TSTP Solution File: RNG088+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG088+1 : 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 : n020.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 08:56:45 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 106
% Syntax : Number of formulae : 312 ( 81 unt; 0 def)
% Number of atoms : 1056 ( 162 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1181 ( 437 ~; 466 |; 145 &)
% ( 90 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 79 ( 77 usr; 71 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-3 aty)
% Number of variables : 509 ( 472 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f644,plain,
$false,
inference(avatar_sat_refutation,[],[f161,f166,f171,f176,f181,f190,f195,f200,f205,f210,f215,f219,f226,f231,f236,f241,f245,f250,f254,f258,f262,f266,f270,f274,f278,f282,f287,f291,f325,f329,f333,f337,f341,f371,f375,f379,f396,f400,f404,f411,f415,f419,f435,f439,f446,f462,f466,f470,f482,f486,f490,f491,f499,f503,f511,f515,f520,f524,f528,f532,f536,f577,f581,f585,f598,f602,f623,f627,f631,f635,f643]) ).
fof(f643,plain,
( ~ spl11_2
| ~ spl11_9
| ~ spl11_11
| spl11_7
| ~ spl11_46 ),
inference(avatar_split_clause,[],[f472,f444,f187,f207,f197,f163]) ).
fof(f163,plain,
( spl11_2
<=> aIdeal0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f197,plain,
( spl11_9
<=> aElementOf0(xl,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
fof(f207,plain,
( spl11_11
<=> aElementOf0(xn,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
fof(f187,plain,
( spl11_7
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
fof(f444,plain,
( spl11_46
<=> ! [X0,X1,X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_46])]) ).
fof(f472,plain,
( ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ)
| spl11_7
| ~ spl11_46 ),
inference(resolution,[],[f445,f189]) ).
fof(f189,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| spl11_7 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f445,plain,
( ! [X3,X0,X1] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) )
| ~ spl11_46 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f635,plain,
spl11_70,
inference(avatar_split_clause,[],[f140,f633]) ).
fof(f633,plain,
( spl11_70
<=> ! [X4,X0,X5,X2,X1] :
( sP2(X0,X1,X2)
| sdtpldt0(X4,X5) != sK6(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_70])]) ).
fof(f140,plain,
! [X2,X0,X1,X4,X5] :
( sP2(X0,X1,X2)
| sdtpldt0(X4,X5) != sK6(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != sK6(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK6(X0,X1,X2),X2) )
& ( ( sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
& aElementOf0(sK8(X0,X1,X2),X0)
& aElementOf0(sK7(X0,X1,X2),X1) )
| aElementOf0(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
& aElementOf0(sK10(X0,X1,X8),X0)
& aElementOf0(sK9(X0,X1,X8),X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f82,f85,f84,f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ! [X5,X4] :
( sdtpldt0(X4,X5) != sK6(X0,X1,X2)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK6(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK6(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( sdtpldt0(X6,X7) = sK6(X0,X1,X2)
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
=> ( sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
& aElementOf0(sK8(X0,X1,X2),X0)
& aElementOf0(sK7(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
=> ( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
& aElementOf0(sK10(X0,X1,X8),X0)
& aElementOf0(sK9(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X0)
& aElementOf0(X6,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X8] :
( ( aElementOf0(X8,X2)
| ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1) ) )
& ( ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X0)
& aElementOf0(X11,X1) )
| ~ aElementOf0(X8,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) ) )
& ( ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,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(f631,plain,
spl11_69,
inference(avatar_split_clause,[],[f139,f629]) ).
fof(f629,plain,
( spl11_69
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
| aElementOf0(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_69])]) ).
fof(f139,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
| aElementOf0(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f627,plain,
spl11_68,
inference(avatar_split_clause,[],[f131,f625]) ).
fof(f625,plain,
( spl11_68
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ aElementOf0(sK5(X0,X1,X2),X0)
| ~ aElementOf0(sK5(X0,X1,X2),X1)
| ~ aElementOf0(sK5(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_68])]) ).
