%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM586+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:26:07 PM UTC 2026
% Result : Theorem 13.77s 5.10s
% Output : CNFRefutation 30.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 15
% Syntax : Number of formulae : 111 ( 36 unt; 5 def)
% Number of atoms : 502 ( 113 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 520 ( 207 ~; 205 |; 87 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 156 ( 0 sgn 140 !; 16 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(f65,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElement0(sdtlpdtrp0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).
fof(f66,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aFunction0(X0) )
=> ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f86,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [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)))) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
fof(f87,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4200) ).
fof(f88,axiom,
aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4200_02) ).
fof(f89,conjecture,
? [X0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) = xx
& aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ ? [X0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) = xx
& aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f107,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f184,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f185,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(X0))
| aElement0(sdtlpdtrp0(X0,X1)) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f186,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f187,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f186]) ).
fof(f190,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f199,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(ennf_transformation,[],[f81]) ).
fof(f200,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(flattening,[],[f199]) ).
fof(f208,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ! [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)))) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(ennf_transformation,[],[f86]) ).
fof(f209,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ! [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)))) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(flattening,[],[f208]) ).
fof(f210,plain,
! [X0] :
( xx != sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(ennf_transformation,[],[f90]) ).
fof(f263,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0))
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f187]) ).
fof(f264,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0))
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(flattening,[],[f263]) ).
fof(f265,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdtlpdtrp0(X0,X4) = X1
& aElementOf0(X4,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(rectify,[],[f264]) ).
fof(f266,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdtlpdtrp0(X0,X4) = X1
& aElementOf0(X4,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK16(X0,X1,X2),X2)
| ( sdtlpdtrp0(X0,sK16(X0,X1,X2)) = X1
& aElementOf0(sK16(X0,X1,X2),szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(sK16(X0,X1,X2),X2)
| sdtlpdtrp0(X0,sK16(X0,X1,X2)) != X1
| ~ aElementOf0(sK16(X0,X1,X2),szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1,X2))],[f265]) ).
fof(f267,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f190]) ).
fof(f268,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(flattening,[],[f267]) ).
fof(f269,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X6] :
( ( ~ aElementOf0(X6,X2)
| ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) ) )
& ( ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) )
| aElementOf0(X6,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(rectify,[],[f268]) ).
fof(f270,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ! [X2] :
( ( sdtlcdtrc0(X0,X1) != X2
| ( ! [X6] :
( ( ~ aElementOf0(X6,X2)
| ( sdtlpdtrp0(X0,sK19(X0,X1,X6)) = X6
& aElementOf0(sK19(X0,X1,X6),X1) ) )
& ( ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) )
| aElementOf0(X6,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK17(X0,X1,X2),X2)
| ( sK17(X0,X1,X2) = sdtlpdtrp0(X0,sK18(X0,X1,X2))
& aElementOf0(sK18(X0,X1,X2),X1) ) )
& ( ~ aElementOf0(sK17(X0,X1,X2),X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != sK17(X0,X1,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X2)
| X2 = sdtlcdtrc0(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X3,sK17(X0,X1,X2)),skolemize(X5,sK18(X0,X1,X2)),skolemize(X8,sK19(X0,X1,X6))],[f269]) ).
fof(f289,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f391,plain,
! [X0] :
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f184]) ).
fof(f392,plain,
! [X0,X1] :
( ~ aFunction0(X0)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aElement0(sdtlpdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f185]) ).
fof(f393,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sdtlpdtrp0(X0,X4) = X1 ),
inference(cnf_transformation,[],[f266]) ).
fof(f395,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f266]) ).
fof(f401,plain,
! [X2,X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlcdtrc0(X0,X1) != X2
| ~ aElementOf0(X6,X2)
| sdtlpdtrp0(X0,sK19(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f270]) ).
fof(f402,plain,
! [X2,X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlcdtrc0(X0,X1) != X2
| ~ aElementOf0(X6,X2)
| aElementOf0(sK19(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f439,plain,
szNzAzT0 = szDzozmdt0(xN),
inference(cnf_transformation,[],[f200]) ).
fof(f440,plain,
aFunction0(xN),
inference(cnf_transformation,[],[f200]) ).
fof(f447,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0)) ),
inference(cnf_transformation,[],[f209]) ).
fof(f448,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aFunction0(sdtlpdtrp0(xC,X0)) ),
inference(cnf_transformation,[],[f209]) ).
