TSTP Solution File: NUM558+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM558+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 : Tue May 21 02:08:55 EDT 2024
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 99 ( 19 unt; 0 def)
% Number of atoms : 509 ( 83 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 675 ( 265 ~; 247 |; 124 &)
% ( 29 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 214 ( 202 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f816,plain,
$false,
inference(resolution,[],[f798,f235]) ).
fof(f235,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f798,plain,
~ aElementOf0(xk,szNzAzT0),
inference(resolution,[],[f792,f234]) ).
fof(f234,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(f792,plain,
( ~ aElementOf0(xx,xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f769,f241]) ).
fof(f241,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(f769,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f767,f244]) ).
fof(f244,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(f767,plain,
! [X0] :
( ~ aSet0(xQ)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f752,f239]) ).
fof(f239,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(f752,plain,
! [X0] :
( ~ aElement0(xy)
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(X0)
| ~ aSet0(xQ) ),
inference(resolution,[],[f724,f373]) ).
fof(f373,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f322]) ).
fof(f322,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtmndt0(X0,X1) != X2
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP2(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP2(X1,X0,X2)
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP2(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP2(X1,X0,X2)
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( sP2(X1,X0,X2)
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f136,f166]) ).
fof(f166,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f136,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f724,plain,
! [X0] :
( ~ aSet0(sdtmndt0(xQ,xy))
| ~ aSet0(X0)
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f722,f264]) ).
fof(f264,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f722,plain,
( ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f720,f471]) ).
fof(f471,plain,
( aElementOf0(xx,xP)
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(superposition,[],[f470,f238]) ).
fof(f238,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f470,plain,
! [X0,X1] :
( aElementOf0(X0,sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literal_removal,[],[f467]) ).
fof(f467,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(X1,X0)) ),
inference(resolution,[],[f375,f374]) ).
fof(f374,plain,
! [X2,X1,X4] :
( ~ sP3(X4,X1,X2)
| ~ aElement0(X4)
| aElementOf0(X4,X2) ),
inference(equality_resolution,[],[f328]) ).
fof(f328,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| X0 != X4
| ~ aElement0(X4)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ( sK14(X0,X1,X2) != X0
& ~ aElementOf0(sK14(X0,X1,X2),X1) )
| ~ aElement0(sK14(X0,X1,X2))
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( ( sK14(X0,X1,X2) = X0
| aElementOf0(sK14(X0,X1,X2),X1) )
& aElement0(sK14(X0,X1,X2)) )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| ( X0 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4) )
& ( ( ( X0 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f214,f215]) ).
fof(f215,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ( X0 = X3
| aElementOf0(X3,X1) )
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
=> ( ( ( sK14(X0,X1,X2) != X0
& ~ aElementOf0(sK14(X0,X1,X2),X1) )
| ~ aElement0(sK14(X0,X1,X2))
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( ( sK14(X0,X1,X2) = X0
| aElementOf0(sK14(X0,X1,X2),X1) )
& aElement0(sK14(X0,X1,X2)) )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f214,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ( X0 = X3
| aElementOf0(X3,X1) )
& aElement0(X3) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| ( X0 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4) )
& ( ( ( X0 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f213]) ).
fof(f213,plain,
! [X1,X0,X2] :
( ( sP3(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) )
& ( ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP3(X1,X0,X2) ) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X1,X0,X2] :
( ( sP3(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) )
& ( ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP3(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X1,X0,X2] :
( sP3(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f375,plain,
! [X0,X1] :
( sP3(X1,X0,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f334]) ).
fof(f334,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| sdtpldt0(X0,X1) != X2
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP3(X1,X0,X2)
& aSet0(X2) )
| sdtpldt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP3(X1,X0,X2)
& aSet0(X2) )
| sdtpldt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( sP3(X1,X0,X2)
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f138,f168]) ).
fof(f138,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(f720,plain,
( ~ aElementOf0(xx,xP)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f715,f236]) ).
fof(f236,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).
fof(f715,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f714,f242]) ).
fof(f242,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f714,plain,
! [X0] :
( ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xx,X0) ),
inference(duplicate_literal_removal,[],[f713]) ).
fof(f713,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[],[f711,f348]) ).
fof(f348,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f144,f171,f170]) ).
fof(f170,plain,
! [X1,X0,X2] :
( sP4(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f171,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> sP4(X1,X0,X2) )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f144,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f711,plain,
! [X0] :
( ~ sP5(xT,xk)
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(resolution,[],[f709,f424]) ).
