TSTP Solution File: NUM557+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM557+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 : n015.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 08:38:01 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 104 ( 36 unt; 0 def)
% Number of atoms : 549 ( 100 equ)
% Maximal formula atoms : 43 ( 5 avg)
% Number of connectives : 651 ( 206 ~; 170 |; 233 &)
% ( 5 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 126 ( 106 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f453,plain,
$false,
inference(global_subsumption,[],[f253,f252,f251,f250,f254,f255,f256,f257,f259,f258,f262,f261,f260,f267,f266,f265,f264,f263,f270,f269,f268,f281,f431,f279,f278,f277,f276,f275,f432,f273,f272,f271,f308,f307,f306,f305,f304,f303,f302,f301,f300,f299,f298,f297,f296,f295,f294,f293,f292,f291,f290,f289,f288,f287,f286,f285,f284,f283,f282,f314,f433,f312,f311,f310,f309,f317,f316]) ).
fof(f316,plain,
aSubsetOf0(xP,xS),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( xk = sbrdtbr0(xP)
& aSubsetOf0(xP,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xP) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,axiom,
( xk = sbrdtbr0(xP)
& aSubsetOf0(xP,xS)
& ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2431) ).
fof(f317,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f88]) ).
fof(f309,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xQ,xy))
| xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) )
& ( ( xy != X0
& aElementOf0(X0,xQ)
& aElement0(X0) )
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(flattening,[],[f190]) ).
fof(f190,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xQ,xy))
| xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) )
& ( ( xy != X0
& aElementOf0(X0,xQ)
& aElement0(X0) )
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,axiom,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( xy != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2411) ).
fof(f310,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f191]) ).
fof(f311,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f191]) ).
fof(f312,plain,
! [X0] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f191]) ).
fof(f433,plain,
~ aElementOf0(xy,sdtmndt0(xQ,xy)),
inference(equality_resolution,[],[f313]) ).
fof(f313,plain,
! [X0] :
( xy != X0
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f191]) ).
fof(f314,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
| xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f282,plain,
aSet0(slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f189]) ).
fof(f189,plain,
( slcrc0 != slbdtsldtrb0(xS,xk)
& aElementOf0(sK7,slbdtsldtrb0(xS,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,xS)
& ( ( ~ aElementOf0(sK8(X1),xS)
& aElementOf0(sK8(X1),X1) )
| ~ aSet0(X1) ) ) )
& ( ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xS)
& ! [X3] :
( aElementOf0(X3,xS)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X4] :
( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
& ! [X5] :
( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| ( ~ aSubsetOf0(X5,xT)
& ( ( ~ aElementOf0(sK9(X5),xT)
& aElementOf0(sK9(X5),X5) )
| ~ aSet0(X5) ) ) )
& ( ( xk = sbrdtbr0(X5)
& aSubsetOf0(X5,xT)
& ! [X7] :
( aElementOf0(X7,xT)
| ~ aElementOf0(X7,X5) )
& aSet0(X5) )
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X8] :
( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ( ~ aElementOf0(sK10(X8),xS)
& aElementOf0(sK10(X8),X8) )
| ~ aSet0(X8) ) ) )
& ( ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X10] :
( aElementOf0(X10,xS)
| ~ aElementOf0(X10,X8) )
& aSet0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f184,f188,f187,f186,f185]) ).
fof(f185,plain,
( ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(sK7,slbdtsldtrb0(xS,xk)) ),
introduced(choice_axiom,[]) ).
fof(f186,plain,
! [X1] :
( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK8(X1),xS)
& aElementOf0(sK8(X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f187,plain,
! [X5] :
( ? [X6] :
( ~ aElementOf0(X6,xT)
& aElementOf0(X6,X5) )
=> ( ~ aElementOf0(sK9(X5),xT)
& aElementOf0(sK9(X5),X5) ) ),
introduced(choice_axiom,[]) ).
fof(f188,plain,
! [X8] :
( ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X8) )
=> ( ~ aElementOf0(sK10(X8),xS)
& aElementOf0(sK10(X8),X8) ) ),
introduced(choice_axiom,[]) ).