fof(f449,plain,
szNzAzT0 = szDzozmdt0(xC),
inference(cnf_transformation,[],[f209]) ).
fof(f450,plain,
aFunction0(xC),
inference(cnf_transformation,[],[f209]) ).
fof(f451,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f87]) ).
fof(f452,plain,
aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi)))),
inference(cnf_transformation,[],[f88]) ).
fof(f453,plain,
! [X0] :
( xx != sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(cnf_transformation,[],[f210]) ).
fof(f477,plain,
! [X2,X0,X4] :
( ~ aElement0(sdtlpdtrp0(X0,X4))
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,sdtlpdtrp0(X0,X4)) != X2
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ),
inference(equality_resolution,[],[f395]) ).
fof(f478,plain,
! [X0,X4] :
( ~ aElement0(sdtlpdtrp0(X0,X4))
| ~ aFunction0(X0)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,sdtlbdtrb0(X0,sdtlpdtrp0(X0,X4))) ),
inference(equality_resolution,[],[f477]) ).
fof(f480,plain,
! [X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| sdtlpdtrp0(X0,X4) = X1 ),
inference(equality_resolution,[],[f393]) ).
fof(f484,plain,
! [X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X6,sdtlcdtrc0(X0,X1))
| aElementOf0(sK19(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f402]) ).
fof(f485,plain,
! [X0,X1,X6] :
( ~ aFunction0(X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X6,sdtlcdtrc0(X0,X1))
| sdtlpdtrp0(X0,sK19(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f401]) ).
tcf(c_61,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_163,plain,
! [X0: $i] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f391]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtlpdtrp0(X1,X0))
| ~ aFunction0(X1)
| ~ aElementOf0(X0,szDzozmdt0(X1)) ),
inference(cnf_transformation,[],[f392]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,sdtlbdtrb0(X0,sdtlpdtrp0(X0,X1)))
| ~ aFunction0(X0)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aElement0(sdtlpdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f478]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtlpdtrp0(X1,X0) = X2 )
| ~ aFunction0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,sdtlbdtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f480]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK19(X1,X2,X0),X2)
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aElementOf0(X0,sdtlcdtrc0(X1,X2)) ),
inference(cnf_transformation,[],[f484]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtlpdtrp0(X1,sK19(X1,X2,X0)) = X0 )
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aElementOf0(X0,sdtlcdtrc0(X1,X2)) ),
inference(cnf_transformation,[],[f485]) ).
tcf(c_208,plain,
aFunction0(xN),
inference(cnf_transformation,[],[f440]) ).
tcf(c_209,plain,
szDzozmdt0(xN) = szNzAzT0,
inference(cnf_transformation,[],[f439]) ).
tcf(c_218,plain,
aFunction0(xC),
inference(cnf_transformation,[],[f450]) ).
tcf(c_219,plain,
szDzozmdt0(xC) = szNzAzT0,
inference(cnf_transformation,[],[f449]) ).
tcf(c_220,plain,
! [X0: $i] :
( aFunction0(sdtlpdtrp0(xC,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f448]) ).
tcf(c_221,plain,
! [X0: $i] :
( ( slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f447]) ).
tcf(c_223,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f451]) ).
tcf(c_224,plain,
aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi)))),
inference(cnf_transformation,[],[f452]) ).
tcf(c_225,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) != xx ) ),
inference(cnf_transformation,[],[f453]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlbdtrb0(X1,sdtlpdtrp0(X1,X0)))
| ~ aFunction0(X1)
| ~ aElementOf0(X0,szDzozmdt0(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_169,c_164]) ).
tcf(c_14844,definition,
iPr_def_10 = sdtlpdtrp0(xC,xi),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_14845,definition,
iPr_def_11 = sdtlpdtrp0(xN,xi),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_14846,definition,
iPr_def_12 = szmzizndt0(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_14847,definition,
iPr_def_13 = sdtmndt0(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_14848,definition,
iPr_def_14 = slbdtsldtrb0(iPr_def_13,xk),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_14849,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,iPr_def_14)
| ( sdtlpdtrp0(iPr_def_10,X0) != xx ) ),
inference(demodulation,[status(thm)],[c_225,c_14846,c_14845,c_14847,c_14848,c_14844]) ).
tcf(c_17723,plain,
( aFunction0(iPr_def_10)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[status(thm)],[c_14844,c_220]) ).
tcf(c_17724,plain,
aFunction0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_17723,c_223]) ).
