TSTP Solution File: NUM594+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM594+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:39:25 EDT 2024
% Result : Theorem 0.15s 0.42s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 94
% Syntax : Number of formulae : 257 ( 86 unt; 0 def)
% Number of atoms : 1228 ( 178 equ)
% Maximal formula atoms : 47 ( 4 avg)
% Number of connectives : 1318 ( 347 ~; 284 |; 544 &)
% ( 79 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 84 ( 82 usr; 49 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 14 con; 0-2 aty)
% Number of variables : 351 ( 302 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1199,plain,
$false,
inference(avatar_sat_refutation,[],[f967,f972,f977,f982,f987,f992,f997,f1002,f1007,f1012,f1017,f1022,f1027,f1032,f1037,f1042,f1047,f1052,f1057,f1062,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1100,f1104,f1108,f1112,f1116,f1120,f1125,f1130,f1135,f1139,f1144,f1149,f1153,f1158,f1167,f1177,f1181,f1185,f1189,f1193,f1197,f1198]) ).
fof(f1198,plain,
( ~ spl92_19
| ~ spl92_1
| ~ spl92_39 ),
inference(avatar_split_clause,[],[f1169,f1146,f965,f1054]) ).
fof(f1054,plain,
( spl92_19
<=> aElementOf0(sK54,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_19])]) ).
fof(f965,plain,
( spl92_1
<=> ! [X0] :
( sdtlpdtrp0(xd,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_1])]) ).
fof(f1146,plain,
( spl92_39
<=> xx = sdtlpdtrp0(xd,sK54) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_39])]) ).
fof(f1169,plain,
( ~ aElementOf0(sK54,szNzAzT0)
| ~ spl92_1
| ~ spl92_39 ),
inference(trivial_inequality_removal,[],[f1168]) ).
fof(f1168,plain,
( xx != xx
| ~ aElementOf0(sK54,szNzAzT0)
| ~ spl92_1
| ~ spl92_39 ),
inference(superposition,[],[f966,f1148]) ).
fof(f1148,plain,
( xx = sdtlpdtrp0(xd,sK54)
| ~ spl92_39 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f966,plain,
( ! [X0] :
( sdtlpdtrp0(xd,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl92_1 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f1197,plain,
spl92_48,
inference(avatar_split_clause,[],[f731,f1195]) ).
fof(f1195,plain,
( spl92_48
<=> ! [X0,X1] :
( sP31(X0)
| ~ sP33(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_48])]) ).
fof(f731,plain,
! [X0,X1] :
( sP31(X0)
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f419]) ).
fof(f419,plain,
! [X0,X1] :
( ( sP32(X1,X0,sK69(X0,X1))
& isCountable0(sK69(X0,X1))
& aSubsetOf0(sK69(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X3,sK69(X0,X1)) )
& aSet0(sK69(X0,X1))
& sP31(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP33(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f417,f418]) ).
fof(f418,plain,
! [X0,X1] :
( ? [X2] :
( sP32(X1,X0,X2)
& isCountable0(X2)
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X3,X2) )
& aSet0(X2)
& sP31(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( sP32(X1,X0,sK69(X0,X1))
& isCountable0(sK69(X0,X1))
& aSubsetOf0(sK69(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X3,sK69(X0,X1)) )
& aSet0(sK69(X0,X1))
& sP31(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f417,plain,
! [X0,X1] :
( ? [X2] :
( sP32(X1,X0,X2)
& isCountable0(X2)
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X3,X2) )
& aSet0(X2)
& sP31(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP33(X0,X1) ),
inference(rectify,[],[f416]) ).
fof(f416,plain,
! [X0,X1] :
( ? [X2] :
( sP32(X1,X0,X2)
& isCountable0(X2)
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X5,X2) )
& aSet0(X2)
& sP31(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP33(X0,X1) ),
inference(nnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1] :
( ? [X2] :
( sP32(X1,X0,X2)
& isCountable0(X2)
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X5,X2) )
& aSet0(X2)
& sP31(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP33(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP33])]) ).
fof(f1193,plain,
spl92_47,
inference(avatar_split_clause,[],[f704,f1191]) ).