fof(f131,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ aElementOf0(sK5(X0,X1,X2),X0)
| ~ aElementOf0(sK5(X0,X1,X2),X1)
| ~ aElementOf0(sK5(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ aElementOf0(sK5(X0,X1,X2),X0)
| ~ aElementOf0(sK5(X0,X1,X2),X1)
| ~ aElementOf0(sK5(X0,X1,X2),X2) )
& ( ( aElementOf0(sK5(X0,X1,X2),X0)
& aElementOf0(sK5(X0,X1,X2),X1) )
| aElementOf0(sK5(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,[sK5])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK5(X0,X1,X2),X0)
| ~ aElementOf0(sK5(X0,X1,X2),X1)
| ~ aElementOf0(sK5(X0,X1,X2),X2) )
& ( ( aElementOf0(sK5(X0,X1,X2),X0)
& aElementOf0(sK5(X0,X1,X2),X1) )
| aElementOf0(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,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,[],[f77]) ).
fof(f77,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,[],[f76]) ).
fof(f76,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,[],[f67]) ).
fof(f67,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(f623,plain,
( spl11_67
| ~ spl11_22
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f560,f517,f260,f620]) ).
fof(f620,plain,
( spl11_67
<=> sz00 = sdtasdt0(sdtpldt0(xk,xm),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_67])]) ).
fof(f260,plain,
( spl11_22
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_22])]) ).
fof(f517,plain,
( spl11_57
<=> aElement0(sdtpldt0(xk,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_57])]) ).
fof(f560,plain,
( sz00 = sdtasdt0(sdtpldt0(xk,xm),sz00)
| ~ spl11_22
| ~ spl11_57 ),
inference(resolution,[],[f519,f261]) ).
fof(f261,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f519,plain,
( aElement0(sdtpldt0(xk,xm))
| ~ spl11_57 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f602,plain,
spl11_66,
inference(avatar_split_clause,[],[f152,f600]) ).
fof(f600,plain,
( spl11_66
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_66])]) ).
fof(f152,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f598,plain,
spl11_65,
inference(avatar_split_clause,[],[f151,f596]) ).
fof(f596,plain,
( spl11_65
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_65])]) ).
fof(f151,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f585,plain,
spl11_64,
inference(avatar_split_clause,[],[f135,f583]) ).
fof(f583,plain,
( spl11_64
<=> ! [X0,X8,X2,X1] :
( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_64])]) ).
fof(f135,plain,
! [X2,X0,X1,X8] :
( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
| ~ aElementOf0(X8,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f581,plain,
spl11_63,
inference(avatar_split_clause,[],[f130,f579]) ).
fof(f579,plain,
( spl11_63
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| aElementOf0(sK5(X0,X1,X2),X0)
| aElementOf0(sK5(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_63])]) ).
fof(f130,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| aElementOf0(sK5(X0,X1,X2),X0)
| aElementOf0(sK5(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f577,plain,
spl11_62,
inference(avatar_split_clause,[],[f129,f575]) ).
fof(f575,plain,
( spl11_62
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| aElementOf0(sK5(X0,X1,X2),X1)
| aElementOf0(sK5(X0,X1,X2),X2)
| ~ aSet0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_62])]) ).
fof(f129,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| aElementOf0(sK5(X0,X1,X2),X1)
| aElementOf0(sK5(X0,X1,X2),X2)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f536,plain,
spl11_61,
inference(avatar_split_clause,[],[f150,f534]) ).
fof(f534,plain,
( spl11_61
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_61])]) ).
fof(f150,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f532,plain,
spl11_60,
inference(avatar_split_clause,[],[f149,f530]) ).
fof(f530,plain,
( spl11_60
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_60])]) ).
fof(f149,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f528,plain,
spl11_59,
inference(avatar_split_clause,[],[f122,f526]) ).
fof(f526,plain,
( spl11_59
<=> ! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK3(X0,X1),X0)
| ~ aElementOf0(sK4(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_59])]) ).
