%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM628+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:16:03 PM UTC 2026
% Result : Theorem 8.72s 2.11s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of formulae : 146 ( 39 unt; 4 def)
% Number of atoms : 515 ( 125 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 615 ( 246 ~; 242 |; 98 &)
% ( 10 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 17 con; 0-3 aty)
% Number of variables : 149 ( 0 sgn 140 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f86,axiom,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,X0))
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4151) ).
fof(f88,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4331) ).
fof(f90,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ? [X1] :
( aElementOf0(X1,xT)
& ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4618) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(f111,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f112,axiom,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5321) ).
fof(f113,axiom,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f114,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f115,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f123,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(flattening,[],[f115]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f142,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f153,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f198,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f199,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f198]) ).
fof(f225,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f226,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f225]) ).
fof(f227,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f234,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,X0))
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f235,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,X0))
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f234]) ).
fof(f237,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f237]) ).
fof(f241,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,xT)
& ! [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f242,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,xT)
& ! [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f241]) ).
fof(f243,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f244,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f245,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f244]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f130]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f257]) ).
fof(f259,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f258]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f259]) ).
fof(f294,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f295,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f294]) ).
fof(f296,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f295]) ).
fof(f297,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f296]) ).
fof(f314,plain,
! [X0] :
( ( aElementOf0(sK27(X0),xT)
& ! [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = sK27(X0)
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f242]) ).
fof(f324,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f355,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f362,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f365,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f418,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f474,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f475,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f476,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f480,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f481,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f485,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f491,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk))
| aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ isCountable0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f238]) ).
fof(f496,plain,
! [X2,X0] :
( ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X2)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = sK27(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f498,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f501,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f518,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f520,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f521,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f522,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f523,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f527,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f529,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f530,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f532,plain,
szDzizrdt0(xd) = sdtlpdtrp0(xd,xn),
inference(cnf_transformation,[],[f112]) ).
fof(f533,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f113]) ).
fof(f534,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(cnf_transformation,[],[f123]) ).
fof(f553,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f418]) ).
fof(f554,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f553]) ).
fof(f572,definition,
sF29 = sdtlpdtrp0(xd,xn),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f573,plain,
sdtlpdtrp0(xd,xn) = sF29,
inference(reorient_equations,[],[f572]) ).
fof(f574,definition,
sF30 = sdtlpdtrp0(xc,xQ),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f575,plain,
sdtlpdtrp0(xc,xQ) = sF30,
inference(reorient_equations,[],[f574]) ).
fof(f576,plain,
sF29 != sF30,
inference(definition_folding,[],[f534,f575,f573]) ).
fof(f578,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f475,f480]) ).
fof(f579,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f476,f481]) ).
fof(f595,plain,
szDzizrdt0(xd) = sF29,
inference(forward_demodulation,[],[f573,f532]) ).
fof(f596,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f578,f481]) ).
fof(f597,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f579,f480]) ).
fof(f598,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f518,f324]) ).
fof(f599,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f598,f362]) ).
fof(f600,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[],[f498,f530]) ).
fof(f601,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[],[f600,f529]) ).
fof(f605,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f481,f324]) ).
fof(f606,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f605,f362]) ).
fof(f623,definition,
( spl31_4
<=> aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
introduced(definition,[new_symbols(definition,[spl31_4])],[avatar_definition]) ).
fof(f624,plain,
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ spl31_4 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f625,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| spl31_4 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f633,plain,
xP = sdtmndt0(xQ,xp),
inference(superposition,[],[f521,f520]) ).
fof(f726,plain,
( xQ = sdtpldt0(sdtmndt0(xQ,xp),xp)
| ~ aSet0(xQ) ),
inference(resolution,[],[f355,f523]) ).
fof(f727,plain,
xQ = sdtpldt0(sdtmndt0(xQ,xp),xp),
inference(forward_subsumption_resolution,[],[f726,f599]) ).
fof(f734,plain,
xQ = sdtpldt0(xP,xp),
inference(forward_demodulation,[],[f727,f633]) ).
fof(f1166,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl31_4 ),
inference(resolution,[],[f625,f606]) ).
fof(f1889,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f554,f527]) ).
fof(f1894,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f1889,f474]) ).
fof(f1897,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(xP)
| sK27(X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f1894,f496]) ).
fof(f1898,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(xP)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f1894,f501]) ).
fof(f1911,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1898,f522]) ).
fof(f1912,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sK27(X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1897,f522]) ).
fof(f1913,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1911,f533]) ).
