TSTP Solution File: RNG089+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG089+2 : 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 08:56:46 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 85
% Syntax : Number of formulae : 247 ( 80 unt; 0 def)
% Number of atoms : 733 ( 94 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 723 ( 237 ~; 234 |; 137 &)
% ( 76 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 65 ( 63 usr; 57 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-3 aty)
% Number of variables : 279 ( 255 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f544,plain,
$false,
inference(avatar_sat_refutation,[],[f182,f187,f192,f197,f202,f207,f212,f221,f226,f231,f236,f241,f246,f251,f256,f261,f266,f270,f277,f282,f287,f292,f297,f302,f307,f312,f316,f320,f324,f328,f332,f336,f340,f344,f348,f352,f373,f397,f401,f405,f409,f419,f453,f457,f461,f473,f485,f489,f497,f501,f505,f507,f513,f517,f531,f535,f543]) ).
fof(f543,plain,
( ~ spl15_13
| ~ spl15_5
| spl15_9
| ~ spl15_49 ),
inference(avatar_split_clause,[],[f492,f487,f218,f199,f238]) ).
fof(f238,plain,
( spl15_13
<=> aElementOf0(xl,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f199,plain,
( spl15_5
<=> aElement0(xz) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f218,plain,
( spl15_9
<=> aElementOf0(sdtasdt0(xz,xl),xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f487,plain,
( spl15_49
<=> ! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).
fof(f492,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| spl15_9
| ~ spl15_49 ),
inference(resolution,[],[f488,f220]) ).
fof(f220,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| spl15_9 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f488,plain,
( ! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) )
| ~ spl15_49 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f535,plain,
spl15_56,
inference(avatar_split_clause,[],[f168,f533]) ).
fof(f533,plain,
( spl15_56
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_56])]) ).
fof(f168,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f531,plain,
spl15_55,
inference(avatar_split_clause,[],[f167,f529]) ).
fof(f529,plain,
( spl15_55
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_55])]) ).
fof(f167,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f517,plain,
spl15_54,
inference(avatar_split_clause,[],[f102,f515]) ).
fof(f515,plain,
( spl15_54
<=> ! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_54])]) ).
fof(f102,plain,
! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( aIdeal0(xJ)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1) )
& ! [X2] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ) ) )
| ~ aElementOf0(X0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI) ) )
| ~ aElementOf0(X3,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X0,X2),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,xI)
=> ( ! [X4] :
( aElement0(X4)
=> aElementOf0(sdtasdt0(X4,X3),xI) )
& ! [X5] :
( aElementOf0(X5,xI)
=> aElementOf0(sdtpldt0(X3,X5),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f513,plain,
spl15_53,
inference(avatar_split_clause,[],[f98,f511]) ).
fof(f511,plain,
( spl15_53
<=> ! [X5,X3] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_53])]) ).
fof(f98,plain,
! [X3,X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) ),
inference(cnf_transformation,[],[f40]) ).
fof(f507,plain,
( ~ spl15_12
| ~ spl15_5
| spl15_8
| ~ spl15_48 ),
inference(avatar_split_clause,[],[f490,f483,f214,f199,f233]) ).
fof(f233,plain,
( spl15_12
<=> aElementOf0(xk,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f214,plain,
( spl15_8
<=> aElementOf0(sdtasdt0(xz,xk),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f483,plain,
( spl15_48
<=> ! [X4,X3] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_48])]) ).
fof(f490,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI)
| spl15_8
| ~ spl15_48 ),
inference(resolution,[],[f484,f216]) ).
fof(f216,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| spl15_8 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f484,plain,
( ! [X3,X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) )
| ~ spl15_48 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f505,plain,
spl15_52,
inference(avatar_split_clause,[],[f176,f503]) ).
fof(f503,plain,
( spl15_52
<=> ! [X0,X1] :
( sP2(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_52])]) ).
fof(f176,plain,
! [X0,X1] :
( sP2(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f163]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP2(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP2(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP2(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP2(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP2(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f54,f74]) ).
fof(f74,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f54,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(f501,plain,
spl15_51,
inference(avatar_split_clause,[],[f148,f499]) ).
fof(f499,plain,
( spl15_51
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).