fof(f1191,plain,
( spl92_47
<=> ! [X0,X1] :
( sP27(X0)
| ~ sP28(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_47])]) ).
fof(f704,plain,
! [X0,X1] :
( sP27(X0)
| ~ sP28(X0,X1) ),
inference(cnf_transformation,[],[f396]) ).
fof(f396,plain,
! [X0,X1] :
( ( aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,X1) )
& sP27(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP28(X0,X1) ),
inference(rectify,[],[f395]) ).
fof(f395,plain,
! [X0,X5] :
( ( aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X7,X5) )
& sP27(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP28(X0,X5) ),
inference(nnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0,X5] :
( ( aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X7,X5) )
& sP27(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP28(X0,X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f1189,plain,
spl92_46,
inference(avatar_split_clause,[],[f698,f1187]) ).
fof(f1187,plain,
( spl92_46
<=> ! [X0,X1] :
( sP25(X0)
| ~ sP29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_46])]) ).
fof(f698,plain,
! [X0,X1] :
( sP25(X0)
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f394]) ).
fof(f394,plain,
! [X0,X1] :
( ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP26(X0,X1)
& sP25(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP29(X0,X1) ),
inference(nnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP26(X0,X1)
& sP25(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP29(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f1185,plain,
spl92_45,
inference(avatar_split_clause,[],[f646,f1183]) ).
fof(f1183,plain,
( spl92_45
<=> ! [X0,X1] :
( sP12(X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_45])]) ).
fof(f646,plain,
! [X0,X1] :
( sP12(X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& sP13(X1,X0)
& sP12(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP15(X0,X1) ),
inference(nnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& sP13(X1,X0)
& sP12(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP15(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f1181,plain,
spl92_44,
inference(avatar_split_clause,[],[f570,f1179]) ).
fof(f1179,plain,
( spl92_44
<=> ! [X0,X1] :
( sP1(X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_44])]) ).
fof(f570,plain,
! [X0,X1] :
( sP1(X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& sP2(X1,X0)
& sP1(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& sP2(X1,X0)
& sP1(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f1177,plain,
spl92_43,
inference(avatar_split_clause,[],[f559,f1175]) ).
fof(f1175,plain,
( spl92_43
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_43])]) ).
fof(f559,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ( ~ aElementOf0(sK50(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK50(X0,X1),X1) )
| ~ aSet0(X1) ) ) )
& sP0(X1,X0) )
| ~ sP6(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f314,f315]) ).
fof(f315,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK50(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK50(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X2,X1) )
| ~ aSet0(X1) ) ) )
& sP0(X1,X0) )
| ~ sP6(X0) ),
inference(rectify,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& sP0(X7,X0) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& sP0(X7,X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f1167,plain,
( spl92_42
| ~ spl92_20
| ~ spl92_37 ),
inference(avatar_split_clause,[],[f1159,f1137,f1059,f1164]) ).
fof(f1164,plain,
( spl92_42
<=> sP8(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_42])]) ).
fof(f1059,plain,
( spl92_20
<=> aElementOf0(sz00,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_20])]) ).
fof(f1137,plain,
( spl92_37
<=> ! [X0] :
( sP8(X0)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_37])]) ).
fof(f1159,plain,
( sP8(sz00)
| ~ spl92_20
| ~ spl92_37 ),
inference(resolution,[],[f1138,f1061]) ).
fof(f1061,plain,
( aElementOf0(sz00,szNzAzT0)
| ~ spl92_20 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1138,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP8(X0) )
| ~ spl92_37 ),
inference(avatar_component_clause,[],[f1137]) ).
fof(f1158,plain,
spl92_41,
inference(avatar_split_clause,[],[f959,f1155]) ).
fof(f1155,plain,
( spl92_41
<=> aElementOf0(xx,sdtlcdtrc0(xd,szNzAzT0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_41])]) ).
fof(f959,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szNzAzT0)),
inference(forward_demodulation,[],[f623,f527]) ).
fof(f527,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
( ! [X0] :
( ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ~ aElementOf0(sK47(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK47(X0,X1),X1) ) ) )
| ~ aSet0(X1) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xd)
& aFunction0(xd) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f116,f302]) ).
