12,X7)
| ord_less(X0,X7,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_linorder__neq__iff) ).
tff(f919,plain,
spl20_49,
inference(avatar_split_clause,[],[f605,f917]) ).
tff(f917,plain,
( spl20_49
<=> ! [X1: $tType,X0: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_49])]) ).
tff(f605,plain,
! [X1: $tType,X0: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: $tType,X1: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(ennf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: $tType] :
( order(X1)
=> order(fun(X0,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X38: $tType,X39: $tType] :
( order(X39)
=> order(fun(X38,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
tff(f915,plain,
spl20_48,
inference(avatar_split_clause,[],[f604,f913]) ).
tff(f913,plain,
( spl20_48
<=> ! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_48])]) ).
tff(f604,plain,
! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(cnf_transformation,[],[f348]) ).
tff(f348,plain,
! [X0: $tType,X1: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(ennf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType,X1: $tType] :
( preorder(X1)
=> preorder(fun(X0,X1)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X38: $tType,X39: $tType] :
( preorder(X39)
=> preorder(fun(X38,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
tff(f911,plain,
spl20_47,
inference(avatar_split_clause,[],[f595,f909]) ).
tff(f909,plain,
( spl20_47
<=> ! [X1: $tType,X0: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_47])]) ).
tff(f595,plain,
! [X1: $tType,X0: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f342]) ).
tff(f342,plain,
! [X0: $tType,X1: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(ennf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType,X1: $tType] :
( ord(X1)
=> ord(fun(X0,X1)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X38: $tType,X39: $tType] :
( ord(X39)
=> ord(fun(X38,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
tff(f907,plain,
spl20_46,
inference(avatar_split_clause,[],[f552,f905]) ).
tff(f905,plain,
( spl20_46
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_46])]) ).
tff(f552,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,X1,X1)
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0] : ord_less_eq(X0,X1,X1) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X4: X0] : ord_less_eq(X0,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_order__refl) ).
tff(f903,plain,
spl20_45,
inference(avatar_split_clause,[],[f551,f901]) ).
tff(f901,plain,
( spl20_45
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_45])]) ).
tff(f551,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: $tType] :
( ! [X1: X0] : ~ ord_less(X0,X1,X1)
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0] : ~ ord_less(X0,X1,X1) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X4: X0] : ~ ord_less(X0,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_order__less__irrefl) ).
tff(f899,plain,
spl20_44,
inference(avatar_split_clause,[],[f652,f896]) ).
tff(f652,plain,
ord_less(real,zero_zero(real),sK19),
inference(cnf_transformation,[],[f453]) ).
tff(f894,plain,
spl20_43,
inference(avatar_split_clause,[],[f518,f892]) ).
tff(f892,plain,
( spl20_43
<=> ! [X0: $tType] :
( zero(poly1(X0))
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_43])]) ).
tff(f518,plain,
! [X0: $tType] :
( zero(poly1(X0))
| ~ zero(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( zero(poly1(X0))
| ~ zero(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( zero(X0)
=> zero(poly1(X0)) ),
inference(rectify,[],[f136]) ).
tff(f136,axiom,
! [X38: $tType] :
( zero(X38)
=> zero(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
tff(f890,plain,
spl20_42,
inference(avatar_split_clause,[],[f517,f888]) ).
tff(f888,plain,
( spl20_42
<=> ! [X0: $tType] :
( comm_semiring_0(poly1(X0))
| ~ comm_semiring_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_42])]) ).
tff(f517,plain,
! [X0: $tType] :
( comm_semiring_0(poly1(X0))
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( comm_semiring_0(poly1(X0))
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( comm_semiring_0(X0)
=> comm_semiring_0(poly1(X0)) ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X38: $tType] :
( comm_semiring_0(X38)
=> comm_semiring_0(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
tff(f886,plain,
spl20_41,
inference(avatar_split_clause,[],[f513,f884]) ).
tff(f884,plain,
( spl20_41
<=> ! [X0: $tType] :
( idom(poly1(X0))
| ~ idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_41])]) ).
tff(f513,plain,
! [X0: $tType] :
( idom(poly1(X0))
| ~ idom(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( idom(poly1(X0))
| ~ idom(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( idom(X0)
=> idom(poly1(X0)) ),
inference(rectify,[],[f137]) ).
tff(f137,axiom,
! [X38: $tType] :
( idom(X38)
=> idom(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
tff(f882,plain,
spl20_40,
inference(avatar_split_clause,[],[f503,f880]) ).
