TSTP Solution File: ITP019_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP019_2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 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 : Mon May 20 22:44:30 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 143
% Syntax : Number of formulae : 353 ( 125 unt; 34 typ; 0 def)
% Number of atoms : 1230 ( 170 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 714 ( 271 ~; 260 |; 40 &)
% ( 84 <=>; 57 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 468 ( 468 fml; 0 var)
% Number of types : 7 ( 5 usr)
% Number of type conns : 31 ( 21 >; 10 *; 0 +; 0 <<)
% Number of predicates : 75 ( 73 usr; 71 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 8 con; 0-3 aty)
% Number of variables : 344 ( 333 !; 11 ?; 197 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(type_def_7,type,
tp__ty_2Enum_2Enum: $tType ).
tff(type_def_8,type,
tp__ty_2Erealax_2Ereal: $tType ).
tff(type_def_9,type,
tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_11,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_13,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_15,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_17,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_18,type,
ty_2Enum_2Enum: del ).
tff(func_def_19,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
tff(func_def_20,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
tff(func_def_22,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
tff(func_def_23,type,
ty_2Erealax_2Ereal: del ).
tff(func_def_24,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
tff(func_def_25,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
tff(func_def_26,type,
ty_2Epair_2Eprod: ( del * del ) > del ).
tff(func_def_27,type,
inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i ).
tff(func_def_28,type,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
tff(func_def_31,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_32,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_33,type,
sK0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
tff(func_def_34,type,
sK1: ( del * $i ) > $i ).
tff(func_def_35,type,
sK2: ( del * tp__o ) > $i ).
tff(func_def_36,type,
sK3: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(f579,plain,
$false,
inference(avatar_sat_refutation,[],[f192,f198,f203,f208,f213,f219,f224,f229,f234,f239,f245,f250,f255,f260,f264,f268,f272,f280,f284,f288,f292,f296,f303,f308,f313,f318,f323,f327,f331,f335,f339,f343,f347,f352,f356,f375,f379,f384,f388,f392,f415,f419,f423,f444,f448,f460,f464,f468,f488,f492,f496,f500,f508,f515,f519,f523,f527,f531,f548,f559,f563,f575,f578]) ).
tff(f578,plain,
( spl4_2
| ~ spl4_6
| ~ spl4_58 ),
inference(avatar_split_clause,[],[f555,f529,f216,f195]) ).
tff(f195,plain,
( spl4_2
<=> ( sK0 = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f216,plain,
( spl4_6
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
tff(f529,plain,
( spl4_58
<=> ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_58])]) ).
tff(f555,plain,
( ( sK0 = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ~ spl4_6
| ~ spl4_58 ),
inference(trivial_inequality_removal,[],[f553]) ).
tff(f553,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ( sK0 = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ~ spl4_6
| ~ spl4_58 ),
inference(superposition,[],[f530,f218]) ).
tff(f218,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f216]) ).
tff(f530,plain,
( ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = X0 ) )
| ~ spl4_58 ),
inference(avatar_component_clause,[],[f529]) ).
tff(f575,plain,
spl4_62,
inference(avatar_split_clause,[],[f181,f573]) ).
tff(f573,plain,
( spl4_62
<=> ! [X0: del,X3,X2,X1: del] :
( ( X2 = X3 )
| ( ap(X2,sK3(X0,X2,X3)) != ap(X3,sK3(X0,X2,X3)) )
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_62])]) ).
tff(f181,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ( X2 = X3 )
| ( ap(X2,sK3(X0,X2,X3)) != ap(X3,sK3(X0,X2,X3)) )
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: del,X1: del,X2] :
( ! [X3] :
( ( X2 = X3 )
| ( ( ap(X2,sK3(X0,X2,X3)) != ap(X3,sK3(X0,X2,X3)) )
& mem(sK3(X0,X2,X3),X0) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f97,f118]) ).
tff(f118,plain,
! [X0: del,X2,X3] :
( ? [X4] :
( ( ap(X2,X4) != ap(X3,X4) )
& mem(X4,X0) )
=> ( ( ap(X2,sK3(X0,X2,X3)) != ap(X3,sK3(X0,X2,X3)) )
& mem(sK3(X0,X2,X3),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f97,plain,
! [X0: del,X1: del,X2] :
( ! [X3] :
( ( X2 = X3 )
| ? [X4] :
( ( ap(X2,X4) != ap(X3,X4) )
& mem(X4,X0) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(flattening,[],[f96]) ).
tff(f96,plain,
! [X0: del,X1: del,X2] :
( ! [X3] :
( ( X2 = X3 )
| ? [X4] :
( ( ap(X2,X4) != ap(X3,X4) )
& mem(X4,X0) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f78]) ).
tff(f78,plain,
! [X0: del,X1: del,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,arr(X0,X1))
=> ( ! [X4] :
( mem(X4,X0)
=> ( ap(X2,X4) = ap(X3,X4) ) )
=> ( X2 = X3 ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: del,X1: del,X2] :
( mem(X2,arr(X0,X1))
=> ! [X6] :
( mem(X6,arr(X0,X1))
=> ( ! [X3] :
( mem(X3,X0)
=> ( ap(X2,X3) = ap(X6,X3) ) )
=> ( X2 = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
tff(f563,plain,
spl4_61,
inference(avatar_split_clause,[],[f180,f561]) ).