fof(f184,plain,
( slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,xS)
& ( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) ) ) )
& ( ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xS)
& ! [X3] :
( aElementOf0(X3,xS)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X4] :
( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
& ! [X5] :
( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| ( ~ aSubsetOf0(X5,xT)
& ( ? [X6] :
( ~ aElementOf0(X6,xT)
& aElementOf0(X6,X5) )
| ~ aSet0(X5) ) ) )
& ( ( xk = sbrdtbr0(X5)
& aSubsetOf0(X5,xT)
& ! [X7] :
( aElementOf0(X7,xT)
| ~ aElementOf0(X7,X5) )
& aSet0(X5) )
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X8] :
( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X8) )
| ~ aSet0(X8) ) ) )
& ( ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X10] :
( aElementOf0(X10,xS)
| ~ aElementOf0(X10,X8) )
& aSet0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
( slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X1] :
( ~ aElementOf0(X1,xS)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) ) ) )
& ( ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X2] :
( aElementOf0(X2,xS)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X4] :
( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
& ! [X5] :
( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| ( ~ aSubsetOf0(X5,xT)
& ( ? [X6] :
( ~ aElementOf0(X6,xT)
& aElementOf0(X6,X5) )
| ~ aSet0(X5) ) ) )
& ( ( xk = sbrdtbr0(X5)
& aSubsetOf0(X5,xT)
& ! [X7] :
( aElementOf0(X7,xT)
| ~ aElementOf0(X7,X5) )
& aSet0(X5) )
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X8] :
( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X8) )
| ~ aSet0(X8) ) ) )
& ( ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X10] :
( aElementOf0(X10,xS)
| ~ aElementOf0(X10,X8) )
& aSet0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
( slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X1] :
( ~ aElementOf0(X1,xS)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) ) ) )
& ( ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X2] :
( aElementOf0(X2,xS)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X4] :
( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
& ! [X5] :
( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| ( ~ aSubsetOf0(X5,xT)
& ( ? [X6] :
( ~ aElementOf0(X6,xT)
& aElementOf0(X6,X5) )
| ~ aSet0(X5) ) ) )
& ( ( xk = sbrdtbr0(X5)
& aSubsetOf0(X5,xT)
& ! [X7] :
( aElementOf0(X7,xT)
| ~ aElementOf0(X7,X5) )
& aSet0(X5) )
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X8] :
( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X8) )
| ~ aSet0(X8) ) ) )
& ( ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X10] :
( aElementOf0(X10,xS)
| ~ aElementOf0(X10,X8) )
& aSet0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
( ~ ( ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) )
& aSet0(X0) ) ) )
=> ( slcrc0 = slbdtsldtrb0(xS,xk)
| ~ ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X4] :
( aElementOf0(X4,slbdtsldtrb0(xS,xk))
=> aElementOf0(X4,slbdtsldtrb0(xT,xk)) )
& ! [X5] :
( ( ( xk = sbrdtbr0(X5)
& ( aSubsetOf0(X5,xT)
| ( ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,xT) )
& aSet0(X5) ) ) )
=> aElementOf0(X5,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
=> ( xk = sbrdtbr0(X5)
& aSubsetOf0(X5,xT)
& ! [X7] :
( aElementOf0(X7,X5)
=> aElementOf0(X7,xT) )
& aSet0(X5) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X8] :
( ( ( xk = sbrdtbr0(X8)
& ( aSubsetOf0(X8,xS)
| ( ! [X9] :
( aElementOf0(X9,X8)
=> aElementOf0(X9,xS) )
& aSet0(X8) ) ) )
=> aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
=> ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X10] :
( aElementOf0(X10,X8)
=> aElementOf0(X10,xS) )
& aSet0(X8) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
( ~ ( ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> ( slcrc0 = slbdtsldtrb0(xS,xk)
| ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xT)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xT)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f283,plain,
! [X8] :
( aSet0(X8)
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f284,plain,
! [X10,X8] :
( aElementOf0(X10,xS)
| ~ aElementOf0(X10,X8)
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f285,plain,
! [X8] :
( aSubsetOf0(X8,xS)
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f286,plain,
! [X8] :
( xk = sbrdtbr0(X8)
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f287,plain,
! [X8] :
( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| aElementOf0(sK10(X8),X8)
| ~ aSet0(X8) ),
inference(cnf_transformation,[],[f189]) ).
fof(f288,plain,
! [X8] :
( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| ~ aElementOf0(sK10(X8),xS)
| ~ aSet0(X8) ),
inference(cnf_transformation,[],[f189]) ).
fof(f289,plain,
! [X8] :
( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| xk != sbrdtbr0(X8)
| ~ aSubsetOf0(X8,xS) ),
inference(cnf_transformation,[],[f189]) ).
fof(f290,plain,
aSet0(slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f189]) ).
fof(f291,plain,
! [X5] :
( aSet0(X5)
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f292,plain,
! [X7,X5] :
( aElementOf0(X7,xT)
| ~ aElementOf0(X7,X5)
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f293,plain,
! [X5] :
( aSubsetOf0(X5,xT)
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f294,plain,
! [X5] :
( xk = sbrdtbr0(X5)
| ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f295,plain,
! [X5] :
( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| aElementOf0(sK9(X5),X5)
| ~ aSet0(X5) ),
inference(cnf_transformation,[],[f189]) ).
fof(f296,plain,
! [X5] :
( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| ~ aElementOf0(sK9(X5),xT)
| ~ aSet0(X5) ),
inference(cnf_transformation,[],[f189]) ).
fof(f297,plain,
! [X5] :
( aElementOf0(X5,slbdtsldtrb0(xT,xk))
| xk != sbrdtbr0(X5)
| ~ aSubsetOf0(X5,xT) ),
inference(cnf_transformation,[],[f189]) ).
fof(f298,plain,
! [X4] :
( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f299,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f189]) ).
fof(f300,plain,
! [X1] :
( aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f301,plain,
! [X3,X1] :
( aElementOf0(X3,xS)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f302,plain,
! [X1] :
( aSubsetOf0(X1,xS)
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f303,plain,
! [X1] :
( sbrdtbr0(X1) = xk
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f304,plain,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| aElementOf0(sK8(X1),X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f189]) ).