fof(f1932,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sK27(xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1912,f533]) ).
fof(f2017,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl31_4 ),
inference(resolution,[],[f1166,f365]) ).
fof(f2019,plain,
( $false
| spl31_4 ),
inference(forward_subsumption_resolution,[],[f2017,f530]) ).
fof(f2020,plain,
spl31_4,
inference(avatar_contradiction_clause,[],[f2019]) ).
fof(f2026,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(forward_subsumption_resolution,[],[f1913,f530]) ).
fof(f2027,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sK27(xn) ),
inference(forward_subsumption_resolution,[],[f1932,f530]) ).
fof(f2412,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(resolution,[],[f491,f597]) ).
fof(f2417,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(duplicate_literal_removal,[],[f2412]) ).
fof(f2421,plain,
! [X0,X1] :
( aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2417,f596]) ).
fof(f2428,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| sdtlpdtrp0(sdtlpdtrp0(xC,X1),X0) = sdtlpdtrp0(xc,sdtpldt0(X0,szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(resolution,[],[f2421,f485]) ).
fof(f2437,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(sdtlpdtrp0(xC,X1),X0) = sdtlpdtrp0(xc,sdtpldt0(X0,szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(duplicate_literal_removal,[],[f2428]) ).
fof(f2447,plain,
! [X0] :
( ~ aSet0(xP)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(resolution,[],[f2437,f1894]) ).
fof(f2453,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(forward_subsumption_resolution,[],[f2447,f522]) ).
fof(f2457,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[],[f2453,f533]) ).
fof(f2461,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(forward_subsumption_resolution,[],[f2457,f530]) ).
fof(f2463,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,xp))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(forward_demodulation,[],[f2461,f601]) ).
fof(f2465,plain,
( sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(forward_demodulation,[],[f2463,f734]) ).
fof(f2498,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ spl31_4 ),
inference(forward_subsumption_resolution,[],[f2026,f624]) ).
fof(f2499,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sK27(xn)
| ~ spl31_4 ),
inference(forward_subsumption_resolution,[],[f2027,f624]) ).
fof(f2557,plain,
( sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ spl31_4 ),
inference(forward_subsumption_resolution,[],[f2465,f624]) ).
fof(f2569,plain,
( szDzizrdt0(xd) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ spl31_4 ),
inference(forward_demodulation,[],[f2498,f532]) ).
fof(f2573,plain,
( sdtlpdtrp0(xc,xQ) = sK27(xn)
| ~ spl31_4 ),
inference(forward_demodulation,[],[f2557,f2499]) ).
fof(f2589,plain,
( szDzizrdt0(xd) = sK27(xn)
| ~ spl31_4 ),
inference(forward_demodulation,[],[f2569,f2499]) ).
fof(f2592,plain,
( sF30 = sK27(xn)
| ~ spl31_4 ),
inference(forward_demodulation,[],[f2573,f575]) ).
fof(f2602,definition,
( spl31_152
<=> sF30 = sK27(xn) ),
introduced(definition,[new_symbols(definition,[spl31_152])],[avatar_definition]) ).
fof(f2604,plain,
( sF30 = sK27(xn)
| ~ spl31_152 ),
inference(avatar_component_clause,[],[f2602]) ).
fof(f2606,plain,
( sF29 = sK27(xn)
| ~ spl31_4 ),
inference(forward_demodulation,[],[f2589,f595]) ).
fof(f2608,plain,
( spl31_152
| ~ spl31_4 ),
inference(avatar_split_clause,[],[f2592,f623,f2602]) ).
fof(f2609,plain,
( sF29 = sF30
| ~ spl31_4
| ~ spl31_152 ),
inference(forward_demodulation,[],[f2604,f2606]) ).
fof(f2610,plain,
( $false
| ~ spl31_4
| ~ spl31_152 ),
inference(forward_subsumption_resolution,[],[f2609,f576]) ).
fof(f2611,plain,
( ~ spl31_4
| ~ spl31_152 ),
inference(avatar_contradiction_clause,[],[f2610]) ).
cnf(s75,plain,
spl31_4,
inference(sat_conversion,[],[f2020]) ).
cnf(s114,plain,
( ~ spl31_4
| spl31_152 ),
inference(sat_conversion,[],[f2608]) ).
cnf(s115,plain,
( ~ spl31_4
| ~ spl31_152 ),
inference(sat_conversion,[],[f2611]) ).
cnf(s116,plain,
~ spl31_152,
inference(rat,[],[s115,s75]) ).
cnf(s117,plain,
$false,
inference(rat,[],[s114,s116,s75]) ).
fof(f2612,plain,
$false,
inference(avatar_sat_refutation,[],[s117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM628+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:50:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.72/2.11 % (149189)Detected formulas, will run a generic FOF schedule.