tff(f561,plain,
( spl4_61
<=> ! [X0: del,X3,X2,X1: del] :
( ( X2 = X3 )
| mem(sK3(X0,X2,X3),X0)
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_61])]) ).
tff(f180,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ( X2 = X3 )
| mem(sK3(X0,X2,X3),X0)
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
tff(f559,plain,
spl4_60,
inference(avatar_split_clause,[],[f172,f557]) ).
tff(f557,plain,
( spl4_60
<=> ! [X0: del,X1,X3] :
( p(ap(X1,X3))
| ~ mem(X3,X0)
| ~ p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_60])]) ).
tff(f172,plain,
! [X3: $i,X0: del,X1: $i] :
( p(ap(X1,X3))
| ~ mem(X3,X0)
| ~ p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f113]) ).
tff(f113,plain,
! [X0: del,X1] :
( ( ( p(ap(c_2Ebool_2E_21(X0),X1))
| ( ~ p(ap(X1,sK1(X0,X1)))
& mem(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( p(ap(X1,X3))
| ~ mem(X3,X0) )
| ~ p(ap(c_2Ebool_2E_21(X0),X1)) ) )
| ~ mem(X1,arr(X0,bool)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f111,f112]) ).
tff(f112,plain,
! [X0: del,X1] :
( ? [X2] :
( ~ p(ap(X1,X2))
& mem(X2,X0) )
=> ( ~ p(ap(X1,sK1(X0,X1)))
& mem(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f111,plain,
! [X0: del,X1] :
( ( ( p(ap(c_2Ebool_2E_21(X0),X1))
| ? [X2] :
( ~ p(ap(X1,X2))
& mem(X2,X0) ) )
& ( ! [X3] :
( p(ap(X1,X3))
| ~ mem(X3,X0) )
| ~ p(ap(c_2Ebool_2E_21(X0),X1)) ) )
| ~ mem(X1,arr(X0,bool)) ),
inference(rectify,[],[f110]) ).
tff(f110,plain,
! [X0: del,X1] :
( ( ( p(ap(c_2Ebool_2E_21(X0),X1))
| ? [X2] :
( ~ p(ap(X1,X2))
& mem(X2,X0) ) )
& ( ! [X2] :
( p(ap(X1,X2))
| ~ mem(X2,X0) )
| ~ p(ap(c_2Ebool_2E_21(X0),X1)) ) )
| ~ mem(X1,arr(X0,bool)) ),
inference(nnf_transformation,[],[f92]) ).
tff(f92,plain,
! [X0: del,X1] :
( ( p(ap(c_2Ebool_2E_21(X0),X1))
<=> ! [X2] :
( p(ap(X1,X2))
| ~ mem(X2,X0) ) )
| ~ mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f75]) ).
tff(f75,plain,
! [X0: del,X1] :
( mem(X1,arr(X0,bool))
=> ( p(ap(c_2Ebool_2E_21(X0),X1))
<=> ! [X2] :
( mem(X2,X0)
=> p(ap(X1,X2)) ) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: del,X4] :
( mem(X4,arr(X0,bool))
=> ( p(ap(c_2Ebool_2E_21(X0),X4))
<=> ! [X3] :
( mem(X3,X0)
=> p(ap(X4,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
tff(f548,plain,
( spl4_59
| ~ spl4_9
| ~ spl4_40 ),
inference(avatar_split_clause,[],[f399,f390,f231,f545]) ).
tff(f545,plain,
( spl4_59
<=> ( c_2Ebool_2EF = ap(i(bool),c_2Ebool_2EF) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_59])]) ).
tff(f231,plain,
( spl4_9
<=> mem(c_2Ebool_2EF,bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
tff(f390,plain,
( spl4_40
<=> ! [X0: del,X1] :
( ( ap(i(X0),X1) = X1 )
| ~ mem(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).
tff(f399,plain,
( ( c_2Ebool_2EF = ap(i(bool),c_2Ebool_2EF) )
| ~ spl4_9
| ~ spl4_40 ),
inference(resolution,[],[f391,f233]) ).
tff(f233,plain,
( mem(c_2Ebool_2EF,bool)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f231]) ).
tff(f391,plain,
( ! [X0: del,X1: $i] :
( ~ mem(X1,X0)
| ( ap(i(X0),X1) = X1 ) )
| ~ spl4_40 ),
inference(avatar_component_clause,[],[f390]) ).
tff(f531,plain,
spl4_58,
inference(avatar_split_clause,[],[f187,f529]) ).
tff(f187,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = X0 ) ),
inference(forward_demodulation,[],[f186,f127]) ).
tff(f127,plain,
c_2Enum_2E0 = inj__ty_2Enum_2Enum(fo__c_2Enum_2E0),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
c_2Enum_2E0 = inj__ty_2Enum_2Enum(fo__c_2Enum_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0) ).
tff(f186,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = X0 )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) ) ),
inference(forward_demodulation,[],[f165,f127]) ).
tff(f165,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = X0 )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) ) ),
inference(cnf_transformation,[],[f108]) ).
tff(f108,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X0 ) )
& ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = X0 )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) ) ) ),
inference(nnf_transformation,[],[f70]) ).