fof(f122,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK3(X0,X1),X0)
| ~ aElementOf0(sK4(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ( ~ aElementOf0(sK3(X0,X1),X0)
& aElementOf0(sK3(X0,X1),X1) )
| ( ~ aElementOf0(sK4(X0,X1),X1)
& aElementOf0(sK4(X0,X1),X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f46,f73,f72]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK3(X0,X1),X0)
& aElementOf0(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sK4(X0,X1),X1)
& aElementOf0(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ? [X3] :
( ~ aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(X3,X1) ) )
=> X0 = X1 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,X1) ) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
fof(f524,plain,
spl11_58,
inference(avatar_split_clause,[],[f121,f522]) ).
fof(f522,plain,
( spl11_58
<=> ! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK3(X0,X1),X0)
| aElementOf0(sK4(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_58])]) ).
fof(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ aElementOf0(sK3(X0,X1),X0)
| aElementOf0(sK4(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f520,plain,
( ~ spl11_19
| spl11_57
| ~ spl11_6
| ~ spl11_21 ),
inference(avatar_split_clause,[],[f492,f256,f183,f517,f247]) ).
fof(f247,plain,
( spl11_19
<=> aSet0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_19])]) ).
fof(f183,plain,
( spl11_6
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
fof(f256,plain,
( spl11_21
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_21])]) ).
fof(f492,plain,
( aElement0(sdtpldt0(xk,xm))
| ~ aSet0(xI)
| ~ spl11_6
| ~ spl11_21 ),
inference(resolution,[],[f184,f257]) ).
fof(f257,plain,
( ! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) )
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f184,plain,
( aElementOf0(sdtpldt0(xk,xm),xI)
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f515,plain,
spl11_56,
inference(avatar_split_clause,[],[f120,f513]) ).
fof(f513,plain,
( spl11_56
<=> ! [X0,X1] :
( X0 = X1
| aElementOf0(sK3(X0,X1),X1)
| ~ aElementOf0(sK4(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_56])]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK3(X0,X1),X1)
| ~ aElementOf0(sK4(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f511,plain,
spl11_55,
inference(avatar_split_clause,[],[f119,f509]) ).
fof(f509,plain,
( spl11_55
<=> ! [X0,X1] :
( X0 = X1
| aElementOf0(sK3(X0,X1),X1)
| aElementOf0(sK4(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_55])]) ).
fof(f119,plain,
! [X0,X1] :
( X0 = X1
| aElementOf0(sK3(X0,X1),X1)
| aElementOf0(sK4(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f503,plain,
spl11_54,
inference(avatar_split_clause,[],[f138,f501]) ).
fof(f501,plain,
( spl11_54
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| aElementOf0(sK8(X0,X1,X2),X0)
| aElementOf0(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_54])]) ).
fof(f138,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| aElementOf0(sK8(X0,X1,X2),X0)
| aElementOf0(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f499,plain,
spl11_53,
inference(avatar_split_clause,[],[f137,f497]) ).
fof(f497,plain,
( spl11_53
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| aElementOf0(sK7(X0,X1,X2),X1)
| aElementOf0(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_53])]) ).
fof(f137,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| aElementOf0(sK7(X0,X1,X2),X1)
| aElementOf0(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f491,plain,
( ~ spl11_1
| ~ spl11_8
| ~ spl11_10
| spl11_6
| ~ spl11_46 ),
inference(avatar_split_clause,[],[f471,f444,f183,f202,f192,f158]) ).
fof(f158,plain,
( spl11_1
<=> aIdeal0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f192,plain,
( spl11_8
<=> aElementOf0(xk,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
fof(f202,plain,
( spl11_10
<=> aElementOf0(xm,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
fof(f471,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI)
| spl11_6
| ~ spl11_46 ),
inference(resolution,[],[f445,f185]) ).
fof(f185,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| spl11_6 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f490,plain,
spl11_52,
inference(avatar_split_clause,[],[f154,f488]) ).
fof(f488,plain,
( spl11_52
<=> ! [X10,X0,X9,X2,X1] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_52])]) ).