fof(f302,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK47(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK47(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
( ! [X0] :
( ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) ) ) ) )
| ~ aSet0(X1) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xd)
& aFunction0(xd) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
( ! [X0] :
( ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) ) ) ) )
| ~ aSet0(X1) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xd)
& aFunction0(xd) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( ( aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) )
& aSet0(X1) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0) ) )
& szNzAzT0 = szDzozmdt0(xd)
& aFunction0(xd) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(f623,plain,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
& xx = sdtlpdtrp0(xd,sK54)
& aElementOf0(sK54,szDzozmdt0(xd)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f94,f344]) ).
fof(f344,plain,
( ? [X0] :
( sdtlpdtrp0(xd,X0) = xx
& aElementOf0(X0,szDzozmdt0(xd)) )
=> ( xx = sdtlpdtrp0(xd,sK54)
& aElementOf0(sK54,szDzozmdt0(xd)) ) ),
introduced(choice_axiom,[]) ).
fof(f94,axiom,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ? [X0] :
( sdtlpdtrp0(xd,X0) = xx
& aElementOf0(X0,szDzozmdt0(xd)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4781) ).
fof(f1153,plain,
spl92_40,
inference(avatar_split_clause,[],[f632,f1151]) ).
fof(f1151,plain,
( spl92_40
<=> ! [X0] :
( sP11(X0)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_40])]) ).
fof(f632,plain,
! [X0] :
( sP11(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0] :
( ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))),xT)
& ! [X1] :
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0)))) )
& sP11(X0)
& aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0)))) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(definition_folding,[],[f125,f252]) ).
fof(f252,plain,
! [X0] :
( ! [X2] :
( aElementOf0(X2,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))))
<=> ? [X3] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X3) = X2
& aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f125,plain,
! [X0] :
( ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))),xT)
& ! [X1] :
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0)))) )
& ! [X2] :
( aElementOf0(X2,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))))
<=> ? [X3] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X3) = X2
& aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0)))) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))),xT)
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))))
=> aElementOf0(X1,xT) )
& ! [X2] :
( aElementOf0(X2,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))))
<=> ? [X3] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X3) = X2
& aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0)))) ) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))),xT)
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))))
=> aElementOf0(X1,xT) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0))))
<=> ? [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1
& aElementOf0(X2,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,X0),szDzozmdt0(sdtlpdtrp0(xC,X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4182) ).
fof(f1149,plain,
spl92_39,
inference(avatar_split_clause,[],[f622,f1146]) ).
fof(f622,plain,
xx = sdtlpdtrp0(xd,sK54),
inference(cnf_transformation,[],[f345]) ).
fof(f1144,plain,
spl92_38,
inference(avatar_split_clause,[],[f605,f1141]) ).
fof(f1141,plain,
( spl92_38
<=> xS = sdtlpdtrp0(xN,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_38])]) ).
fof(f605,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f339]) ).
fof(f339,plain,
( ! [X0] :
( sP10(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( ~ aElementOf0(sK52(X0),szNzAzT0)
& aElementOf0(sK52(X0),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f251,f338]) ).
fof(f338,plain,
! [X0] :
( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
=> ( ~ aElementOf0(sK52(X0),szNzAzT0)
& aElementOf0(sK52(X0),sdtlpdtrp0(xN,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
( ! [X0] :
( sP10(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(definition_folding,[],[f122,f250,f249]) ).
fof(f249,plain,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f250,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP9(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f122,plain,
( ! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
( ! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f1139,plain,
spl92_37,
inference(avatar_split_clause,[],[f590,f1137]) ).
fof(f590,plain,
! [X0] :
( sP8(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
( ! [X0] :
( sP8(X0)
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(definition_folding,[],[f120,f247,f246,f245,f244,f243,f242,f241,f240,f239]) ).