fof(f305,plain,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| ~ aElementOf0(sK8(X1),xS)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f189]) ).
fof(f306,plain,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,xS) ),
inference(cnf_transformation,[],[f189]) ).
fof(f307,plain,
aElementOf0(sK7,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f189]) ).
fof(f308,plain,
slcrc0 != slbdtsldtrb0(xS,xk),
inference(cnf_transformation,[],[f189]) ).
fof(f271,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( ( aElementOf0(X0,xP)
| ( xx != X0
& ~ aElementOf0(X0,sdtmndt0(xQ,xy)) )
| ~ aElement0(X0) )
& ( ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) )
| ~ aElementOf0(X0,xP) ) )
& aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xy = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1) )
& ( ( xy != X1
& aElementOf0(X1,xQ)
& aElement0(X1) )
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(flattening,[],[f182]) ).
fof(f182,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( ( aElementOf0(X0,xP)
| ( xx != X0
& ~ aElementOf0(X0,sdtmndt0(xQ,xy)) )
| ~ aElement0(X0) )
& ( ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) )
| ~ aElementOf0(X0,xP) ) )
& aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xy = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1) )
& ( ( xy != X1
& aElementOf0(X1,xQ)
& aElement0(X1) )
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( xy != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( xy != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f272,plain,
! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f273,plain,
! [X1] :
( aElementOf0(X1,xQ)
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f432,plain,
~ aElementOf0(xy,sdtmndt0(xQ,xy)),
inference(equality_resolution,[],[f274]) ).
fof(f274,plain,
! [X1] :
( xy != X1
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f183]) ).
fof(f275,plain,
! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
| xy = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f183]) ).
fof(f276,plain,
aSet0(xP),
inference(cnf_transformation,[],[f183]) ).
fof(f277,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f183]) ).
fof(f278,plain,
! [X0] :
( xx = X0
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f183]) ).
fof(f279,plain,
! [X0] :
( aElementOf0(X0,xP)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f431,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(equality_resolution,[],[f280]) ).
fof(f280,plain,
! [X0] :
( aElementOf0(X0,xP)
| xx != X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f281,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f183]) ).
fof(f268,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
( sz00 != xk
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f269,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f270,plain,
sz00 != xk,
inference(cnf_transformation,[],[f62]) ).
fof(f263,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& xk = sbrdtbr0(xQ)
& aSubsetOf0(xQ,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) )
& aSet0(xQ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& xk = sbrdtbr0(xQ)
& aSubsetOf0(xQ,xS)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f264,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f85]) ).
fof(f265,plain,
aSubsetOf0(xQ,xS),
inference(cnf_transformation,[],[f85]) ).
fof(f266,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f85]) ).
fof(f267,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f85]) ).
fof(f260,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
( xk = sbrdtbr0(xQ)
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f261,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f262,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f258,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f259,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f67]) ).
fof(f257,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f256,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(f255,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).
fof(f254,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2323) ).
fof(f250,plain,
( xk != sbrdtbr0(xP)
| aElementOf0(sK6,xP) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( xk != sbrdtbr0(xP)
| ( ~ aSubsetOf0(xP,xS)
& ~ aElementOf0(sK6,xS)
& aElementOf0(sK6,xP) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f180]) ).
fof(f180,plain,
( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xP) )
=> ( ~ aElementOf0(sK6,xS)
& aElementOf0(sK6,xP) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( xk != sbrdtbr0(xP)
| ( ~ aSubsetOf0(xP,xS)
& ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,xP) ) ) ) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,negated_conjecture,
~ ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(xP)
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ) ),
inference(negated_conjecture,[],[f73]) ).
fof(f73,conjecture,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(xP)
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f251,plain,
( xk != sbrdtbr0(xP)
| ~ aElementOf0(sK6,xS) ),
inference(cnf_transformation,[],[f181]) ).
fof(f252,plain,
( xk != sbrdtbr0(xP)
| ~ aSubsetOf0(xP,xS) ),
inference(cnf_transformation,[],[f181]) ).
fof(f253,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 15:07:52 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (21771)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (21774)WARNING: value z3 for option sas not known
% 0.21/0.37 % (21772)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (21775)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (21778)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)
% 0.21/0.37 % (21776)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)
% 0.21/0.37 % (21777)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)
% 0.21/0.37 % (21774)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)
% 0.21/0.37 % (21773)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (21774)First to succeed.
% 0.21/0.38 % (21777)Also succeeded, but the first one will report.
% 0.21/0.38 % (21776)Also succeeded, but the first one will report.
% 0.21/0.38 % (21774)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21771"
% 0.21/0.38 % (21774)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (21774)------------------------------
% 0.21/0.38 % (21774)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38 % (21774)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (21774)Memory used [KB]: 1011
% 0.21/0.38 % (21774)Time elapsed: 0.011 s
% 0.21/0.38 % (21774)Instructions burned: 15 (million)
% 0.21/0.38 % (21771)Success in time 0.018 s
%------------------------------------------------------------------------------