fof(f148,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ aElementOf0(sK9(X0,X1,X2),X0)
| ~ aElementOf0(sK9(X0,X1,X2),X1)
| ~ aElementOf0(sK9(X0,X1,X2),X2) )
& ( ( aElementOf0(sK9(X0,X1,X2),X0)
& aElementOf0(sK9(X0,X1,X2),X1) )
| aElementOf0(sK9(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f85,f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK9(X0,X1,X2),X0)
| ~ aElementOf0(sK9(X0,X1,X2),X1)
| ~ aElementOf0(sK9(X0,X1,X2),X2) )
& ( ( aElementOf0(sK9(X0,X1,X2),X0)
& aElementOf0(sK9(X0,X1,X2),X1) )
| aElementOf0(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f84]) ).
fof(f84,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f497,plain,
spl15_50,
inference(avatar_split_clause,[],[f147,f495]) ).
fof(f495,plain,
( spl15_50
<=> ! [X4,X0,X1,X2] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).
fof(f147,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f489,plain,
spl15_49,
inference(avatar_split_clause,[],[f103,f487]) ).
fof(f103,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f40]) ).
fof(f485,plain,
spl15_48,
inference(avatar_split_clause,[],[f99,f483]) ).
fof(f99,plain,
! [X3,X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) ),
inference(cnf_transformation,[],[f40]) ).
fof(f473,plain,
( ~ spl15_3
| spl15_47
| ~ spl15_13
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f358,f322,f238,f470,f189]) ).
fof(f189,plain,
( spl15_3
<=> aSet0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f470,plain,
( spl15_47
<=> aElement0(xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_47])]) ).
fof(f322,plain,
( spl15_30
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).
fof(f358,plain,
( aElement0(xl)
| ~ aSet0(xJ)
| ~ spl15_13
| ~ spl15_30 ),
inference(resolution,[],[f323,f240]) ).
fof(f240,plain,
( aElementOf0(xl,xJ)
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) )
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f461,plain,
spl15_46,
inference(avatar_split_clause,[],[f174,f459]) ).
fof(f459,plain,
( spl15_46
<=> ! [X0,X1] :
( sP0(X1,X0,sdtasasdt0(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_46])]) ).
fof(f174,plain,
! [X0,X1] :
( sP0(X1,X0,sdtasasdt0(X0,X1))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtasasdt0(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2 ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f457,plain,
spl15_45,
inference(avatar_split_clause,[],[f136,f455]) ).
fof(f455,plain,
( spl15_45
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).
fof(f136,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aElement0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(f453,plain,
spl15_44,
inference(avatar_split_clause,[],[f135,f451]) ).
fof(f451,plain,
( spl15_44
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).
fof(f135,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f419,plain,
spl15_43,
inference(avatar_split_clause,[],[f177,f417]) ).
fof(f417,plain,
( spl15_43
<=> ! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
fof(f177,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f162]) ).
fof(f162,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f409,plain,
spl15_42,
inference(avatar_split_clause,[],[f166,f407]) ).
fof(f407,plain,
( spl15_42
<=> ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
fof(f166,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f405,plain,
spl15_41,
inference(avatar_split_clause,[],[f165,f403]) ).
fof(f403,plain,
( spl15_41
<=> ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).
fof(f165,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f401,plain,
spl15_40,
inference(avatar_split_clause,[],[f134,f399]) ).
fof(f399,plain,
( spl15_40
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
fof(f134,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(f397,plain,
spl15_39,
inference(avatar_split_clause,[],[f133,f395]) ).
fof(f395,plain,
( spl15_39
<=> ! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).
fof(f133,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f373,plain,
( ~ spl15_1
| spl15_38
| ~ spl15_12
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f357,f322,f233,f370,f179]) ).
fof(f179,plain,
( spl15_1
<=> aSet0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f370,plain,
( spl15_38
<=> aElement0(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).
fof(f357,plain,
( aElement0(xk)
| ~ aSet0(xI)
| ~ spl15_12
| ~ spl15_30 ),
inference(resolution,[],[f323,f235]) ).
fof(f235,plain,
( aElementOf0(xk,xI)
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f352,plain,
spl15_37,
inference(avatar_split_clause,[],[f153,f350]) ).
fof(f350,plain,
( spl15_37
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).
fof(f153,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f52,f72,f71]) ).
fof(f52,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).
fof(f348,plain,
spl15_36,
inference(avatar_split_clause,[],[f132,f346]) ).
fof(f346,plain,
( spl15_36
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
fof(f132,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f344,plain,
spl15_35,
inference(avatar_split_clause,[],[f131,f342]) ).
fof(f342,plain,
( spl15_35
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).
fof(f131,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f340,plain,
spl15_34,
inference(avatar_split_clause,[],[f130,f338]) ).