fof(f239,plain,
! [X7,X0] :
( ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ~ sP0(X7,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f240,plain,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f241,plain,
! [X1,X0] :
( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f242,plain,
! [X0,X1] :
( ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f244,plain,
! [X0] :
( ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP3(X0,X1)
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| sP4(X0,X1)
| ~ aSet0(X1) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f247,plain,
! [X0] :
( ( sP7(X0)
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& sP6(X0)
& sP5(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f120,plain,
( ! [X0] :
( ( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) ) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(X1) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& ( ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
( ! [X0] :
( ( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) ) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(X1) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& ( ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( ( ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) )
& aSet0(X1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( aElementOf0(X6,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X7] :
( ( ( xk = sbrdtbr0(X7)
& ( aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X7) ) ) )
=> aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,X7)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X7) ) ) )
& ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( aElementOf0(X11,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( ( ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) )
& aSet0(X1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| aElementOf0(X2,X1) )
& aElement0(X2) ) )
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X1] :
( ( ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1) ) ) )
=> aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1) ) ) )
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
fof(f1135,plain,
spl92_36,
inference(avatar_split_clause,[],[f541,f1132]) ).
fof(f1132,plain,
( spl92_36
<=> aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_36])]) ).
fof(f541,plain,
aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(cnf_transformation,[],[f308]) ).
fof(f308,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [X1] :
( ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X2] :
( sdtlpdtrp0(xc,X2) != X1
| ~ aElementOf0(X2,szDzozmdt0(xc)) ) )
& ( ( sdtlpdtrp0(xc,sK48(X1)) = X1
& aElementOf0(sK48(X1),szDzozmdt0(xc)) )
| ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X4] :
( ( aElementOf0(X4,szDzozmdt0(xc))
| xK != sbrdtbr0(X4)
| ( ~ aSubsetOf0(X4,xS)
& ( ( ~ aElementOf0(sK49(X4),xS)
& aElementOf0(sK49(X4),X4) )
| ~ aSet0(X4) ) ) )
& ( ( xK = sbrdtbr0(X4)
& aSubsetOf0(X4,xS)
& ! [X6] :
( aElementOf0(X6,xS)
| ~ aElementOf0(X6,X4) )
& aSet0(X4) )
| ~ aElementOf0(X4,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f305,f307,f306]) ).
fof(f306,plain,
! [X1] :
( ? [X3] :
( sdtlpdtrp0(xc,X3) = X1
& aElementOf0(X3,szDzozmdt0(xc)) )
=> ( sdtlpdtrp0(xc,sK48(X1)) = X1
& aElementOf0(sK48(X1),szDzozmdt0(xc)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X4] :
( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,X4) )
=> ( ~ aElementOf0(sK49(X4),xS)
& aElementOf0(sK49(X4),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [X1] :
( ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X2] :
( sdtlpdtrp0(xc,X2) != X1
| ~ aElementOf0(X2,szDzozmdt0(xc)) ) )
& ( ? [X3] :
( sdtlpdtrp0(xc,X3) = X1
& aElementOf0(X3,szDzozmdt0(xc)) )
| ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X4] :
( ( aElementOf0(X4,szDzozmdt0(xc))
| xK != sbrdtbr0(X4)
| ( ~ aSubsetOf0(X4,xS)
& ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,X4) )
| ~ aSet0(X4) ) ) )
& ( ( xK = sbrdtbr0(X4)
& aSubsetOf0(X4,xS)
& ! [X6] :
( aElementOf0(X6,xS)
| ~ aElementOf0(X6,X4) )
& aSet0(X4) )
| ~ aElementOf0(X4,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(rectify,[],[f304]) ).
fof(f304,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [X1] :
( ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X2] :
( sdtlpdtrp0(xc,X2) != X1
| ~ aElementOf0(X2,szDzozmdt0(xc)) ) )
& ( ? [X2] :
( sdtlpdtrp0(xc,X2) = X1
& aElementOf0(X2,szDzozmdt0(xc)) )
| ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X3] :
( ( aElementOf0(X3,szDzozmdt0(xc))
| sbrdtbr0(X3) != xK
| ( ~ aSubsetOf0(X3,xS)
& ( ? [X4] :
( ~ aElementOf0(X4,xS)
& aElementOf0(X4,X3) )
| ~ aSet0(X3) ) ) )
& ( ( sbrdtbr0(X3) = xK
& aSubsetOf0(X3,xS)
& ! [X5] :
( aElementOf0(X5,xS)
| ~ aElementOf0(X5,X3) )
& aSet0(X3) )
| ~ aElementOf0(X3,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(nnf_transformation,[],[f118]) ).