fof(f154,plain,
! [X2,X10,X0,X1,X9] :
( aElementOf0(sdtpldt0(X9,X10),X2)
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP2(X0,X1,X2) ),
inference(equality_resolution,[],[f136]) ).
fof(f136,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X2)
| sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X0)
| ~ aElementOf0(X9,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f486,plain,
spl11_51,
inference(avatar_split_clause,[],[f148,f484]) ).
fof(f484,plain,
( spl11_51
<=> ! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_51])]) ).
fof(f148,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(f482,plain,
spl11_50,
inference(avatar_split_clause,[],[f143,f480]) ).
fof(f480,plain,
( spl11_50
<=> ! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP2(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_50])]) ).
fof(f143,plain,
! [X2,X0,X1] :
( sdtpldt1(X0,X1) = X2
| ~ sP2(X1,X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,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,[],[f87]) ).
fof(f87,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,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP2(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f50,f70]) ).
fof(f50,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,[],[f49]) ).
fof(f49,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(f470,plain,
spl11_49,
inference(avatar_split_clause,[],[f134,f468]) ).
fof(f468,plain,
( spl11_49
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK10(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_49])]) ).
fof(f134,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK10(X0,X1,X8),X0)
| ~ aElementOf0(X8,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f466,plain,
spl11_48,
inference(avatar_split_clause,[],[f133,f464]) ).
fof(f464,plain,
( spl11_48
<=> ! [X0,X8,X2,X1] :
( aElementOf0(sK9(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_48])]) ).
fof(f133,plain,
! [X2,X0,X1,X8] :
( aElementOf0(sK9(X0,X1,X8),X1)
| ~ aElementOf0(X8,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f462,plain,
spl11_47,
inference(avatar_split_clause,[],[f128,f460]) ).
fof(f460,plain,
( spl11_47
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_47])]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f446,plain,
spl11_46,
inference(avatar_split_clause,[],[f117,f444]) ).
fof(f117,plain,
! [X3,X0,X1] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,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,[],[f35]) ).
fof(f35,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,[],[f33]) ).
fof(f33,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(f439,plain,
spl11_45,
inference(avatar_split_clause,[],[f124,f437]) ).
fof(f437,plain,
( spl11_45
<=> ! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP0(X1,X0,X2)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_45])]) ).
fof(f124,plain,
! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP0(X1,X0,X2)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,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,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f435,plain,
spl11_44,
inference(avatar_split_clause,[],[f118,f433]) ).
fof(f433,plain,
( spl11_44
<=> ! [X2,X0,X1] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_44])]) ).
fof(f118,plain,
! [X2,X0,X1] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f419,plain,
spl11_43,
inference(avatar_split_clause,[],[f147,f417]) ).
fof(f417,plain,
( spl11_43
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_43])]) ).
fof(f147,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,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(f415,plain,
spl11_42,
inference(avatar_split_clause,[],[f146,f413]) ).
fof(f413,plain,
( spl11_42
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_42])]) ).
fof(f146,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,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(f411,plain,
( ~ spl11_19
| spl11_41
| ~ spl11_8
| ~ spl11_21 ),
inference(avatar_split_clause,[],[f294,f256,f192,f408,f247]) ).
fof(f408,plain,
( spl11_41
<=> aElement0(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_41])]) ).
fof(f294,plain,
( aElement0(xk)
| ~ aSet0(xI)
| ~ spl11_8
| ~ spl11_21 ),
inference(resolution,[],[f257,f194]) ).
fof(f194,plain,
( aElementOf0(xk,xI)
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f404,plain,
spl11_40,
inference(avatar_split_clause,[],[f155,f402]) ).
fof(f402,plain,
( spl11_40
<=> ! [X0,X1] :
( sP2(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_40])]) ).
fof(f155,plain,
! [X0,X1] :
( sP2(X1,X0,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f142]) ).
fof(f142,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f400,plain,
spl11_39,
inference(avatar_split_clause,[],[f127,f398]) ).
fof(f398,plain,
( spl11_39
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_39])]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f396,plain,
spl11_38,
inference(avatar_split_clause,[],[f126,f394]) ).