tcf(c_18002,plain,
aElementOf0(xx,sdtlcdtrc0(iPr_def_10,szDzozmdt0(iPr_def_10))),
inference(light_normalisation,[status(thm)],[c_224,c_14844]) ).
tcf(c_18720,plain,
! [X0: $i] :
( aElement0(sdtlpdtrp0(xN,X0))
| ~ aFunction0(xN)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_209,c_164]) ).
tcf(c_18721,plain,
! [X0: $i] :
( aElement0(sdtlpdtrp0(xC,X0))
| ~ aFunction0(xC)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_219,c_164]) ).
tcf(c_18722,plain,
! [X0: $i] :
( aElement0(sdtlpdtrp0(xC,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18721,c_218]) ).
tcf(c_18725,plain,
! [X0: $i] :
( aElement0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18720,c_208]) ).
tcf(c_18777,plain,
( aElement0(iPr_def_10)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[status(thm)],[c_14844,c_18722]) ).
tcf(c_18778,plain,
aElement0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_18777,c_223]) ).
tcf(c_18784,plain,
( aElement0(iPr_def_11)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[status(thm)],[c_14845,c_18725]) ).
tcf(c_18785,plain,
aElement0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_18784,c_223]) ).
tcf(c_20930,plain,
( aElementOf0(xi,sdtlbdtrb0(xC,iPr_def_10))
| ~ aFunction0(xC)
| ~ aElementOf0(xi,szDzozmdt0(xC)) ),
inference(superposition,[status(thm)],[c_14844,c_660]) ).
tcf(c_20931,plain,
( aElementOf0(xi,sdtlbdtrb0(xN,iPr_def_11))
| ~ aFunction0(xN)
| ~ aElementOf0(xi,szDzozmdt0(xN)) ),
inference(superposition,[status(thm)],[c_14845,c_660]) ).
tcf(c_20935,plain,
( aElementOf0(xi,sdtlbdtrb0(xN,iPr_def_11))
| ~ aFunction0(xN)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_20931,c_209]) ).
tcf(c_20936,plain,
aElementOf0(xi,sdtlbdtrb0(xN,iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_20935,c_208,c_223]) ).
tcf(c_20937,plain,
( aElementOf0(xi,sdtlbdtrb0(xC,iPr_def_10))
| ~ aFunction0(xC)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_20930,c_219]) ).
tcf(c_20938,plain,
aElementOf0(xi,sdtlbdtrb0(xC,iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_20937,c_218,c_223]) ).
tcf(c_23074,plain,
( ( sdtlpdtrp0(xC,xi) = iPr_def_10 )
| ~ aFunction0(xC)
| ~ aElement0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20938,c_171]) ).
tcf(c_23075,plain,
( ( sdtlpdtrp0(xN,xi) = iPr_def_11 )
| ~ aFunction0(xN)
| ~ aElement0(iPr_def_11) ),
inference(superposition,[status(thm)],[c_20936,c_171]) ).
tcf(c_23076,plain,
sdtlpdtrp0(xN,xi) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_23075,c_208,c_18785]) ).
tcf(c_23077,plain,
sdtlpdtrp0(xC,xi) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_23074,c_218,c_18778]) ).
tcf(c_26841,plain,
slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) = szDzozmdt0(sdtlpdtrp0(xC,xi)),
inference(superposition,[status(thm)],[c_223,c_221]) ).
tcf(c_26844,plain,
szDzozmdt0(iPr_def_10) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_26841,c_14846,c_14847,c_14848,c_23076,c_23077]) ).
tcf(c_26888,plain,
aElementOf0(xx,sdtlcdtrc0(iPr_def_10,iPr_def_14)),
inference(demodulation,[status(thm)],[c_18002,c_26844]) ).
tcf(c_27254,plain,
( aSet0(iPr_def_14)
| ~ aFunction0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_26844,c_163]) ).
tcf(c_27255,plain,
aSet0(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_27254,c_17724]) ).
tcf(c_30616,plain,
( ( sdtlpdtrp0(iPr_def_10,sK19(iPr_def_10,iPr_def_14,xx)) = xx )
| ~ aFunction0(iPr_def_10)
| ~ aSubsetOf0(iPr_def_14,szDzozmdt0(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26888,c_179]) ).