% 8.72/2.11 % (149198)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2663948156:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.72/2.11 % (149198)Instruction limit reached!
% 8.72/2.11 % (149198)------------------------------
% 8.72/2.11 % (149198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149198)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149198)Termination reason: Instruction limit
% 8.72/2.11 % (149198)Termination phase: Saturation
% 8.72/2.11 % (149198)Time elapsed: 0.042 s
% 8.72/2.11 % (149198)Peak memory usage: 89 MB
% 8.72/2.11 % (149198)Instructions burned: 120 (million)
% 8.72/2.11 % (149196)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3573598021:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.72/2.11 % (149197)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3007831199:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.72/2.11 % (149195)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1995975764:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.72/2.11 % (149194)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3524413154:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.72/2.11 % (149199)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3208385339:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.72/2.11 % (149200)dis-21_1_sil=8000:lcm=predicate:random_seed=1215196234:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.72/2.11 % (149197)Instruction limit reached!
% 8.72/2.11 % (149197)------------------------------
% 8.72/2.11 % (149197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149197)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149197)Termination reason: Instruction limit
% 8.72/2.11 % (149197)Termination phase: Saturation
% 8.72/2.11 % (149197)Time elapsed: 0.071 s
% 8.72/2.11 % (149197)Peak memory usage: 89 MB
% 8.72/2.11 % (149197)Instructions burned: 110 (million)
% 8.72/2.11 % (149202)lrs+10_1_sil=8000:sp=occurrence:random_seed=1262107797:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.72/2.11 % (149200)Instruction limit reached!
% 8.72/2.11 % (149200)------------------------------
% 8.72/2.11 % (149200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149200)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149200)Termination reason: Instruction limit
% 8.72/2.11 % (149200)Termination phase: Saturation
% 8.72/2.11 % (149200)Time elapsed: 0.076 s
% 8.72/2.11 % (149200)Peak memory usage: 91 MB
% 8.72/2.11 % (149200)Instructions burned: 131 (million)
% 8.72/2.11 % (149199)Instruction limit reached!
% 8.72/2.11 % (149199)------------------------------
% 8.72/2.11 % (149199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149199)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149199)Termination reason: Instruction limit
% 8.72/2.11 % (149199)Termination phase: Saturation
% 8.72/2.11 % (149199)Time elapsed: 0.103 s
% 8.72/2.11 % (149199)Peak memory usage: 90 MB
% 8.72/2.11 % (149199)Instructions burned: 139 (million)
% 8.72/2.11 % (149202)Instruction limit reached!
% 8.72/2.11 % (149202)------------------------------
% 8.72/2.11 % (149202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149202)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149202)Termination reason: Instruction limit
% 8.72/2.11 % (149202)Termination phase: Saturation
% 8.72/2.11 % (149202)Time elapsed: 0.100 s
% 8.72/2.11 % (149202)Peak memory usage: 92 MB
% 8.72/2.11 % (149202)Instructions burned: 285 (million)
% 8.72/2.11 % (149209)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3339400117:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.72/2.11 % (149209)Refutation not found, incomplete strategy
% 8.72/2.11 % (149209)------------------------------
% 8.72/2.11 % (149209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149209)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149209)Termination reason: Refutation not found, incomplete strategy
% 8.72/2.11 % (149209)Time elapsed: 0.003 s
% 8.72/2.11 % (149209)Peak memory usage: 89 MB
% 8.72/2.11 % (149209)Instructions burned: 3 (million)
% 8.72/2.11 % (149211)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3125004273:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.72/2.11 % (149212)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1700373496:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.72/2.11 % (149213)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=248759815:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 8.72/2.11 % (149213)Instruction limit reached!
% 8.72/2.11 % (149213)------------------------------
% 8.72/2.11 % (149213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149213)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149213)Termination reason: Instruction limit
% 8.72/2.11 % (149213)Termination phase: Saturation
% 8.72/2.11 % (149213)Time elapsed: 0.100 s
% 8.72/2.11 % (149213)Peak memory usage: 90 MB
% 8.72/2.11 % (149213)Instructions burned: 295 (million)
% 8.72/2.11 % (149212)Instruction limit reached!