fof(f338,plain,
( spl15_34
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).
fof(f130,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(f336,plain,
spl15_33,
inference(avatar_split_clause,[],[f129,f334]) ).
fof(f334,plain,
( spl15_33
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).
fof(f129,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f332,plain,
spl15_32,
inference(avatar_split_clause,[],[f128,f330]) ).
fof(f330,plain,
( spl15_32
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).
fof(f128,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f328,plain,
spl15_31,
inference(avatar_split_clause,[],[f127,f326]) ).
fof(f326,plain,
( spl15_31
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
fof(f127,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f324,plain,
spl15_30,
inference(avatar_split_clause,[],[f125,f322]) ).
fof(f125,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f320,plain,
spl15_29,
inference(avatar_split_clause,[],[f146,f318]) ).
fof(f318,plain,
( spl15_29
<=> ! [X2,X0,X1] :
( aSet0(X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).
fof(f146,plain,
! [X2,X0,X1] :
( aSet0(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f316,plain,
spl15_28,
inference(avatar_split_clause,[],[f126,f314]) ).
fof(f314,plain,
( spl15_28
<=> ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).
fof(f126,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(f312,plain,
spl15_27,
inference(avatar_split_clause,[],[f120,f309]) ).
fof(f309,plain,
( spl15_27
<=> aElementOf0(xy,sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).
fof(f120,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& xy = sdtpldt0(sK3,sK4)
& aElementOf0(sK4,xJ)
& aElementOf0(sK3,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& xx = sdtpldt0(sK5,sK6)
& aElementOf0(sK6,xJ)
& aElementOf0(sK5,xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f33,f77,f76]) ).
fof(f76,plain,
( ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
=> ( xy = sdtpldt0(sK3,sK4)
& aElementOf0(sK4,xJ)
& aElementOf0(sK3,xI) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X2,X3] :
( xx = sdtpldt0(X2,X3)
& aElementOf0(X3,xJ)
& aElementOf0(X2,xI) )
=> ( xx = sdtpldt0(sK5,sK6)
& aElementOf0(sK6,xJ)
& aElementOf0(sK5,xI) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X2,X3] :
( xx = sdtpldt0(X2,X3)
& aElementOf0(X3,xJ)
& aElementOf0(X2,xI) ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xx
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f307,plain,
spl15_26,
inference(avatar_split_clause,[],[f119,f304]) ).
fof(f304,plain,
( spl15_26
<=> xy = sdtpldt0(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).
fof(f119,plain,
xy = sdtpldt0(sK3,sK4),
inference(cnf_transformation,[],[f78]) ).
fof(f302,plain,
spl15_25,
inference(avatar_split_clause,[],[f116,f299]) ).
fof(f299,plain,
( spl15_25
<=> aElementOf0(xx,sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).
fof(f116,plain,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f78]) ).
fof(f297,plain,
spl15_24,
inference(avatar_split_clause,[],[f115,f294]) ).
fof(f294,plain,
( spl15_24
<=> xx = sdtpldt0(sK5,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
fof(f115,plain,
xx = sdtpldt0(sK5,sK6),
inference(cnf_transformation,[],[f78]) ).
fof(f292,plain,
spl15_23,
inference(avatar_split_clause,[],[f112,f289]) ).
fof(f289,plain,
( spl15_23
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
fof(f112,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
fof(f287,plain,
spl15_22,
inference(avatar_split_clause,[],[f111,f284]) ).
fof(f284,plain,
( spl15_22
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).
fof(f111,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(cnf_transformation,[],[f29]) ).
fof(f282,plain,
spl15_21,
inference(avatar_split_clause,[],[f110,f279]) ).
fof(f279,plain,
( spl15_21
<=> xx = sdtpldt0(xk,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
fof(f110,plain,
xx = sdtpldt0(xk,xl),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(f277,plain,
spl15_20,
inference(avatar_split_clause,[],[f107,f274]) ).
fof(f274,plain,
( spl15_20
<=> xy = sdtpldt0(xm,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).
fof(f107,plain,
xy = sdtpldt0(xm,xn),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
fof(f270,plain,
spl15_19,
inference(avatar_split_clause,[],[f137,f268]) ).
fof(f268,plain,
( spl15_19
<=> ! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).
fof(f137,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( aIdeal0(X0)
=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(unused_predicate_definition_removal,[],[f36]) ).
fof(f36,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f266,plain,
~ spl15_18,
inference(avatar_split_clause,[],[f124,f263]) ).
fof(f263,plain,
( spl15_18
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).