fof(f394,plain,
( spl11_38
<=> ! [X4,X0,X1,X2] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_38])]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f379,plain,
spl11_37,
inference(avatar_split_clause,[],[f153,f377]) ).
fof(f377,plain,
( spl11_37
<=> ! [X0,X1] :
( sP0(X1,X0,sdtasasdt0(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_37])]) ).
fof(f153,plain,
! [X0,X1] :
( sP0(X1,X0,sdtasasdt0(X0,X1))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f123]) ).
fof(f123,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f375,plain,
spl11_36,
inference(avatar_split_clause,[],[f115,f373]) ).
fof(f373,plain,
( spl11_36
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_36])]) ).
fof(f115,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,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(f371,plain,
spl11_35,
inference(avatar_split_clause,[],[f114,f369]) ).
fof(f369,plain,
( spl11_35
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_35])]) ).
fof(f114,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f341,plain,
spl11_34,
inference(avatar_split_clause,[],[f156,f339]) ).
fof(f339,plain,
( spl11_34
<=> ! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_34])]) ).
fof(f156,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f141]) ).
fof(f141,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f337,plain,
spl11_33,
inference(avatar_split_clause,[],[f145,f335]) ).
fof(f335,plain,
( spl11_33
<=> ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_33])]) ).
fof(f145,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,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(f333,plain,
spl11_32,
inference(avatar_split_clause,[],[f144,f331]) ).
fof(f331,plain,
( spl11_32
<=> ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).
fof(f144,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,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(f329,plain,
spl11_31,
inference(avatar_split_clause,[],[f113,f327]) ).
fof(f327,plain,
( spl11_31
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).
fof(f113,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,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(f325,plain,
spl11_30,
inference(avatar_split_clause,[],[f112,f323]) ).
fof(f323,plain,
( spl11_30
<=> ! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_30])]) ).
fof(f112,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f291,plain,
spl11_29,
inference(avatar_split_clause,[],[f132,f289]) ).
fof(f289,plain,
( spl11_29
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_29])]) ).
fof(f132,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f48,f68,f67]) ).
fof(f48,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,[],[f47]) ).
fof(f47,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(f287,plain,
( spl11_28
| ~ spl11_2
| ~ spl11_13 ),
inference(avatar_split_clause,[],[f221,f217,f163,f284]) ).
fof(f284,plain,
( spl11_28
<=> aSet0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_28])]) ).
fof(f217,plain,
( spl11_13
<=> ! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
fof(f221,plain,
( aSet0(xJ)
| ~ spl11_2
| ~ spl11_13 ),
inference(resolution,[],[f218,f165]) ).
fof(f165,plain,
( aIdeal0(xJ)
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f218,plain,
( ! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f282,plain,
spl11_27,
inference(avatar_split_clause,[],[f111,f280]) ).
fof(f280,plain,
( spl11_27
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_27])]) ).
fof(f111,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,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(f278,plain,
spl11_26,
inference(avatar_split_clause,[],[f110,f276]) ).
fof(f276,plain,
( spl11_26
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_26])]) ).
fof(f110,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f274,plain,
spl11_25,
inference(avatar_split_clause,[],[f109,f272]) ).
fof(f272,plain,
( spl11_25
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_25])]) ).
fof(f109,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,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(f270,plain,
spl11_24,
inference(avatar_split_clause,[],[f108,f268]) ).
fof(f268,plain,
( spl11_24
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_24])]) ).
fof(f108,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f266,plain,
spl11_23,
inference(avatar_split_clause,[],[f107,f264]) ).
fof(f264,plain,
( spl11_23
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_23])]) ).
fof(f107,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,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(f262,plain,
spl11_22,
inference(avatar_split_clause,[],[f106,f260]) ).
fof(f106,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f258,plain,
spl11_21,
inference(avatar_split_clause,[],[f104,f256]) ).
fof(f104,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,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(f254,plain,
spl11_20,
inference(avatar_split_clause,[],[f125,f252]) ).
fof(f252,plain,
( spl11_20
<=> ! [X2,X0,X1] :
( aSet0(X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_20])]) ).