tff(f70,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) )
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = X0 ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X13: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X13))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) )
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
tff(f527,plain,
spl4_57,
inference(avatar_split_clause,[],[f174,f525]) ).
tff(f525,plain,
( spl4_57
<=> ! [X0: del,X1] :
( p(ap(c_2Ebool_2E_21(X0),X1))
| ~ p(ap(X1,sK1(X0,X1)))
| ~ mem(X1,arr(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_57])]) ).
tff(f174,plain,
! [X0: del,X1: $i] :
( p(ap(c_2Ebool_2E_21(X0),X1))
| ~ p(ap(X1,sK1(X0,X1)))
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f113]) ).
tff(f523,plain,
spl4_56,
inference(avatar_split_clause,[],[f170,f521]) ).
tff(f521,plain,
( spl4_56
<=> ! [X2,X0: del,X1] :
( ( X1 = X2 )
| ~ p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
| ~ mem(X2,X0)
| ~ mem(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_56])]) ).
tff(f170,plain,
! [X2: $i,X0: del,X1: $i] :
( ( X1 = X2 )
| ~ p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
| ~ mem(X2,X0)
| ~ mem(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,plain,
! [X0: del,X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ p(ap(ap(c_2Emin_2E_3D(X0),X1),X2)) ) )
| ~ mem(X2,X0) )
| ~ mem(X1,X0) ),
inference(nnf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: del,X1] :
( ! [X2] :
( ( p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
<=> ( X1 = X2 ) )
| ~ mem(X2,X0) )
| ~ mem(X1,X0) ),
inference(ennf_transformation,[],[f74]) ).
tff(f74,plain,
! [X0: del,X1] :
( mem(X1,X0)
=> ! [X2] :
( mem(X2,X0)
=> ( p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
<=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: del,X3] :
( mem(X3,X0)
=> ! [X7] :
( mem(X7,X0)
=> ( p(ap(ap(c_2Emin_2E_3D(X0),X3),X7))
<=> ( X3 = X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
tff(f519,plain,
spl4_55,
inference(avatar_split_clause,[],[f161,f517]) ).
tff(f517,plain,
( spl4_55
<=> ! [X0,X1] :
( p(X1)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_55])]) ).
tff(f161,plain,
! [X0: $i,X1: $i] :
( p(X1)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f107]) ).
tff(f107,plain,
! [X0] :
( ! [X1] :
( ( ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f106]) ).
tff(f106,plain,
! [X0] :
( ! [X1] :
( ( ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f88]) ).
tff(f88,plain,
! [X0] :
( ! [X1] :
( ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
<=> ( p(X1)
| ~ p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f68]) ).
tff(f68,plain,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
<=> ( p(X0)
=> p(X1) ) ) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X4] :
( mem(X4,bool)
=> ! [X5] :
( mem(X5,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X4),X5))
<=> ( p(X4)
=> p(X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).
tff(f515,plain,
spl4_54,
inference(avatar_split_clause,[],[f160,f513]) ).
tff(f513,plain,
( spl4_54
<=> ! [X0,X1] :
( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_54])]) ).
tff(f160,plain,
! [X0: $i,X1: $i] :
( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f105]) ).
tff(f105,plain,
! [X0] :
( ! [X1] :
( ( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f104]) ).
tff(f104,plain,
! [X0] :
( ! [X1] :
( ( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1)) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f87]) ).
tff(f87,plain,
! [X0] :
( ! [X1] :
( ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
<=> ( p(X1)
& p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f67]) ).
tff(f67,plain,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
<=> ( p(X1)
& p(X0) ) ) ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X4] :
( mem(X4,bool)
=> ! [X5] :
( mem(X5,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X4),X5))
<=> ( p(X5)
& p(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
tff(f508,plain,
spl4_53,
inference(avatar_split_clause,[],[f173,f506]) ).
tff(f506,plain,
( spl4_53
<=> ! [X0: del,X1] :
( p(ap(c_2Ebool_2E_21(X0),X1))
| mem(sK1(X0,X1),X0)
| ~ mem(X1,arr(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).
tff(f173,plain,
! [X0: del,X1: $i] :
( p(ap(c_2Ebool_2E_21(X0),X1))
| mem(sK1(X0,X1),X0)
| ~ mem(X1,arr(X0,bool)) ),
inference(cnf_transformation,[],[f113]) ).
tff(f500,plain,
spl4_52,
inference(avatar_split_clause,[],[f163,f498]) ).
tff(f498,plain,
( spl4_52
<=> ! [X0,X1] :
( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).
tff(f163,plain,
! [X0: $i,X1: $i] :
( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f107]) ).
tff(f496,plain,
spl4_51,
inference(avatar_split_clause,[],[f162,f494]) ).
tff(f494,plain,
( spl4_51
<=> ! [X0,X1] :
( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).
tff(f162,plain,
! [X0: $i,X1: $i] :
( p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f107]) ).
tff(f492,plain,
spl4_50,
inference(avatar_split_clause,[],[f159,f490]) ).
tff(f490,plain,
( spl4_50
<=> ! [X0,X1] :
( p(X1)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).
tff(f159,plain,
! [X0: $i,X1: $i] :
( p(X1)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f105]) ).
tff(f488,plain,
spl4_49,
inference(avatar_split_clause,[],[f158,f486]) ).