tff(f880,plain,
( spl20_40
<=> ! [X0: $tType] :
( order(poly1(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_40])]) ).
tff(f503,plain,
! [X0: $tType] :
( order(poly1(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( order(poly1(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> order(poly1(X0)) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X38: $tType] :
( linordered_idom(X38)
=> order(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Oorder) ).
tff(f878,plain,
spl20_39,
inference(avatar_split_clause,[],[f502,f876]) ).
tff(f876,plain,
( spl20_39
<=> ! [X0: $tType] :
( preorder(poly1(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_39])]) ).
tff(f502,plain,
! [X0: $tType] :
( preorder(poly1(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( preorder(poly1(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> preorder(poly1(X0)) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X38: $tType] :
( linordered_idom(X38)
=> preorder(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Opreorder) ).
tff(f874,plain,
spl20_38,
inference(avatar_split_clause,[],[f501,f872]) ).
tff(f872,plain,
( spl20_38
<=> ! [X0: $tType] :
( ord(poly1(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_38])]) ).
tff(f501,plain,
! [X0: $tType] :
( ord(poly1(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ord(poly1(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ord(poly1(X0)) ),
inference(rectify,[],[f135]) ).
tff(f135,axiom,
! [X38: $tType] :
( linordered_idom(X38)
=> ord(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Oord) ).
tff(f870,plain,
spl20_37,
inference(avatar_split_clause,[],[f500,f868]) ).
tff(f868,plain,
( spl20_37
<=> ! [X0: $tType] :
( linorder(poly1(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_37])]) ).
tff(f500,plain,
! [X0: $tType] :
( linorder(poly1(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( linorder(poly1(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> linorder(poly1(X0)) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X38: $tType] :
( linordered_idom(X38)
=> linorder(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Olinorder) ).
tff(f866,plain,
spl20_36,
inference(avatar_split_clause,[],[f499,f864]) ).
tff(f864,plain,
( spl20_36
<=> ! [X0: $tType] :
( ring_char_0(poly1(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_36])]) ).
tff(f499,plain,
! [X0: $tType] :
( ring_char_0(poly1(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ring_char_0(poly1(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ring_char_0(poly1(X0)) ),
inference(rectify,[],[f134]) ).
tff(f134,axiom,
! [X38: $tType] :
( linordered_idom(X38)
=> ring_char_0(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
tff(f862,plain,
spl20_35,
inference(avatar_split_clause,[],[f498,f860]) ).
tff(f860,plain,
( spl20_35
<=> ! [X0: $tType] :
( linordered_idom(poly1(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_35])]) ).
tff(f498,plain,
! [X0: $tType] :
( linordered_idom(poly1(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( linordered_idom(poly1(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> linordered_idom(poly1(X0)) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X38: $tType] :
( linordered_idom(X38)
=> linordered_idom(poly1(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
tff(f858,plain,
spl20_34,
inference(avatar_split_clause,[],[f491,f856]) ).
tff(f856,plain,
( spl20_34
<=> ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_34])]) ).
tff(f491,plain,
! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X27: nat] : ord_less_eq(nat,zero_zero(nat),X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_le0) ).
tff(f854,plain,
spl20_33,
inference(avatar_split_clause,[],[f488,f852]) ).
tff(f852,plain,
( spl20_33
<=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_33])]) ).
tff(f488,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X27: nat] : ~ ord_less(nat,X27,zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__zeroE) ).
tff(f850,plain,
spl20_32,
inference(avatar_split_clause,[],[f690,f848]) ).
tff(f848,plain,
( spl20_32
<=> ! [X1: real] : ord_less_eq(real,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_32])]) ).
tff(f690,plain,
! [X1: real] : ord_less_eq(real,X1,X1),
inference(equality_resolution,[],[f637]) ).
tff(f637,plain,
! [X0: real,X1: real] :
( ord_less_eq(real,X1,X0)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f443]) ).
tff(f846,plain,
spl20_31,
inference(avatar_split_clause,[],[f487,f844]) ).
tff(f844,plain,
( spl20_31
<=> ! [X0: nat] : ord_less_eq(nat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_31])]) ).
tff(f487,plain,
! [X0: nat] : ord_less_eq(nat,X0,X0),
inference(cnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: nat] : ord_less_eq(nat,X0,X0),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X27: nat] : ord_less_eq(nat,X27,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_le__refl) ).