fof(f125,plain,
! [X2,X0,X1] :
( aSet0(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f250,plain,
( spl11_19
| ~ spl11_1
| ~ spl11_13 ),
inference(avatar_split_clause,[],[f220,f217,f158,f247]) ).
fof(f220,plain,
( aSet0(xI)
| ~ spl11_1
| ~ spl11_13 ),
inference(resolution,[],[f218,f160]) ).
fof(f160,plain,
( aIdeal0(xI)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f245,plain,
spl11_18,
inference(avatar_split_clause,[],[f105,f243]) ).
fof(f243,plain,
( spl11_18
<=> ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
fof(f105,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,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(f241,plain,
spl11_17,
inference(avatar_split_clause,[],[f99,f238]) ).
fof(f238,plain,
( spl11_17
<=> aElementOf0(xy,sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
fof(f99,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f236,plain,
spl11_16,
inference(avatar_split_clause,[],[f98,f233]) ).
fof(f233,plain,
( spl11_16
<=> aElementOf0(xx,sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
fof(f98,plain,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f26]) ).
fof(f231,plain,
spl11_15,
inference(avatar_split_clause,[],[f97,f228]) ).
fof(f228,plain,
( spl11_15
<=> xy = sdtpldt0(xm,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
fof(f97,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(f226,plain,
spl11_14,
inference(avatar_split_clause,[],[f94,f223]) ).
fof(f223,plain,
( spl11_14
<=> xx = sdtpldt0(xk,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
fof(f94,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(f219,plain,
spl11_13,
inference(avatar_split_clause,[],[f116,f217]) ).
fof(f116,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f215,plain,
~ spl11_12,
inference(avatar_split_clause,[],[f103,f212]) ).
fof(f212,plain,
( spl11_12
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
fof(f103,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f210,plain,
spl11_11,
inference(avatar_split_clause,[],[f96,f207]) ).
fof(f96,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f205,plain,
spl11_10,
inference(avatar_split_clause,[],[f95,f202]) ).
fof(f95,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f200,plain,
spl11_9,
inference(avatar_split_clause,[],[f93,f197]) ).
fof(f93,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f195,plain,
spl11_8,
inference(avatar_split_clause,[],[f92,f192]) ).
fof(f92,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f190,plain,
( ~ spl11_6
| ~ spl11_7 ),
inference(avatar_split_clause,[],[f89,f187,f183]) ).
fof(f89,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f181,plain,
spl11_5,
inference(avatar_split_clause,[],[f102,f178]) ).
fof(f178,plain,
( spl11_5
<=> aElement0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
fof(f102,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f176,plain,
spl11_4,
inference(avatar_split_clause,[],[f101,f173]) ).
fof(f173,plain,
( spl11_4
<=> aElement0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
fof(f101,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f171,plain,
spl11_3,
inference(avatar_split_clause,[],[f100,f168]) ).
fof(f168,plain,
( spl11_3
<=> aElement0(xz) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
fof(f100,plain,
aElement0(xz),
inference(cnf_transformation,[],[f26]) ).
fof(f166,plain,
spl11_2,
inference(avatar_split_clause,[],[f91,f163]) ).
fof(f91,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f161,plain,
spl11_1,
inference(avatar_split_clause,[],[f90,f158]) ).
fof(f90,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 18:21:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (7665)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (7671)WARNING: value z3 for option sas not known
% 0.14/0.38 % (7670)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (7669)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (7673)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (7672)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (7675)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (7671)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (7674)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 % (7673)First to succeed.
% 0.14/0.40 TRYING [3]
% 0.14/0.40 % (7673)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7665"
% 0.14/0.40 % (7673)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (7673)------------------------------
% 0.14/0.40 % (7673)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (7673)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (7673)Memory used [KB]: 1133
% 0.14/0.40 % (7673)Time elapsed: 0.021 s
% 0.14/0.40 % (7673)Instructions burned: 30 (million)
% 0.14/0.40 % (7665)Success in time 0.035 s
%------------------------------------------------------------------------------