fof(f124,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f261,plain,
spl15_17,
inference(avatar_split_clause,[],[f118,f258]) ).
fof(f258,plain,
( spl15_17
<=> aElementOf0(sK4,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).
fof(f118,plain,
aElementOf0(sK4,xJ),
inference(cnf_transformation,[],[f78]) ).
fof(f256,plain,
spl15_16,
inference(avatar_split_clause,[],[f117,f253]) ).
fof(f253,plain,
( spl15_16
<=> aElementOf0(sK3,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f117,plain,
aElementOf0(sK3,xI),
inference(cnf_transformation,[],[f78]) ).
fof(f251,plain,
spl15_15,
inference(avatar_split_clause,[],[f114,f248]) ).
fof(f248,plain,
( spl15_15
<=> aElementOf0(sK6,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f114,plain,
aElementOf0(sK6,xJ),
inference(cnf_transformation,[],[f78]) ).
fof(f246,plain,
spl15_14,
inference(avatar_split_clause,[],[f113,f243]) ).
fof(f243,plain,
( spl15_14
<=> aElementOf0(sK5,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f113,plain,
aElementOf0(sK5,xI),
inference(cnf_transformation,[],[f78]) ).
fof(f241,plain,
spl15_13,
inference(avatar_split_clause,[],[f109,f238]) ).
fof(f109,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f236,plain,
spl15_12,
inference(avatar_split_clause,[],[f108,f233]) ).
fof(f108,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f231,plain,
spl15_11,
inference(avatar_split_clause,[],[f106,f228]) ).
fof(f228,plain,
( spl15_11
<=> aElementOf0(xn,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f106,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f226,plain,
spl15_10,
inference(avatar_split_clause,[],[f105,f223]) ).
fof(f223,plain,
( spl15_10
<=> aElementOf0(xm,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f105,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f221,plain,
( ~ spl15_8
| ~ spl15_9 ),
inference(avatar_split_clause,[],[f96,f218,f214]) ).
fof(f96,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f212,plain,
spl15_7,
inference(avatar_split_clause,[],[f123,f209]) ).
fof(f209,plain,
( spl15_7
<=> aElement0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f123,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f207,plain,
spl15_6,
inference(avatar_split_clause,[],[f122,f204]) ).
fof(f204,plain,
( spl15_6
<=> aElement0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f122,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f202,plain,
spl15_5,
inference(avatar_split_clause,[],[f121,f199]) ).
fof(f121,plain,
aElement0(xz),
inference(cnf_transformation,[],[f78]) ).
fof(f197,plain,
spl15_4,
inference(avatar_split_clause,[],[f104,f194]) ).
fof(f194,plain,
( spl15_4
<=> aIdeal0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f104,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f40]) ).
fof(f192,plain,
spl15_3,
inference(avatar_split_clause,[],[f101,f189]) ).
fof(f101,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f40]) ).
fof(f187,plain,
spl15_2,
inference(avatar_split_clause,[],[f100,f184]) ).
fof(f184,plain,
( spl15_2
<=> aIdeal0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f100,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f40]) ).
fof(f182,plain,
spl15_1,
inference(avatar_split_clause,[],[f97,f179]) ).
fof(f97,plain,
aSet0(xI),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG089+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n011.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 : Fri May 3 18:16:38 EDT 2024
% 0.20/0.36 % CPUTime :
% 0.20/0.36 % (4927)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38 % (4930)WARNING: value z3 for option sas not known
% 0.20/0.38 % (4930)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)
% 0.20/0.38 % (4929)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38 % (4934)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)
% 0.20/0.38 % (4933)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)
% 0.20/0.38 % (4931)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (4932)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)
% 0.20/0.38 % (4928)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.39 TRYING [1]
% 0.20/0.39 % (4932)First to succeed.
% 0.20/0.39 TRYING [2]
% 0.20/0.39 % (4933)Also succeeded, but the first one will report.
% 0.20/0.39 % (4932)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4927"
% 0.20/0.39 TRYING [3]
% 0.20/0.39 TRYING [1]
% 0.20/0.39 % (4932)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (4932)------------------------------
% 0.20/0.39 % (4932)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.39 % (4932)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (4932)Memory used [KB]: 1055
% 0.20/0.39 % (4932)Time elapsed: 0.013 s
% 0.20/0.39 % (4932)Instructions burned: 21 (million)
% 0.20/0.39 % (4927)Success in time 0.029 s
%------------------------------------------------------------------------------