fof(f118,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X2] :
( sdtlpdtrp0(xc,X2) = X1
& aElementOf0(X2,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X3] :
( ( aElementOf0(X3,szDzozmdt0(xc))
| sbrdtbr0(X3) != xK
| ( ~ aSubsetOf0(X3,xS)
& ( ? [X4] :
( ~ aElementOf0(X4,xS)
& aElementOf0(X4,X3) )
| ~ aSet0(X3) ) ) )
& ( ( sbrdtbr0(X3) = xK
& aSubsetOf0(X3,xS)
& ! [X5] :
( aElementOf0(X5,xS)
| ~ aElementOf0(X5,X3) )
& aSet0(X3) )
| ~ aElementOf0(X3,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X2] :
( sdtlpdtrp0(xc,X2) = X1
& aElementOf0(X2,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X3] :
( ( aElementOf0(X3,szDzozmdt0(xc))
| sbrdtbr0(X3) != xK
| ( ~ aSubsetOf0(X3,xS)
& ( ? [X4] :
( ~ aElementOf0(X4,xS)
& aElementOf0(X4,X3) )
| ~ aSet0(X3) ) ) )
& ( ( sbrdtbr0(X3) = xK
& aSubsetOf0(X3,xS)
& ! [X5] :
( aElementOf0(X5,xS)
| ~ aElementOf0(X5,X3) )
& aSet0(X3) )
| ~ aElementOf0(X3,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X0,xT) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X2] :
( sdtlpdtrp0(xc,X2) = X1
& aElementOf0(X2,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X3] :
( ( ( sbrdtbr0(X3) = xK
& ( aSubsetOf0(X3,xS)
| ( ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,xS) )
& aSet0(X3) ) ) )
=> aElementOf0(X3,szDzozmdt0(xc)) )
& ( aElementOf0(X3,szDzozmdt0(xc))
=> ( sbrdtbr0(X3) = xK
& aSubsetOf0(X3,xS)
& ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,xS) )
& aSet0(X3) ) ) )
& aFunction0(xc) ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X0,xT) )
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X1] :
( sdtlpdtrp0(xc,X1) = X0
& aElementOf0(X1,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( ( sbrdtbr0(X0) = xK
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
=> ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f1130,plain,
( ~ spl92_14
| ~ spl92_35 ),
inference(avatar_split_clause,[],[f934,f1127,f1029]) ).
fof(f1029,plain,
( spl92_14
<=> aSet0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_14])]) ).
fof(f1127,plain,
( spl92_35
<=> isCountable0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_35])]) ).
fof(f934,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f833]) ).
fof(f833,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f192]) ).
fof(f192,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> slcrc0 != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f1125,plain,
spl92_34,
inference(avatar_split_clause,[],[f757,f1122]) ).
fof(f1122,plain,
( spl92_34
<=> slcrc0 = slbdtrb0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_34])]) ).
fof(f757,plain,
slcrc0 = slbdtrb0(sz00),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
slcrc0 = slbdtrb0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(f1120,plain,
spl92_33,
inference(avatar_split_clause,[],[f667,f1118]) ).
fof(f1118,plain,
( spl92_33
<=> ! [X0] :
( sP20(X0)
| ~ sP23(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_33])]) ).
fof(f667,plain,
! [X0] :
( sP20(X0)
| ~ sP23(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ( ~ aSubsetOf0(sdtlcdtrc0(X0,szDzozmdt0(X0)),xT)
& sP20(X0)
& sP19(X0)
& aSet0(sdtlcdtrc0(X0,szDzozmdt0(X0))) )
| ~ sP23(X0) ),
inference(rectify,[],[f367]) ).
fof(f367,plain,
! [X3] :
( ( ~ aSubsetOf0(sdtlcdtrc0(X3,szDzozmdt0(X3)),xT)
& sP20(X3)
& sP19(X3)
& aSet0(sdtlcdtrc0(X3,szDzozmdt0(X3))) )
| ~ sP23(X3) ),
inference(nnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X3] :
( ( ~ aSubsetOf0(sdtlcdtrc0(X3,szDzozmdt0(X3)),xT)
& sP20(X3)
& sP19(X3)
& aSet0(sdtlcdtrc0(X3,szDzozmdt0(X3))) )
| ~ sP23(X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f1116,plain,
spl92_32,
inference(avatar_split_clause,[],[f666,f1114]) ).