fof(f424,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ sP5(X0,X1) ),
inference(resolution,[],[f377,f341]) ).
fof(f341,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| aSet0(X2) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ( ( sbrdtbr0(sK16(X0,X1,X2)) != X0
| ~ aSubsetOf0(sK16(X0,X1,X2),X1)
| ~ aElementOf0(sK16(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK16(X0,X1,X2)) = X0
& aSubsetOf0(sK16(X0,X1,X2),X1) )
| aElementOf0(sK16(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X0
| ~ aSubsetOf0(X4,X1) )
& ( ( sbrdtbr0(X4) = X0
& aSubsetOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f224,f225]) ).
fof(f225,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( sbrdtbr0(X3) != X0
| ~ aSubsetOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X0
& aSubsetOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( sbrdtbr0(sK16(X0,X1,X2)) != X0
| ~ aSubsetOf0(sK16(X0,X1,X2),X1)
| ~ aElementOf0(sK16(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK16(X0,X1,X2)) = X0
& aSubsetOf0(sK16(X0,X1,X2),X1) )
| aElementOf0(sK16(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X0
| ~ aSubsetOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X0
& aSubsetOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X0
| ~ aSubsetOf0(X4,X1) )
& ( ( sbrdtbr0(X4) = X0
& aSubsetOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f223]) ).
fof(f223,plain,
! [X1,X0,X2] :
( ( sP4(X1,X0,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X1,X0,X2) ) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X1,X0,X2] :
( ( sP4(X1,X0,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f170]) ).
fof(f377,plain,
! [X0,X1] :
( sP4(X1,X0,slbdtsldtrb0(X0,X1))
| ~ sP5(X0,X1) ),
inference(equality_resolution,[],[f339]) ).
fof(f339,plain,
! [X2,X0,X1] :
( sP4(X1,X0,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ~ sP4(X1,X0,X2) )
& ( sP4(X1,X0,X2)
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f171]) ).
fof(f709,plain,
! [X0] :
( ~ aSet0(slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f653,f247]) ).
fof(f247,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
( slcrc0 != slbdtsldtrb0(xS,xk)
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f653,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X2,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,X2)
| ~ aElementOf0(xx,X0)
| ~ aSet0(slbdtsldtrb0(xT,X1)) ),
inference(resolution,[],[f639,f269]) ).
fof(f269,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK6(X0,X1),X0)
& aElementOf0(sK6(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f177,f178]) ).
fof(f178,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK6(X0,X1),X0)
& aElementOf0(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f177,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f639,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(resolution,[],[f638,f242]) ).
fof(f638,plain,
! [X0,X1] :
( ~ aSet0(xT)
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(duplicate_literal_removal,[],[f637]) ).
fof(f637,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(xx,X0)
| ~ aSet0(xT)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[],[f633,f348]) ).
fof(f633,plain,
! [X0,X1] :
( ~ sP5(xT,X1)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(xx,X0)
| ~ aSet0(xT) ),
inference(resolution,[],[f443,f505]) ).
fof(f505,plain,
! [X0] :
( ~ aSubsetOf0(X0,xT)
| ~ aElementOf0(xx,X0)
| ~ aSet0(xT) ),
inference(resolution,[],[f269,f231]) ).
fof(f231,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
~ aElementOf0(xx,xT),
inference(flattening,[],[f73]) ).
fof(f73,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[],[f72]) ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f443,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X1)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2))
| ~ sP5(X1,X2) ),
inference(resolution,[],[f342,f377]) ).
fof(f342,plain,
! [X2,X0,X1,X4] :
( ~ sP4(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X1) ),
inference(cnf_transformation,[],[f226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM558+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n019.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 : Mon May 20 04:08:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (11666)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (11669)WARNING: value z3 for option sas not known
% 0.14/0.38 % (11667)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (11670)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (11669)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 % (11671)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 % (11668)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 % (11672)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 % (11673)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)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 % (11672)First to succeed.
% 0.21/0.41 % (11672)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11666"
% 0.21/0.41 % (11672)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for theBenchmark
% 0.21/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (11672)------------------------------
% 0.21/0.41 % (11672)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41 % (11672)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (11672)Memory used [KB]: 1289
% 0.21/0.41 % (11672)Time elapsed: 0.029 s
% 0.21/0.41 % (11672)Instructions burned: 44 (million)
% 0.21/0.41 % (11666)Success in time 0.044 s
%------------------------------------------------------------------------------