TSTP Solution File: RNG112+4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n017.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 : Thu Aug 31 14:01:21 EDT 2023
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 70 ( 14 unt; 0 def)
% Number of atoms : 576 ( 189 equ)
% Maximal formula atoms : 34 ( 8 avg)
% Number of connectives : 715 ( 209 ~; 168 |; 301 &)
% ( 13 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-2 aty)
% Number of variables : 268 (; 141 !; 127 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4471,plain,
$false,
inference(unit_resulting_resolution,[],[f507,f4470,f217]) ).
fof(f217,plain,
! [X0] :
( sz00 != sK6(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ( iLess0(sbrdtbr0(sK6(X0)),sbrdtbr0(X0))
& sz00 != sK6(X0)
& aElementOf0(sK6(X0),xI)
& sK6(X0) = sdtpldt0(sK7(X0),sK8(X0))
& aElementOf0(sK8(X0),slsdtgt0(xb))
& aElementOf0(sK7(X0),slsdtgt0(xa)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f128,f130,f129]) ).
fof(f129,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ( iLess0(sbrdtbr0(sK6(X0)),sbrdtbr0(X0))
& sz00 != sK6(X0)
& aElementOf0(sK6(X0),xI)
& ? [X3,X2] :
( sdtpldt0(X2,X3) = sK6(X0)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
! [X0] :
( ? [X3,X2] :
( sdtpldt0(X2,X3) = sK6(X0)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) )
=> ( sK6(X0) = sdtpldt0(sK7(X0),sK8(X0))
& aElementOf0(sK8(X0),slsdtgt0(xb))
& aElementOf0(sK7(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f4470,plain,
sz00 = sK6(sK20),
inference(subsumption_resolution,[],[f4469,f507]) ).
fof(f4469,plain,
( sz00 = sK6(sK20)
| ~ sP0(sK20) ),
inference(resolution,[],[f4468,f216]) ).
fof(f216,plain,
! [X0] :
( aElementOf0(sK6(X0),xI)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f4468,plain,
( ~ aElementOf0(sK6(sK20),xI)
| sz00 = sK6(sK20) ),
inference(subsumption_resolution,[],[f4467,f507]) ).
fof(f4467,plain,
( sz00 = sK6(sK20)
| ~ aElementOf0(sK6(sK20),xI)
| ~ sP0(sK20) ),
inference(resolution,[],[f503,f218]) ).
fof(f218,plain,
! [X0] :
( iLess0(sbrdtbr0(sK6(X0)),sbrdtbr0(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f503,plain,
! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20))
| sz00 = X1
| ~ aElementOf0(X1,xI) ),
inference(subsumption_resolution,[],[f277,f499]) ).
fof(f499,plain,
sP3,
inference(subsumption_resolution,[],[f496,f290]) ).
fof(f290,plain,
sz00 != sK23,
inference(cnf_transformation,[],[f163]) ).
fof(f163,plain,
( sz00 != sK23
& aElementOf0(sK23,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sK23 = sdtpldt0(sK24,sK25)
& aElementOf0(sK25,slsdtgt0(xb))
& aElementOf0(sK24,slsdtgt0(xa))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ( sdtasdt0(xb,sK26(X3)) = X3
& aElement0(sK26(X3)) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ( sdtasdt0(xa,sK27(X6)) = X6
& aElement0(sK27(X6)) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25,sK26,sK27])],[f158,f162,f161,f160,f159]) ).
fof(f159,plain,
( ? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
=> ( sz00 != sK23
& aElementOf0(sK23,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X2,X1] :
( sdtpldt0(X1,X2) = sK23
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
( ? [X2,X1] :
( sdtpldt0(X1,X2) = sK23
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
=> ( sK23 = sdtpldt0(sK24,sK25)
& aElementOf0(sK25,slsdtgt0(xb))
& aElementOf0(sK24,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X3] :
( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
=> ( sdtasdt0(xb,sK26(X3)) = X3
& aElement0(sK26(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X6] :
( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
=> ( sdtasdt0(xa,sK27(X6)) = X6
& aElement0(sK27(X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f157]) ).
fof(f157,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( sdtasdt0(xb,X2) = X1
& aElement0(X2) ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1HmsUnNrVf/Vampire---4.8_26240',m__2228) ).
fof(f496,plain,
( sz00 = sK23
| sP3 ),
inference(resolution,[],[f279,f433]) ).
fof(f433,plain,
aElementOf0(sK23,xI),
inference(forward_demodulation,[],[f432,f410]) ).
fof(f410,plain,
xI = sdtpldt1(sF50,sF49),
inference(forward_demodulation,[],[f409,f405]) ).
fof(f405,plain,
slsdtgt0(xa) = sF50,
introduced(function_definition,[]) ).
fof(f409,plain,
xI = sdtpldt1(slsdtgt0(xa),sF49),
inference(forward_demodulation,[],[f235,f404]) ).
fof(f404,plain,
slsdtgt0(xb) = sF49,
introduced(function_definition,[]) ).
fof(f235,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ( sdtpldt0(sK9(X0),sK10(X0)) = X0
& aElementOf0(sK10(X0),slsdtgt0(xb))
& aElementOf0(sK9(X0),slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(xb,sK11(X5)) = X5
& aElement0(sK11(X5)) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ( sdtasdt0(xa,sK12(X8)) = X8
& aElement0(sK12(X8)) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f134,f137,f136,f135]) ).