tff(f842,plain,
spl20_30,
inference(avatar_split_clause,[],[f485,f840]) ).
tff(f840,plain,
( spl20_30
<=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_30])]) ).
tff(f485,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X27: nat] : ~ ord_less(nat,X27,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_less__not__refl) ).
tff(f838,plain,
spl20_29,
inference(avatar_split_clause,[],[f484,f835]) ).
tff(f835,plain,
( spl20_29
<=> order(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_29])]) ).
tff(f484,plain,
order(nat),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
order(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
tff(f833,plain,
spl20_28,
inference(avatar_split_clause,[],[f483,f830]) ).
tff(f830,plain,
( spl20_28
<=> order(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_28])]) ).
tff(f483,plain,
order(real),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
order(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
tff(f828,plain,
spl20_27,
inference(avatar_split_clause,[],[f482,f825]) ).
tff(f825,plain,
( spl20_27
<=> order(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_27])]) ).
tff(f482,plain,
order(bool),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
order(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
tff(f823,plain,
spl20_26,
inference(avatar_split_clause,[],[f481,f820]) ).
tff(f820,plain,
( spl20_26
<=> preorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_26])]) ).
tff(f481,plain,
preorder(nat),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
preorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
tff(f818,plain,
spl20_25,
inference(avatar_split_clause,[],[f480,f815]) ).
tff(f480,plain,
preorder(real),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
preorder(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Opreorder) ).
tff(f813,plain,
spl20_24,
inference(avatar_split_clause,[],[f479,f810]) ).
tff(f810,plain,
( spl20_24
<=> preorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_24])]) ).
tff(f479,plain,
preorder(bool),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
preorder(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
tff(f808,plain,
spl20_23,
inference(avatar_split_clause,[],[f478,f805]) ).
tff(f805,plain,
( spl20_23
<=> ord(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_23])]) ).
tff(f478,plain,
ord(nat),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
ord(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
tff(f803,plain,
spl20_22,
inference(avatar_split_clause,[],[f477,f800]) ).
tff(f800,plain,
( spl20_22
<=> ord(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_22])]) ).
tff(f477,plain,
ord(real),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
ord(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
tff(f798,plain,
spl20_21,
inference(avatar_split_clause,[],[f476,f795]) ).
tff(f795,plain,
( spl20_21
<=> ord(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_21])]) ).
tff(f476,plain,
ord(bool),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
ord(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
tff(f793,plain,
spl20_20,
inference(avatar_split_clause,[],[f475,f790]) ).
tff(f790,plain,
( spl20_20
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_20])]) ).
tff(f475,plain,
pp(fTrue),
inference(cnf_transformation,[],[f139]) ).
tff(f139,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f788,plain,
spl20_19,
inference(avatar_split_clause,[],[f474,f785]) ).
tff(f785,plain,
( spl20_19
<=> linorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_19])]) ).
tff(f474,plain,
linorder(nat),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
linorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
tff(f783,plain,
spl20_18,
inference(avatar_split_clause,[],[f473,f780]) ).
tff(f780,plain,
( spl20_18
<=> linorder(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_18])]) ).
tff(f473,plain,
linorder(real),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
linorder(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
tff(f778,plain,
spl20_17,
inference(avatar_split_clause,[],[f472,f775]) ).
tff(f775,plain,
( spl20_17
<=> linorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_17])]) ).
tff(f472,plain,
linorder(bool),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
linorder(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
tff(f773,plain,
spl20_16,
inference(avatar_split_clause,[],[f471,f770]) ).
tff(f770,plain,
( spl20_16
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_16])]) ).
tff(f471,plain,
zero(nat),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f768,plain,
spl20_15,
inference(avatar_split_clause,[],[f470,f765]) ).
tff(f765,plain,
( spl20_15
<=> comm_semiring_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_15])]) ).
tff(f470,plain,
comm_semiring_0(nat),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
comm_semiring_0(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__0) ).
tff(f763,plain,
spl20_14,
inference(avatar_split_clause,[],[f469,f760]) ).
tff(f760,plain,
( spl20_14
<=> comm_semiring_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_14])]) ).
tff(f469,plain,
comm_semiring_0(real),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
comm_semiring_0(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__0) ).
tff(f758,plain,
spl20_13,
inference(avatar_split_clause,[],[f468,f755]) ).
tff(f755,plain,
( spl20_13
<=> zero(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_13])]) ).