tff(f486,plain,
( spl4_49
<=> ! [X0,X1] :
( p(X0)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).
tff(f158,plain,
! [X0: $i,X1: $i] :
( p(X0)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f105]) ).
tff(f468,plain,
spl4_48,
inference(avatar_split_clause,[],[f179,f466]) ).
tff(f466,plain,
( spl4_48
<=> ! [X0: del,X3,X2,X1: del] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).
tff(f179,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f95]) ).
tff(f95,plain,
! [X0: del,X1: del,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: del,X1: del,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f464,plain,
spl4_47,
inference(avatar_split_clause,[],[f157,f462]) ).
tff(f462,plain,
( spl4_47
<=> ! [X0,X1] :
( ( X0 = X1 )
| ~ p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).
tff(f157,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f103]) ).
tff(f103,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1 )
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f86]) ).
tff(f86,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f85]) ).
tff(f85,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f66]) ).
tff(f66,plain,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X4] :
( mem(X4,bool)
=> ! [X5] :
( mem(X5,bool)
=> ( ( p(X4)
<=> p(X5) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
tff(f460,plain,
spl4_46,
inference(avatar_split_clause,[],[f156,f458]) ).
tff(f458,plain,
( spl4_46
<=> ! [X0,X1] :
( ( X0 = X1 )
| p(X1)
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).
tff(f156,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| p(X1)
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f103]) ).
tff(f448,plain,
spl4_45,
inference(avatar_split_clause,[],[f168,f446]) ).
tff(f446,plain,
( spl4_45
<=> ! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Emin_2E_3D_3D_3E(X0,X1)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X0)),inj__o(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).
tff(f168,plain,
! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Emin_2E_3D_3D_3E(X0,X1)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X0)),inj__o(X1)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f72,plain,
! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Emin_2E_3D_3D_3E(X0,X1)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X0)),inj__o(X1)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X8: tp__o,X9: tp__o] : ( inj__o(fo__c_2Emin_2E_3D_3D_3E(X8,X9)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X8)),inj__o(X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Emin_2E_3D_3D_3E) ).
tff(f444,plain,
spl4_44,
inference(avatar_split_clause,[],[f167,f442]) ).
tff(f442,plain,
( spl4_44
<=> ! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Ebool_2E_2F_5C(X0,X1)) = ap(ap(c_2Ebool_2E_2F_5C,inj__o(X0)),inj__o(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).
tff(f167,plain,
! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Ebool_2E_2F_5C(X0,X1)) = ap(ap(c_2Ebool_2E_2F_5C,inj__o(X0)),inj__o(X1)) ),
inference(cnf_transformation,[],[f71]) ).
tff(f71,plain,
! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Ebool_2E_2F_5C(X0,X1)) = ap(ap(c_2Ebool_2E_2F_5C,inj__o(X0)),inj__o(X1)) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X8: tp__o,X9: tp__o] : ( inj__o(fo__c_2Ebool_2E_2F_5C(X8,X9)) = ap(ap(c_2Ebool_2E_2F_5C,inj__o(X8)),inj__o(X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2E_2F_5C) ).
tff(f423,plain,
spl4_43,
inference(avatar_split_clause,[],[f184,f421]) ).
tff(f421,plain,
( spl4_43
<=> ! [X2,X0: del] :
( p(ap(ap(c_2Emin_2E_3D(X0),X2),X2))
| ~ mem(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).
tff(f184,plain,
! [X2: $i,X0: del] :
( p(ap(ap(c_2Emin_2E_3D(X0),X2),X2))
| ~ mem(X2,X0) ),
inference(duplicate_literal_removal,[],[f183]) ).
tff(f183,plain,
! [X2: $i,X0: del] :
( p(ap(ap(c_2Emin_2E_3D(X0),X2),X2))
| ~ mem(X2,X0)
| ~ mem(X2,X0) ),
inference(equality_resolution,[],[f171]) ).
tff(f171,plain,
! [X2: $i,X0: del,X1: $i] :
( p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
| ( X1 != X2 )
| ~ mem(X2,X0)
| ~ mem(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
tff(f419,plain,
spl4_42,
inference(avatar_split_clause,[],[f178,f417]) ).
tff(f417,plain,
( spl4_42
<=> ! [X2,X0: del,X1] :
( ( ap(k(X0,X1),X2) = X1 )
| ~ mem(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).
tff(f178,plain,
! [X2: $i,X0: del,X1: $i] :
( ( ap(k(X0,X1),X2) = X1 )
| ~ mem(X2,X0) ),
inference(cnf_transformation,[],[f94]) ).
tff(f94,plain,
! [X0: del,X1,X2] :
( ( ap(k(X0,X1),X2) = X1 )
| ~ mem(X2,X0) ),
inference(ennf_transformation,[],[f77]) ).
tff(f77,plain,
! [X0: del,X1,X2] :
( mem(X2,X0)
=> ( ap(k(X0,X1),X2) = X1 ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: del,X7,X3] :
( mem(X3,X0)
=> ( ap(k(X0,X7),X3) = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kbeta) ).
tff(f415,plain,
spl4_41,
inference(avatar_split_clause,[],[f164,f413]) ).
tff(f413,plain,
( spl4_41
<=> ! [X0] :
( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).