fof(f1114,plain,
( spl92_32
<=> ! [X0] :
( sP19(X0)
| ~ sP23(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_32])]) ).
fof(f666,plain,
! [X0] :
( sP19(X0)
| ~ sP23(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f1112,plain,
spl92_31,
inference(avatar_split_clause,[],[f594,f1110]) ).
fof(f1110,plain,
( spl92_31
<=> ! [X0] :
( sP9(X0)
| ~ sP10(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_31])]) ).
fof(f594,plain,
! [X0] :
( sP9(X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP9(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP10(X0) ),
inference(rectify,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP9(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f250]) ).
fof(f1108,plain,
spl92_30,
inference(avatar_split_clause,[],[f554,f1106]) ).
fof(f1106,plain,
( spl92_30
<=> ! [X0] :
( sP7(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_30])]) ).
fof(f554,plain,
! [X0] :
( sP7(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ( sP7(X0)
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& sP6(X0)
& sP5(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ sP8(X0) ),
inference(rectify,[],[f309]) ).
fof(f309,plain,
! [X0] :
( ( sP7(X0)
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& sP6(X0)
& sP5(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f247]) ).
fof(f1104,plain,
spl92_29,
inference(avatar_split_clause,[],[f552,f1102]) ).
fof(f1102,plain,
( spl92_29
<=> ! [X0] :
( sP6(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_29])]) ).
fof(f552,plain,
! [X0] :
( sP6(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f1100,plain,
spl92_28,
inference(avatar_split_clause,[],[f551,f1098]) ).
fof(f1098,plain,
( spl92_28
<=> ! [X0] :
( sP5(X0)
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_28])]) ).
fof(f551,plain,
! [X0] :
( sP5(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f1096,plain,
spl92_27,
inference(avatar_split_clause,[],[f958,f1093]) ).
fof(f1093,plain,
( spl92_27
<=> aSet0(sdtlcdtrc0(xd,szNzAzT0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_27])]) ).
fof(f958,plain,
aSet0(sdtlcdtrc0(xd,szNzAzT0)),
inference(forward_demodulation,[],[f617,f527]) ).
fof(f617,plain,
aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [X1] :
( sdtlpdtrp0(xd,X1) != X0
| ~ aElementOf0(X1,szDzozmdt0(xd)) ) )
& ( ( sdtlpdtrp0(xd,sK53(X0)) = X0
& aElementOf0(sK53(X0),szDzozmdt0(xd)) )
| ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd))) ) )
& aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f341,f342]) ).
fof(f342,plain,
! [X0] :
( ? [X2] :
( sdtlpdtrp0(xd,X2) = X0
& aElementOf0(X2,szDzozmdt0(xd)) )
=> ( sdtlpdtrp0(xd,sK53(X0)) = X0
& aElementOf0(sK53(X0),szDzozmdt0(xd)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [X1] :
( sdtlpdtrp0(xd,X1) != X0
| ~ aElementOf0(X1,szDzozmdt0(xd)) ) )
& ( ? [X2] :
( sdtlpdtrp0(xd,X2) = X0
& aElementOf0(X2,szDzozmdt0(xd)) )
| ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd))) ) )
& aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(rectify,[],[f340]) ).
fof(f340,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [X1] :
( sdtlpdtrp0(xd,X1) != X0
| ~ aElementOf0(X1,szDzozmdt0(xd)) ) )
& ( ? [X1] :
( sdtlpdtrp0(xd,X1) = X0
& aElementOf0(X1,szDzozmdt0(xd)) )
| ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd))) ) )
& aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,axiom,
( ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [X1] :
( sdtlpdtrp0(xd,X1) = X0
& aElementOf0(X1,szDzozmdt0(xd)) ) )
& aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4769) ).
fof(f1091,plain,
spl92_26,
inference(avatar_split_clause,[],[f616,f1088]) ).
fof(f1088,plain,
( spl92_26
<=> xK = szszuzczcdt0(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_26])]) ).