% 8.72/2.11 % (149212)------------------------------
% 8.72/2.11 % (149212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149212)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149212)Termination reason: Instruction limit
% 8.72/2.11 % (149212)Termination phase: Saturation
% 8.72/2.11 % (149212)Time elapsed: 0.151 s
% 8.72/2.11 % (149212)Peak memory usage: 92 MB
% 8.72/2.11 % (149212)Instructions burned: 251 (million)
% 8.72/2.11 % (149211)Instruction limit reached!
% 8.72/2.11 % (149211)------------------------------
% 8.72/2.11 % (149211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149211)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149211)Termination reason: Instruction limit
% 8.72/2.11 % (149211)Termination phase: Saturation
% 8.72/2.11 % (149211)Time elapsed: 0.228 s
% 8.72/2.11 % (149211)Peak memory usage: 92 MB
% 8.72/2.11 % (149211)Instructions burned: 325 (million)
% 8.72/2.11 % (149209)------------------------------
% 8.72/2.11 % (149209)------------------------------
% 8.72/2.11 % (149218)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1388853589:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.72/2.11 % (149219)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2957495103:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.72/2.11 % (149220)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2700614057:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.72/2.11 % (149221)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1624045439:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 8.72/2.11 % (149219)Instruction limit reached!
% 8.72/2.11 % (149219)------------------------------
% 8.72/2.11 % (149219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149219)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149219)Termination reason: Instruction limit
% 8.72/2.11 % (149219)Termination phase: Saturation
% 8.72/2.11 % (149219)Time elapsed: 0.075 s
% 8.72/2.11 % (149219)Peak memory usage: 91 MB
% 8.72/2.11 % (149219)Instructions burned: 114 (million)
% 8.72/2.11 % (149220)Instruction limit reached!
% 8.72/2.11 % (149220)------------------------------
% 8.72/2.11 % (149220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149220)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149220)Termination reason: Instruction limit
% 8.72/2.11 % (149220)Termination phase: Saturation
% 8.72/2.11 % (149220)Time elapsed: 0.069 s
% 8.72/2.11 % (149220)Peak memory usage: 89 MB
% 8.72/2.11 % (149220)Instructions burned: 129 (million)
% 8.72/2.11 % (149221)Instruction limit reached!
% 8.72/2.11 % (149221)------------------------------
% 8.72/2.11 % (149221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149221)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149221)Termination reason: Instruction limit
% 8.72/2.11 % (149221)Termination phase: Saturation
% 8.72/2.11 % (149221)Time elapsed: 0.073 s
% 8.72/2.11 % (149221)Peak memory usage: 89 MB
% 8.72/2.11 % (149221)Instructions burned: 115 (million)
% 8.72/2.11 % (149226)lrs+10_1_sil=8000:sp=occurrence:random_seed=1973683208:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.72/2.11 % (149227)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2493055803:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.72/2.11 % (149228)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=298298502:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 8.72/2.11 % (149194)First to succeed.
% 8.72/2.11 % (149194)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-149189"
% 8.72/2.11 % (149227)Instruction limit reached!
% 8.72/2.11 % (149227)------------------------------
% 8.72/2.11 % (149227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.11 % (149227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.11 % (149227)CaDiCaL version: 2.1.3
% 8.72/2.11 % (149227)Termination reason: Instruction limit
% 8.72/2.11 % (149227)Termination phase: Saturation
% 8.72/2.11 % (149227)Time elapsed: 0.274 s
% 8.72/2.11 % (149227)Peak memory usage: 92 MB
% 8.72/2.11 % (149227)Instructions burned: 438 (million)
% 8.72/2.11 % (149194)Refutation found. Thanks to Tanya!
% 8.72/2.11 % SZS status Theorem for theBenchmark
% 8.72/2.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/2.31 % (149194)------------------------------
% 0.15/2.31 % (149194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/2.31 % (149194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/2.31 % (149194)CaDiCaL version: 2.1.3
% 0.15/2.31 % (149194)Termination reason: Refutation
% 0.15/2.31 % (149194)Time elapsed: 0.854 s
% 0.15/2.31 % (149194)Peak memory usage: 133 MB
% 0.15/2.31 % (149194)Instructions burned: 1264 (million)
% 0.15/2.31 % (149194)------------------------------
% 0.15/2.31 % (149194)------------------------------
% 0.15/2.31 % (149189)Success in time 1.264 s
% 0.15/2.31 % Vampire exiting
%------------------------------------------------------------------------------