tff(f164,plain,
! [X0: $i] :
( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(cnf_transformation,[],[f89]) ).
tff(f89,plain,
! [X0] :
( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(ennf_transformation,[],[f69]) ).
tff(f69,plain,
! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X3] :
( mem(X3,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X3)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).
tff(f392,plain,
spl4_40,
inference(avatar_split_clause,[],[f169,f390]) ).
tff(f169,plain,
! [X0: del,X1: $i] :
( ( ap(i(X0),X1) = X1 )
| ~ mem(X1,X0) ),
inference(cnf_transformation,[],[f90]) ).
tff(f90,plain,
! [X0: del,X1] :
( ( ap(i(X0),X1) = X1 )
| ~ mem(X1,X0) ),
inference(ennf_transformation,[],[f73]) ).
tff(f73,plain,
! [X0: del,X1] :
( mem(X1,X0)
=> ( ap(i(X0),X1) = X1 ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: del,X3] :
( mem(X3,X0)
=> ( ap(i(X0),X3) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ibeta) ).
tff(f388,plain,
spl4_39,
inference(avatar_split_clause,[],[f155,f386]) ).
tff(f386,plain,
( spl4_39
<=> ! [X0] :
( p(ap(c_2Ebool_2E_7E,X0))
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).
tff(f155,plain,
! [X0: $i] :
( p(ap(c_2Ebool_2E_7E,X0))
| p(X0)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f102]) ).
tff(f102,plain,
! [X0] :
( ( ( p(ap(c_2Ebool_2E_7E,X0))
| p(X0) )
& ( ~ p(X0)
| ~ p(ap(c_2Ebool_2E_7E,X0)) ) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f84]) ).
tff(f84,plain,
! [X0] :
( ( p(ap(c_2Ebool_2E_7E,X0))
<=> ~ p(X0) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f65]) ).
tff(f65,plain,
! [X0] :
( mem(X0,bool)
=> ( p(ap(c_2Ebool_2E_7E,X0))
<=> ~ p(X0) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X4] :
( mem(X4,bool)
=> ( p(ap(c_2Ebool_2E_7E,X4))
<=> ~ p(X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
tff(f384,plain,
( spl4_38
| ~ spl4_14
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f299,f290,f257,f381]) ).
tff(f381,plain,
( spl4_38
<=> ( fo__c_2Ebool_2ET = surj__o(c_2Ebool_2ET) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
tff(f257,plain,
( spl4_14
<=> ( c_2Ebool_2ET = inj__o(fo__c_2Ebool_2ET) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
tff(f290,plain,
( spl4_21
<=> ! [X0: tp__o] : ( surj__o(inj__o(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
tff(f299,plain,
( ( fo__c_2Ebool_2ET = surj__o(c_2Ebool_2ET) )
| ~ spl4_14
| ~ spl4_21 ),
inference(superposition,[],[f291,f259]) ).
tff(f259,plain,
( ( c_2Ebool_2ET = inj__o(fo__c_2Ebool_2ET) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f257]) ).
tff(f291,plain,
( ! [X0: tp__o] : ( surj__o(inj__o(X0)) = X0 )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f290]) ).
tff(f379,plain,
spl4_37,
inference(avatar_split_clause,[],[f154,f377]) ).
tff(f377,plain,
( spl4_37
<=> ! [X0] :
( ~ p(X0)
| ~ p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
tff(f154,plain,
! [X0: $i] :
( ~ p(X0)
| ~ p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f102]) ).
tff(f375,plain,
spl4_36,
inference(avatar_split_clause,[],[f134,f372]) ).
tff(f372,plain,
( spl4_36
<=> mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
tff(f134,plain,
mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
mem(c_2Ecomplex_2Ecomplex__inv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__inv) ).
tff(f356,plain,
spl4_35,
inference(avatar_split_clause,[],[f175,f354]) ).
tff(f354,plain,
( spl4_35
<=> ! [X0: del,X1: tp__o] :
( p(inj__o(X1))
| mem(sK2(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
tff(f175,plain,
! [X0: del,X1: tp__o] :
( p(inj__o(X1))
| mem(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: del,X1: tp__o] :
( ( ! [X2] :
( p(inj__o(X1))
| ~ mem(X2,X0) )
| ~ p(inj__o(X1)) )
& ( p(inj__o(X1))
| ( ~ p(inj__o(X1))
& mem(sK2(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f115,f116]) ).
tff(f116,plain,
! [X0: del,X1: tp__o] :
( ? [X3] :
( ~ p(inj__o(X1))
& mem(X3,X0) )
=> ( ~ p(inj__o(X1))
& mem(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f115,plain,
! [X0: del,X1: tp__o] :
( ( ! [X2] :
( p(inj__o(X1))
| ~ mem(X2,X0) )
| ~ p(inj__o(X1)) )
& ( p(inj__o(X1))
| ? [X3] :
( ~ p(inj__o(X1))
& mem(X3,X0) ) ) ),
inference(rectify,[],[f114]) ).
tff(f114,plain,
! [X0: del,X1: tp__o] :
( ( ! [X2] :
( p(inj__o(X1))
| ~ mem(X2,X0) )
| ~ p(inj__o(X1)) )
& ( p(inj__o(X1))
| ? [X2] :
( ~ p(inj__o(X1))
& mem(X2,X0) ) ) ),
inference(nnf_transformation,[],[f93]) ).