fof(f616,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
( xK = szszuzczcdt0(xk)
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f1086,plain,
spl92_25,
inference(avatar_split_clause,[],[f604,f1083]) ).
fof(f1083,plain,
( spl92_25
<=> szNzAzT0 = szDzozmdt0(xN) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_25])]) ).
fof(f604,plain,
szNzAzT0 = szDzozmdt0(xN),
inference(cnf_transformation,[],[f339]) ).
fof(f1081,plain,
spl92_24,
inference(avatar_split_clause,[],[f589,f1078]) ).
fof(f1078,plain,
( spl92_24
<=> szNzAzT0 = szDzozmdt0(xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_24])]) ).
fof(f589,plain,
szNzAzT0 = szDzozmdt0(xC),
inference(cnf_transformation,[],[f248]) ).
fof(f1076,plain,
spl92_23,
inference(avatar_split_clause,[],[f527,f1073]) ).
fof(f1073,plain,
( spl92_23
<=> szNzAzT0 = szDzozmdt0(xd) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_23])]) ).
fof(f1071,plain,
spl92_22,
inference(avatar_split_clause,[],[f522,f1068]) ).
fof(f1068,plain,
( spl92_22
<=> szNzAzT0 = szDzozmdt0(xe) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_22])]) ).
fof(f522,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
( ! [X0] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xe)
& aFunction0(xe) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szNzAzT0 = szDzozmdt0(xe)
& aFunction0(xe) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(f1066,plain,
spl92_21,
inference(avatar_split_clause,[],[f939,f1064]) ).
fof(f1064,plain,
( spl92_21
<=> ! [X2] : ~ aElementOf0(X2,slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_21])]) ).
fof(f939,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f846]) ).
fof(f846,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f482]) ).
fof(f482,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK85(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f480,f481]) ).
fof(f481,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK85(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f480,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f479]) ).
fof(f479,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f478]) ).
fof(f478,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( slcrc0 = X0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( slcrc0 = X0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f1062,plain,
spl92_20,
inference(avatar_split_clause,[],[f756,f1059]) ).
fof(f756,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f1057,plain,
spl92_19,
inference(avatar_split_clause,[],[f960,f1054]) ).
fof(f960,plain,
aElementOf0(sK54,szNzAzT0),
inference(forward_demodulation,[],[f621,f527]) ).
fof(f621,plain,
aElementOf0(sK54,szDzozmdt0(xd)),
inference(cnf_transformation,[],[f345]) ).
fof(f1052,plain,
spl92_18,
inference(avatar_split_clause,[],[f615,f1049]) ).
fof(f1049,plain,
( spl92_18
<=> aElementOf0(xk,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_18])]) ).
fof(f615,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f1047,plain,
spl92_17,
inference(avatar_split_clause,[],[f613,f1044]) ).
fof(f1044,plain,
( spl92_17
<=> aSubsetOf0(xS,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_17])]) ).
fof(f613,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f1042,plain,
spl92_16,
inference(avatar_split_clause,[],[f520,f1039]) ).
fof(f1039,plain,
( spl92_16
<=> aElementOf0(xK,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_16])]) ).
fof(f520,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f1037,plain,
~ spl92_15,
inference(avatar_split_clause,[],[f518,f1034]) ).
fof(f1034,plain,
( spl92_15
<=> sz00 = xK ),
introduced(avatar_definition,[new_symbols(naming,[spl92_15])]) ).
fof(f518,plain,
sz00 != xK,
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
sz00 != xK,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).
fof(f1032,plain,
spl92_14,
inference(avatar_split_clause,[],[f940,f1029]) ).
fof(f940,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f845]) ).
fof(f845,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f482]) ).
fof(f1027,plain,
spl92_13,
inference(avatar_split_clause,[],[f759,f1024]) ).
fof(f1024,plain,
( spl92_13
<=> isCountable0(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_13])]) ).
fof(f759,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f1022,plain,
spl92_12,
inference(avatar_split_clause,[],[f758,f1019]) ).
fof(f1019,plain,
( spl92_12
<=> aSet0(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_12])]) ).
fof(f758,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f1017,plain,
spl92_11,
inference(avatar_split_clause,[],[f755,f1014]) ).
fof(f1014,plain,
( spl92_11
<=> isFinite0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_11])]) ).