fof(f135,plain,
! [X0] :
( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
=> ( sdtpldt0(sK9(X0),sK10(X0)) = X0
& aElementOf0(sK10(X0),slsdtgt0(xb))
& aElementOf0(sK9(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X5] :
( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(xb,sK11(X5)) = X5
& aElement0(sK11(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X8] :
( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
=> ( sdtasdt0(xa,sK12(X8)) = X8
& aElement0(sK12(X8)) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(rectify,[],[f133]) ).
fof(f133,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( aElementOf0(X7,xI)
=> ( ! [X8] :
( aElement0(X8)
=> aElementOf0(sdtasdt0(X8,X7),xI) )
& ! [X9] :
( aElementOf0(X9,xI)
=> aElementOf0(sdtpldt0(X7,X9),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/tmp/tmp.1HmsUnNrVf/Vampire---4.8_26240',m__2174) ).
fof(f432,plain,
aElementOf0(sK23,sdtpldt1(sF50,sF49)),
inference(forward_demodulation,[],[f431,f405]) ).
fof(f431,plain,
aElementOf0(sK23,sdtpldt1(slsdtgt0(xa),sF49)),
inference(forward_demodulation,[],[f289,f404]) ).
fof(f289,plain,
aElementOf0(sK23,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f163]) ).
fof(f279,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| sP3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( sP3
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f68,f123]) ).
fof(f123,plain,
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ sP3 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f68,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X3] :
( ! [X4] :
( ( sz00 != X4
& ( aElementOf0(X4,xI)
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ( sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X1] :
( ! [X2] :
( ( sz00 != X2
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1HmsUnNrVf/Vampire---4.8_26240',m__2351) ).
fof(f277,plain,
! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20))
| sz00 = X1
| ~ aElementOf0(X1,xI)
| ~ sP3 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( ( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != sK20
& aElementOf0(sK20,xI)
& sK20 = sdtpldt0(sK21,sK22)
& aElementOf0(sK22,slsdtgt0(xb))
& aElementOf0(sK21,slsdtgt0(xa)) )
| ~ sP3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f153,f155,f154]) ).
fof(f154,plain,
( ? [X0] :
( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != X0
& aElementOf0(X0,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
=> ( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != sK20
& aElementOf0(sK20,xI)
& ? [X5,X4] :
( sdtpldt0(X4,X5) = sK20
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f155,plain,
( ? [X5,X4] :
( sdtpldt0(X4,X5) = sK20
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) )
=> ( sK20 = sdtpldt0(sK21,sK22)
& aElementOf0(sK22,slsdtgt0(xb))
& aElementOf0(sK21,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
( ? [X0] :
( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != X0
& aElementOf0(X0,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
| ~ sP3 ),
inference(rectify,[],[f152]) ).
fof(f152,plain,
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ sP3 ),
inference(nnf_transformation,[],[f123]) ).
fof(f507,plain,
sP0(sK20),
inference(subsumption_resolution,[],[f446,f499]) ).
fof(f446,plain,
( sP0(sK20)
| ~ sP3 ),
inference(subsumption_resolution,[],[f445,f275]) ).
fof(f275,plain,
( sz00 != sK20
| ~ sP3 ),
inference(cnf_transformation,[],[f156]) ).
fof(f445,plain,
( ~ sP3
| sz00 = sK20
| sP0(sK20) ),
inference(resolution,[],[f274,f220]) ).
fof(f220,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| sP0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( sP0(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f119]) ).
fof(f119,plain,
! [X0] :
( sP0(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f63,f118]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(negated_conjecture,[],[f46]) ).
fof(f46,conjecture,
? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1HmsUnNrVf/Vampire---4.8_26240',m__) ).
fof(f274,plain,
( aElementOf0(sK20,xI)
| ~ sP3 ),
inference(cnf_transformation,[],[f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.36 % CPULimit : 300
% 0.21/0.36 % WCLimit : 300
% 0.21/0.36 % DateTime : Sun Aug 27 00:59:11 EDT 2023
% 0.21/0.37 % CPUTime :
% 0.21/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.21/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.1HmsUnNrVf/Vampire---4.8_26240
% 0.21/0.37 % (26389)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (26397)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.21/0.43 % (26401)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.21/0.43 % (26400)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.43 % (26394)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.21/0.43 % (26391)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.21/0.43 % (26402)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.21/0.44 % (26399)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.21/0.51 % (26391)First to succeed.
% 0.21/0.52 % (26391)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for Vampire---4
% 0.21/0.52 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.52 % (26391)------------------------------
% 0.21/0.52 % (26391)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.52 % (26391)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.52 % (26391)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (26391)Memory used [KB]: 2558
% 0.21/0.52 % (26391)Time elapsed: 0.083 s
% 0.21/0.52 % (26391)------------------------------
% 0.21/0.52 % (26391)------------------------------
% 0.21/0.52 % (26389)Success in time 0.145 s
% 0.21/0.52 % Vampire---4.8 exiting
%------------------------------------------------------------------------------