tff(f93,plain,
! [X0: del,X1: tp__o] :
( ! [X2] :
( p(inj__o(X1))
| ~ mem(X2,X0) )
<=> p(inj__o(X1)) ),
inference(ennf_transformation,[],[f76]) ).
tff(f76,plain,
! [X0: del,X1: tp__o] :
( ! [X2] :
( mem(X2,X0)
=> p(inj__o(X1)) )
<=> p(inj__o(X1)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X10: del,X11: tp__o] :
( ! [X12] :
( mem(X12,X10)
=> p(inj__o(X11)) )
<=> p(inj__o(X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EFORALL__SIMP) ).
tff(f352,plain,
( spl4_34
| ~ spl4_13
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f298,f290,f252,f349]) ).
tff(f349,plain,
( spl4_34
<=> ( fo__c_2Ebool_2EF = surj__o(c_2Ebool_2EF) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
tff(f252,plain,
( spl4_13
<=> ( c_2Ebool_2EF = inj__o(fo__c_2Ebool_2EF) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
tff(f298,plain,
( ( fo__c_2Ebool_2EF = surj__o(c_2Ebool_2EF) )
| ~ spl4_13
| ~ spl4_21 ),
inference(superposition,[],[f291,f254]) ).
tff(f254,plain,
( ( c_2Ebool_2EF = inj__o(fo__c_2Ebool_2EF) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f252]) ).
tff(f347,plain,
spl4_33,
inference(avatar_split_clause,[],[f153,f345]) ).
tff(f345,plain,
( spl4_33
<=> ! [X0] :
( ( inj__o(surj__o(X0)) = X0 )
| ~ mem(X0,bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
tff(f153,plain,
! [X0: $i] :
( ( inj__o(surj__o(X0)) = X0 )
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f83]) ).
tff(f83,plain,
! [X0] :
( ( inj__o(surj__o(X0)) = X0 )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f64]) ).
tff(f64,plain,
! [X0] :
( mem(X0,bool)
=> ( inj__o(surj__o(X0)) = X0 ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X3] :
( mem(X3,bool)
=> ( inj__o(surj__o(X3)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
tff(f343,plain,
spl4_32,
inference(avatar_split_clause,[],[f152,f341]) ).
tff(f341,plain,
( spl4_32
<=> ! [X0] :
( ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Erealax_2Ereal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
tff(f152,plain,
! [X0: $i] :
( ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(cnf_transformation,[],[f82]) ).
tff(f82,plain,
! [X0] :
( ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) = X0 )
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(ennf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0] :
( mem(X0,ty_2Erealax_2Ereal)
=> ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X0)) = X0 ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X3] :
( mem(X3,ty_2Erealax_2Ereal)
=> ( inj__ty_2Erealax_2Ereal(surj__ty_2Erealax_2Ereal(X3)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal) ).
tff(f339,plain,
spl4_31,
inference(avatar_split_clause,[],[f151,f337]) ).
tff(f337,plain,
( spl4_31
<=> ! [X0] :
( ( inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X0)) = X0 )
| ~ mem(X0,ty_2Enum_2Enum) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
tff(f151,plain,
! [X0: $i] :
( ( inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X0)) = X0 )
| ~ mem(X0,ty_2Enum_2Enum) ),
inference(cnf_transformation,[],[f81]) ).
tff(f81,plain,
! [X0] :
( ( inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X0)) = X0 )
| ~ mem(X0,ty_2Enum_2Enum) ),
inference(ennf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0] :
( mem(X0,ty_2Enum_2Enum)
=> ( inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X0)) = X0 ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X3] :
( mem(X3,ty_2Enum_2Enum)
=> ( inj__ty_2Enum_2Enum(surj__ty_2Enum_2Enum(X3)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Enum_2Enum) ).
tff(f335,plain,
spl4_30,
inference(avatar_split_clause,[],[f145,f333]) ).
tff(f333,plain,
( spl4_30
<=> ! [X0: del] : mem(c_2Emin_2E_3D(X0),arr(X0,arr(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
tff(f145,plain,
! [X0: del] : mem(c_2Emin_2E_3D(X0),arr(X0,arr(X0,bool))),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
! [X0: del] : mem(c_2Emin_2E_3D(X0),arr(X0,arr(X0,bool))),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X10: del] : mem(c_2Emin_2E_3D(X10),arr(X10,arr(X10,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
tff(f331,plain,
spl4_29,
inference(avatar_split_clause,[],[f144,f329]) ).
tff(f329,plain,
( spl4_29
<=> ! [X0: del] : mem(c_2Ebool_2E_21(X0),arr(arr(X0,bool),bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
tff(f144,plain,
! [X0: del] : mem(c_2Ebool_2E_21(X0),arr(arr(X0,bool),bool)),
inference(cnf_transformation,[],[f57]) ).
tff(f57,plain,
! [X0: del] : mem(c_2Ebool_2E_21(X0),arr(arr(X0,bool),bool)),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X10: del] : mem(c_2Ebool_2E_21(X10),arr(arr(X10,bool),bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
tff(f327,plain,
spl4_28,
inference(avatar_split_clause,[],[f143,f325]) ).