fof(f755,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(f1012,plain,
spl92_10,
inference(avatar_split_clause,[],[f614,f1009]) ).
fof(f1009,plain,
( spl92_10
<=> isCountable0(xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_10])]) ).
fof(f614,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f123]) ).
fof(f1007,plain,
spl92_9,
inference(avatar_split_clause,[],[f611,f1004]) ).
fof(f1004,plain,
( spl92_9
<=> aSet0(xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_9])]) ).
fof(f611,plain,
aSet0(xS),
inference(cnf_transformation,[],[f123]) ).
fof(f1002,plain,
spl92_8,
inference(avatar_split_clause,[],[f610,f999]) ).
fof(f999,plain,
( spl92_8
<=> isFinite0(xT) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_8])]) ).
fof(f610,plain,
isFinite0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
( isFinite0(xT)
& aSet0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(f997,plain,
spl92_7,
inference(avatar_split_clause,[],[f609,f994]) ).
fof(f994,plain,
( spl92_7
<=> aSet0(xT) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_7])]) ).
fof(f609,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f992,plain,
spl92_6,
inference(avatar_split_clause,[],[f603,f989]) ).
fof(f989,plain,
( spl92_6
<=> aFunction0(xN) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_6])]) ).
fof(f603,plain,
aFunction0(xN),
inference(cnf_transformation,[],[f339]) ).
fof(f987,plain,
spl92_5,
inference(avatar_split_clause,[],[f588,f984]) ).
fof(f984,plain,
( spl92_5
<=> aFunction0(xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_5])]) ).
fof(f588,plain,
aFunction0(xC),
inference(cnf_transformation,[],[f248]) ).
fof(f982,plain,
spl92_4,
inference(avatar_split_clause,[],[f532,f979]) ).
fof(f979,plain,
( spl92_4
<=> aFunction0(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_4])]) ).
fof(f532,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f308]) ).
fof(f977,plain,
spl92_3,
inference(avatar_split_clause,[],[f526,f974]) ).
fof(f974,plain,
( spl92_3
<=> aFunction0(xd) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_3])]) ).
fof(f526,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f303]) ).
fof(f972,plain,
spl92_2,
inference(avatar_split_clause,[],[f521,f969]) ).
fof(f969,plain,
( spl92_2
<=> aFunction0(xe) ),
introduced(avatar_definition,[new_symbols(naming,[spl92_2])]) ).
fof(f521,plain,
aFunction0(xe),
inference(cnf_transformation,[],[f114]) ).
fof(f967,plain,
spl92_1,
inference(avatar_split_clause,[],[f517,f965]) ).
fof(f517,plain,
! [X0] :
( sdtlpdtrp0(xd,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( sdtlpdtrp0(xd,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,negated_conjecture,
~ ? [X0] :
( sdtlpdtrp0(xd,X0) = xx
& aElementOf0(X0,szNzAzT0) ),
inference(negated_conjecture,[],[f95]) ).
fof(f95,conjecture,
? [X0] :
( sdtlpdtrp0(xd,X0) = xx
& aElementOf0(X0,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM594+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 3 15:15:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (6761)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (6772)WARNING: value z3 for option sas not known
% 0.15/0.39 % (6770)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (6773)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (6775)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (6771)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (6776)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (6777)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % (6772)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.41 % (6775)First to succeed.
% 0.15/0.42 % (6772)Also succeeded, but the first one will report.
% 0.15/0.42 % (6776)Also succeeded, but the first one will report.
% 0.15/0.42 % (6775)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6761"
% 0.15/0.42 % (6775)Refutation found. Thanks to Tanya!
% 0.15/0.42 % SZS status Theorem for theBenchmark
% 0.15/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.42 % (6775)------------------------------
% 0.15/0.42 % (6775)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.42 % (6775)Termination reason: Refutation
% 0.15/0.42
% 0.15/0.42 % (6775)Memory used [KB]: 1550
% 0.15/0.42 % (6775)Time elapsed: 0.028 s
% 0.15/0.42 % (6775)Instructions burned: 47 (million)
% 0.15/0.42 % (6761)Success in time 0.05 s
%------------------------------------------------------------------------------