%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:26:00 PM UTC 2026
% Result : Theorem 3.19s 1.67s
% Output : CNFRefutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 18 unt; 0 def)
% Number of atoms : 382 ( 62 equ)
% Maximal formula atoms : 43 ( 8 avg)
% Number of connectives : 465 ( 127 ~; 109 |; 194 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 74 !; 14 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( ~ ( ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xT)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xT)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(f70,axiom,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f71,axiom,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f73,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f80,plain,
( ~ ( ! [X7] :
( ( ( xk = sbrdtbr0(X7)
& ( aSubsetOf0(X7,xS)
| ( ! [X9] :
( aElementOf0(X9,X7)
=> aElementOf0(X9,xS) )
& aSet0(X7) ) ) )
=> aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
=> ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,xS)
& ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,xS) )
& aSet0(X7) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xS,xk))
=> aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( ( sbrdtbr0(X3) = xk
& ( aSubsetOf0(X3,xT)
| ( ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,xT) )
& aSet0(X3) ) ) )
=> aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(rectify,[],[f63]) ).
fof(f81,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(rectify,[],[f70]) ).
fof(f82,plain,
~ aElementOf0(xx,xT),
inference(flattening,[],[f73]) ).
fof(f84,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f165,plain,
( ! [X7] :
( ( xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,xS)
& ( ? [X9] :
( aElementOf0(X9,X7)
& ~ aElementOf0(X9,xS) )
| ~ aSet0(X7) ) )
| aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,xS)
& ! [X8] :
( ~ aElementOf0(X8,X7)
| aElementOf0(X8,xS) )
& aSet0(X7) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f80]) ).
fof(f166,plain,
( ! [X7] :
( ( xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,xS)
& ( ? [X9] :
( aElementOf0(X9,X7)
& ~ aElementOf0(X9,xS) )
| ~ aSet0(X7) ) )
| aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,xS)
& ! [X8] :
( ~ aElementOf0(X8,X7)
| aElementOf0(X8,xS) )
& aSet0(X7) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(flattening,[],[f165]) ).
fof(f168,plain,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xS) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f220,plain,
( ! [X8] :
( ( xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ? [X10] :
( aElementOf0(X10,X8)
& ~ aElementOf0(X10,xS) )
| ~ aSet0(X8) ) )
| aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X9] :
( ~ aElementOf0(X9,X8)
| aElementOf0(X9,xS) )
& aSet0(X8) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& ? [X7] : aElementOf0(X7,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(rectify,[],[f166]) ).
fof(f221,plain,
( ! [X8] :
( ( xk != sbrdtbr0(X8)
| ( ~ aSubsetOf0(X8,xS)
& ( ( aElementOf0(sK18(X8),X8)
& ~ aElementOf0(sK18(X8),xS) )
| ~ aSet0(X8) ) )
| aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( xk = sbrdtbr0(X8)
& aSubsetOf0(X8,xS)
& ! [X9] :
( ~ aElementOf0(X9,X8)
| aElementOf0(X9,xS) )
& aSet0(X8) ) ) )
& slcrc0 != slbdtsldtrb0(xS,xk)
& aElementOf0(sK17,slbdtsldtrb0(xS,xk))
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& ! [X3] :
( ( sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ( aElementOf0(sK16(X3),X3)
& ~ aElementOf0(sK16(X3),xT) )
| ~ aSet0(X3) ) )
| aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) )
& aSet0(X3) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ( aElementOf0(sK15(X0),X0)
& ~ aElementOf0(sK15(X0),xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18]),skolemize(X2,sK15(X0)),skolemize(X5,sK16(X3)),skolemize(X7,sK17),skolemize(X10,sK18(X8))],[f220]) ).
fof(f222,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xQ,xy)) )
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& aSet0(xP)
& ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ( xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(nnf_transformation,[],[f81]) ).