tff(f325,plain,
( spl4_28
<=> ! [X0: tp__o] : ( inj__o(fo__c_2Ebool_2E_7E(X0)) = ap(c_2Ebool_2E_7E,inj__o(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
tff(f143,plain,
! [X0: tp__o] : ( inj__o(fo__c_2Ebool_2E_7E(X0)) = ap(c_2Ebool_2E_7E,inj__o(X0)) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
! [X0: tp__o] : ( inj__o(fo__c_2Ebool_2E_7E(X0)) = ap(c_2Ebool_2E_7E,inj__o(X0)) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X8: tp__o] : ( inj__o(fo__c_2Ebool_2E_7E(X8)) = ap(c_2Ebool_2E_7E,inj__o(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2E_7E) ).
tff(f323,plain,
spl4_27,
inference(avatar_split_clause,[],[f133,f320]) ).
tff(f320,plain,
( spl4_27
<=> mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
tff(f133,plain,
mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))),
inference(cnf_transformation,[],[f35]) ).
tff(f35,axiom,
mem(c_2Ecomplex_2Ecomplex__of__num,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__of__num) ).
tff(f318,plain,
( spl4_26
| ~ spl4_12
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f297,f286,f247,f315]) ).
tff(f315,plain,
( spl4_26
<=> ( fo__c_2Enum_2E0 = surj__ty_2Enum_2Enum(c_2Enum_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
tff(f247,plain,
( spl4_12
<=> ( c_2Enum_2E0 = inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
tff(f286,plain,
( spl4_20
<=> ! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
tff(f297,plain,
( ( fo__c_2Enum_2E0 = surj__ty_2Enum_2Enum(c_2Enum_2E0) )
| ~ spl4_12
| ~ spl4_20 ),
inference(superposition,[],[f287,f249]) ).
tff(f249,plain,
( ( c_2Enum_2E0 = inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f247]) ).
tff(f287,plain,
( ! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X0)) = X0 )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f286]) ).
tff(f313,plain,
spl4_25,
inference(avatar_split_clause,[],[f132,f310]) ).
tff(f310,plain,
( spl4_25
<=> mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
tff(f132,plain,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[],[f21]) ).
tff(f21,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
tff(f308,plain,
spl4_24,
inference(avatar_split_clause,[],[f131,f305]) ).
tff(f305,plain,
( spl4_24
<=> mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
tff(f131,plain,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
tff(f303,plain,
spl4_23,
inference(avatar_split_clause,[],[f142,f301]) ).
tff(f301,plain,
( spl4_23
<=> ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : mem(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
tff(f142,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : mem(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f55]) ).
tff(f55,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : mem(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X3: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : mem(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X3),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).
tff(f296,plain,
spl4_22,
inference(avatar_split_clause,[],[f141,f294]) ).
tff(f294,plain,
( spl4_22
<=> ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
tff(f141,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0)) = X0 ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X3: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).
tff(f292,plain,
spl4_21,
inference(avatar_split_clause,[],[f140,f290]) ).
tff(f140,plain,
! [X0: tp__o] : ( surj__o(inj__o(X0)) = X0 ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: tp__o] : ( surj__o(inj__o(X0)) = X0 ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X3: tp__o] : ( surj__o(inj__o(X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
tff(f288,plain,
spl4_20,
inference(avatar_split_clause,[],[f139,f286]) ).
tff(f139,plain,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X0)) = X0 ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X0)) = X0 ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X3: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Enum_2Enum) ).
tff(f284,plain,
spl4_19,
inference(avatar_split_clause,[],[f138,f282]) ).
tff(f282,plain,
( spl4_19
<=> ! [X0: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
tff(f138,plain,
! [X0: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X0)) = X0 ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,plain,
! [X0: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X0)) = X0 ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X3: tp__ty_2Erealax_2Ereal] : ( surj__ty_2Erealax_2Ereal(inj__ty_2Erealax_2Ereal(X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal) ).
tff(f280,plain,
spl4_18,
inference(avatar_split_clause,[],[f130,f277]) ).
tff(f277,plain,
( spl4_18
<=> mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
tff(f130,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
tff(f272,plain,
spl4_17,
inference(avatar_split_clause,[],[f137,f270]) ).
tff(f270,plain,
( spl4_17
<=> ! [X0: tp__o] : mem(inj__o(X0),bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
tff(f137,plain,
! [X0: tp__o] : mem(inj__o(X0),bool),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: tp__o] : mem(inj__o(X0),bool),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X3: tp__o] : mem(inj__o(X3),bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
tff(f268,plain,
spl4_16,
inference(avatar_split_clause,[],[f136,f266]) ).
tff(f266,plain,
( spl4_16
<=> ! [X0: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X0),ty_2Enum_2Enum) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
tff(f136,plain,
! [X0: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X0),ty_2Enum_2Enum),
inference(cnf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X0),ty_2Enum_2Enum),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X3: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X3),ty_2Enum_2Enum),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Enum_2Enum) ).
tff(f264,plain,
spl4_15,
inference(avatar_split_clause,[],[f135,f262]) ).
tff(f262,plain,
( spl4_15
<=> ! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
tff(f135,plain,
! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X3: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X3),ty_2Erealax_2Ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal) ).
tff(f260,plain,
spl4_14,
inference(avatar_split_clause,[],[f129,f257]) ).