tcf(c_30617,plain,
( ( sdtlpdtrp0(iPr_def_10,sK19(iPr_def_10,iPr_def_14,xx)) = xx )
| ~ aFunction0(iPr_def_10)
| ~ aSubsetOf0(iPr_def_14,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_30616,c_26844]) ).
tcf(c_30618,plain,
( ( sdtlpdtrp0(iPr_def_10,sK19(iPr_def_10,iPr_def_14,xx)) = xx )
| ~ aSubsetOf0(iPr_def_14,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30617,c_17724]) ).
tcf(c_48442,plain,
( ( sdtlpdtrp0(iPr_def_10,sK19(iPr_def_10,iPr_def_14,xx)) = xx )
| ~ aSet0(iPr_def_14) ),
inference(superposition,[status(thm)],[c_61,c_30618]) ).
tcf(c_48443,plain,
sdtlpdtrp0(iPr_def_10,sK19(iPr_def_10,iPr_def_14,xx)) = xx,
inference(forward_subsumption_resolution,[status(thm)],[c_48442,c_27255]) ).
tcf(c_48450,plain,
~ aElementOf0(sK19(iPr_def_10,iPr_def_14,xx),iPr_def_14),
inference(superposition,[status(thm)],[c_48443,c_14849]) ).
tcf(c_48481,plain,
( ~ aFunction0(iPr_def_10)
| ~ aSubsetOf0(iPr_def_14,szDzozmdt0(iPr_def_10))
| ~ aElementOf0(xx,sdtlcdtrc0(iPr_def_10,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_178,c_48450]) ).
tcf(c_48482,plain,
( ~ aFunction0(iPr_def_10)
| ~ aSubsetOf0(iPr_def_14,iPr_def_14)
| ~ aElementOf0(xx,sdtlcdtrc0(iPr_def_10,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_48481,c_26844]) ).
tcf(c_48483,plain,
~ aSubsetOf0(iPr_def_14,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_48482,c_17724,c_26888]) ).
tcf(c_48501,plain,
~ aSet0(iPr_def_14),
inference(superposition,[status(thm)],[c_61,c_48483]) ).
tcf(c_48502,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_48501,c_27255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM586+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.45 % Computer : n011.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Thu Sep 24 04:46:29 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.53
% 0.22/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.53
% 0.22/0.53 % Detected problem language: tptp
% 0.22/0.55 % Proving...
% 13.77/5.10 % SZS status Started for theBenchmark.p
% 13.77/5.10 % SZS status Theorem for theBenchmark.p
% 13.77/5.10
% 13.77/5.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 13.77/5.10
% 13.77/5.10 % ------ iProver source info
% 13.77/5.10
% 13.77/5.10 % git: date: 2026-07-19 20:42:38 +0200
% 13.77/5.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 13.77/5.10 % git: non_committed_changes: false
% 13.77/5.10
% 13.77/5.10 % ------ Parsing...
% 13.77/5.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 13.77/5.10
% 13.77/5.10 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 13.77/5.10
% 13.77/5.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 13.77/5.10
% 13.77/5.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 13.77/5.10 % ------ Proving...
% 13.77/5.10 % ------ Problem Properties
% 13.77/5.10
% 13.77/5.10 %
% 13.77/5.10 % clauses 178
% 13.77/5.10 % conjectures 1
% 13.77/5.10 % EPR 40
% 13.77/5.10 % Horn 139
% 13.77/5.10 % unary 32
% 13.77/5.10 % binary 24
% 13.77/5.10 % lits 611
% 13.77/5.10 % lits eq 101
% 13.77/5.10 % fd_pure 0
% 13.77/5.10 % fd_pseudo 0
% 13.77/5.10 % fd_cond 10
% 13.77/5.10 % fd_pseudo_cond 25
% 13.77/5.10 % AC symbols 0
% 13.77/5.10
% 13.77/5.10 % ------ Schedule dynamic 5 is on
% 13.77/5.10
% 13.77/5.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 13.77/5.10
% 13.77/5.10
% 13.77/5.10 % ------
% 13.77/5.10 % Current options:
% 13.77/5.10 % ------
% 13.77/5.10
% 13.77/5.10
% 13.77/5.10 %
% 13.77/5.10
% 13.77/5.10 % ------ Proving...
% 13.77/5.10 %
% 13.77/5.10
% 13.77/5.10 % SZS status Theorem for theBenchmark.p
% 13.77/5.10
% 13.77/5.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 30.14/5.10
% 30.14/5.10
%------------------------------------------------------------------------------