tff(f468,plain,
zero(real),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
zero(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
tff(f753,plain,
spl20_12,
inference(avatar_split_clause,[],[f467,f750]) ).
tff(f750,plain,
( spl20_12
<=> comm_semiring_0(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_12])]) ).
tff(f467,plain,
comm_semiring_0(complex),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
comm_semiring_0(complex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
tff(f748,plain,
spl20_11,
inference(avatar_split_clause,[],[f466,f745]) ).
tff(f745,plain,
( spl20_11
<=> zero(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_11])]) ).
tff(f466,plain,
zero(complex),
inference(cnf_transformation,[],[f128]) ).
tff(f128,axiom,
zero(complex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
tff(f743,plain,
spl20_10,
inference(avatar_split_clause,[],[f465,f740]) ).
tff(f740,plain,
( spl20_10
<=> idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_10])]) ).
tff(f465,plain,
idom(real),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
idom(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
tff(f738,plain,
spl20_9,
inference(avatar_split_clause,[],[f464,f735]) ).
tff(f735,plain,
( spl20_9
<=> idom(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_9])]) ).
tff(f464,plain,
idom(complex),
inference(cnf_transformation,[],[f129]) ).
tff(f129,axiom,
idom(complex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oidom) ).
tff(f733,plain,
spl20_8,
inference(avatar_split_clause,[],[f463,f730]) ).
tff(f730,plain,
( spl20_8
<=> ring_char_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_8])]) ).
tff(f463,plain,
ring_char_0(real),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
ring_char_0(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
tff(f728,plain,
spl20_7,
inference(avatar_split_clause,[],[f462,f725]) ).
tff(f725,plain,
( spl20_7
<=> ring_char_0(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_7])]) ).
tff(f462,plain,
ring_char_0(complex),
inference(cnf_transformation,[],[f127]) ).
tff(f127,axiom,
ring_char_0(complex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
tff(f723,plain,
spl20_6,
inference(avatar_split_clause,[],[f461,f720]) ).
tff(f461,plain,
real_normed_vector(real),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
real_normed_vector(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
tff(f718,plain,
spl20_5,
inference(avatar_split_clause,[],[f460,f715]) ).
tff(f715,plain,
( spl20_5
<=> linordered_idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_5])]) ).
tff(f460,plain,
linordered_idom(real),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
linordered_idom(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
tff(f713,plain,
spl20_4,
inference(avatar_split_clause,[],[f459,f710]) ).
tff(f459,plain,
real_normed_vector(complex),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
real_normed_vector(complex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
tff(f708,plain,
spl20_3,
inference(avatar_split_clause,[],[f458,f705]) ).
tff(f705,plain,
( spl20_3
<=> dense_linorder(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_3])]) ).
tff(f458,plain,
dense_linorder(real),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
dense_linorder(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Odense__linorder) ).
tff(f703,plain,
~ spl20_2,
inference(avatar_split_clause,[],[f457,f700]) ).
tff(f700,plain,
( spl20_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
tff(f457,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f138]) ).
tff(f138,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f698,plain,
~ spl20_1,
inference(avatar_split_clause,[],[f454,f695]) ).
tff(f454,plain,
~ thesis,
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
~ thesis,
inference(flattening,[],[f142]) ).
tff(f142,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f141]) ).
tff(f141,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW485_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 02:54:35 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (24380)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (24383)WARNING: value z3 for option sas not known
% 0.14/0.38 % (24381)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (24382)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (24385)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)
% 0.14/0.38 % (24384)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (24386)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 % (24387)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)
% 0.14/0.38 % (24383)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)
% 0.14/0.38 % (24387)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 % (24392)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (24394)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)
% 0.14/0.40 % (24393)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)
% 0.14/0.40 % (24385)First to succeed.
% 0.14/0.40 % (24392)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 % (24393)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.41 % (24385)Refutation found. Thanks to Tanya!
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.42 % (24385)------------------------------
% 0.14/0.42 % (24385)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.42 % (24385)Termination reason: Refutation
% 0.14/0.42
% 0.14/0.42 % (24385)Memory used [KB]: 1526
% 0.14/0.42 % (24385)Time elapsed: 0.034 s
% 0.14/0.42 % (24385)Instructions burned: 55 (million)
% 0.14/0.42 % (24385)------------------------------
% 0.14/0.42 % (24385)------------------------------
% 0.14/0.42 % (24380)Success in time 0.055 s
%------------------------------------------------------------------------------