tff(f129,plain,
c_2Ebool_2ET = inj__o(fo__c_2Ebool_2ET),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
c_2Ebool_2ET = inj__o(fo__c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2ET) ).
tff(f255,plain,
spl4_13,
inference(avatar_split_clause,[],[f128,f252]) ).
tff(f128,plain,
c_2Ebool_2EF = inj__o(fo__c_2Ebool_2EF),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
c_2Ebool_2EF = inj__o(fo__c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2EF) ).
tff(f250,plain,
spl4_12,
inference(avatar_split_clause,[],[f127,f247]) ).
tff(f245,plain,
( spl4_11
| ~ spl4_6
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f240,f236,f216,f242]) ).
tff(f242,plain,
( spl4_11
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
tff(f236,plain,
( spl4_10
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
tff(f240,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0))))) )
| ~ spl4_6
| ~ spl4_10 ),
inference(forward_demodulation,[],[f238,f218]) ).
tff(f238,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0)))))) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f236]) ).
tff(f239,plain,
spl4_10,
inference(avatar_split_clause,[],[f185,f236]) ).
tff(f185,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0)))))),
inference(forward_demodulation,[],[f182,f121]) ).
tff(f121,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))),
inference(cnf_transformation,[],[f99]) ).
tff(f99,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) )
& ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f79,f98]) ).
tff(f98,plain,
( ? [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) )
& ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X0 ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) )
& ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != sK0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f79,plain,
? [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) )
& ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X0 ) ),
inference(ennf_transformation,[],[f47]) ).
tff(f47,plain,
~ ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X0 )
=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) ) ),
inference(rectify,[],[f46]) ).
tff(f46,negated_conjecture,
~ ! [X13: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X13 )
=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X13))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ),
inference(negated_conjecture,[],[f45]) ).
tff(f45,conjecture,
! [X13: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X13 )
=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X13))) != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
tff(f182,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))),
inference(equality_resolution,[],[f166]) ).
tff(f166,plain,
! [X0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(X0))) )
| ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != X0 ) ),
inference(cnf_transformation,[],[f108]) ).
tff(f234,plain,
spl4_9,
inference(avatar_split_clause,[],[f126,f231]) ).
tff(f126,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
tff(f229,plain,
spl4_8,
inference(avatar_split_clause,[],[f125,f226]) ).
tff(f226,plain,
( spl4_8
<=> mem(c_2Ebool_2ET,bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
tff(f125,plain,
mem(c_2Ebool_2ET,bool),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
tff(f224,plain,
spl4_7,
inference(avatar_split_clause,[],[f124,f221]) ).
tff(f221,plain,
( spl4_7
<=> mem(c_2Enum_2E0,ty_2Enum_2Enum) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
tff(f124,plain,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
inference(cnf_transformation,[],[f27]) ).
tff(f27,axiom,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0) ).
tff(f219,plain,
( spl4_6
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f214,f210,f216]) ).
tff(f210,plain,
( spl4_5
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
tff(f214,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| ~ spl4_5 ),
inference(forward_demodulation,[],[f212,f127]) ).
tff(f212,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__inv,inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(sK0))) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f210]) ).
tff(f213,plain,
spl4_5,
inference(avatar_split_clause,[],[f121,f210]) ).
tff(f208,plain,
spl4_4,
inference(avatar_split_clause,[],[f123,f205]) ).
tff(f205,plain,
( spl4_4
<=> p(c_2Ebool_2ET) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
tff(f123,plain,
p(c_2Ebool_2ET),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
tff(f203,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f122,f200]) ).
tff(f200,plain,
( spl4_3
<=> p(c_2Ebool_2EF) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
tff(f122,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
tff(f198,plain,
( ~ spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f193,f189,f195]) ).
tff(f189,plain,
( spl4_1
<=> ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f193,plain,
( ( sK0 != surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) )
| spl4_1 ),
inference(forward_demodulation,[],[f191,f127]) ).
tff(f191,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != sK0 )
| spl4_1 ),
inference(avatar_component_clause,[],[f189]) ).
tff(f192,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f120,f189]) ).
tff(f120,plain,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(ap(c_2Ecomplex_2Ecomplex__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) != sK0,
inference(cnf_transformation,[],[f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP019_2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 17:34:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (899)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (902)WARNING: value z3 for option sas not known
% 0.14/0.38 % (901)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 % (903)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (900)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (902)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 % (904)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 % (909)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 % (907)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)
% 0.14/0.39 TRYING [1,1,1,1,1,1]
% 0.14/0.39 TRYING [1,1,1,1,1,2]
% 0.14/0.39 TRYING [1,2,1,1,1,2]
% 0.14/0.39 % (904)First to succeed.
% 0.14/0.40 TRYING [2,2,1,1,1,2]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 % (904)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-899"
% 0.14/0.40 TRYING [2]
% 0.14/0.40 % (904)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (904)------------------------------
% 0.14/0.40 % (904)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (904)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (904)Memory used [KB]: 1038
% 0.14/0.40 % (904)Time elapsed: 0.019 s
% 0.14/0.40 % (904)Instructions burned: 26 (million)
% 0.14/0.40 % (899)Success in time 0.036 s
%------------------------------------------------------------------------------