fof(f223,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xQ,xy)) )
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& aSet0(xP)
& ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ( xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(flattening,[],[f222]) ).
fof(f224,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f336,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f347,plain,
! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f353,plain,
! [X3,X4] :
( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) ),
inference(cnf_transformation,[],[f221]) ).
fof(f364,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f380,plain,
! [X1] :
( xx != X1
| ~ aElement0(X1)
| aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f223]) ).
fof(f388,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f168]) ).
fof(f392,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f82]) ).
fof(f416,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(equality_resolution,[],[f380]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_159,plain,
aSet0(xS),
inference(cnf_transformation,[],[f336]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_178,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_189,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f364]) ).
tcf(c_209,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_216,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f388]) ).
tcf(c_217,negated_conjecture,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f392]) ).
tcf(c_11282,negated_conjecture,
~ aElementOf0(xx,xT),
inference(demodulation,[status(thm)],[c_217]) ).
tcf(c_13512,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_189,c_49]) ).
tcf(c_13518,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_13512,c_159]) ).
tcf(c_13529,plain,
aElementOf0(xx,xP),
inference(backward_subsumption_resolution,[status(thm)],[c_209,c_13518]) ).
tcf(c_14038,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(superposition,[status(thm)],[c_216,c_178]) ).
tcf(c_14860,plain,
! [X0: $i] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,xP) ),
inference(superposition,[status(thm)],[c_14038,c_172]) ).
tcf(c_14975,plain,
aElementOf0(xx,xT),
inference(superposition,[status(thm)],[c_13529,c_14860]) ).
tcf(c_14977,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14975,c_11282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 04:39:33 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 Running first-order theorem proving
% 0.11/0.38 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39
% 0.11/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.39
% 0.11/0.39 % Detected problem language: tptp
% 0.11/0.40 % Proving...
% 3.19/1.67 % SZS status Started for theBenchmark.p
% 3.19/1.67 % SZS status Theorem for theBenchmark.p
% 3.19/1.67
% 3.19/1.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.19/1.67
% 3.19/1.67 % ------ iProver source info
% 3.19/1.67
% 3.19/1.67 % git: date: 2026-07-19 20:42:38 +0200
% 3.19/1.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.19/1.67 % git: non_committed_changes: false
% 3.19/1.67
% 3.19/1.67 % ------ Parsing...
% 3.19/1.67 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.19/1.67
% 3.19/1.67 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.19/1.67
% 3.19/1.67 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.19/1.67
% 3.19/1.67 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.19/1.67 % ------ Proving...
% 3.19/1.67 % ------ Problem Properties
% 3.19/1.67
% 3.19/1.67 %
% 3.19/1.67 % clauses 159
% 3.19/1.67 % conjectures 1
% 3.19/1.67 % EPR 47
% 3.19/1.67 % Horn 124
% 3.19/1.67 % unary 35
% 3.19/1.67 % binary 30
% 3.19/1.67 % lits 474
% 3.19/1.67 % lits eq 72
% 3.19/1.67 % fd_pure 0
% 3.19/1.67 % fd_pseudo 0
% 3.19/1.67 % fd_cond 11
% 3.19/1.67 % fd_pseudo_cond 18
% 3.19/1.67 % AC symbols 0
% 3.19/1.67
% 3.19/1.67 % ------ Schedule dynamic 5 is on
% 3.19/1.67
% 3.19/1.67 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.19/1.67
% 3.19/1.67
% 3.19/1.67 % ------
% 3.19/1.67 % Current options:
% 3.19/1.67 % ------
% 3.19/1.67
% 3.19/1.67
% 3.19/1.67 %
% 3.19/1.67
% 3.19/1.67 % ------ Proving...
% 3.19/1.67 %
% 3.19/1.67
% 3.19/1.67 % SZS status Theorem for theBenchmark.p
% 3.19/1.67
% 3.19/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.19/1.67
% 3.19/1.67
%------------------------------------------------------------------------------