%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 08:17:23 AM UTC 2026
% Result : Theorem 65.88s 14.98s
% Output : CNFRefutation 65.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 102 ( 33 unt; 0 def)
% Number of atoms : 424 ( 96 equ)
% Maximal formula atoms : 67 ( 4 avg)
% Number of connectives : 491 ( 169 ~; 158 |; 134 &)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDiffCons,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aElement0(W0) )
=> ( ~ aElementOf0(W0,W1)
=> sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ),
file('theBenchmark.p',mDiffCons) ).
fof(mFConsSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtpldt0(W1,W0)) ) ),
file('theBenchmark.p',mFConsSet) ).
fof(mFDiffSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('theBenchmark.p',mFDiffSet) ).
fof(mCardDiff,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( aElementOf0(W1,W0)
& isFinite0(W0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ),
file('theBenchmark.p',mCardDiff) ).
fof(m__2202_02,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
fof(m__2227,axiom,
( ~ ( ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xT)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('theBenchmark.p',m__2227) ).
fof(m__2270,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('theBenchmark.p',m__2270) ).
fof(m__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__2304,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('theBenchmark.p',m__2304) ).
fof(m__2357,axiom,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) ) )
& aSet0(xP)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('theBenchmark.p',m__2357) ).
fof(m__2411,axiom,
( ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
file('theBenchmark.p',m__2411) ).
fof(m__,conjecture,
( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_65,plain,
( sbrdtbr0(xP) != xk
| ( ~ aSubsetOf0(xP,xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,xP) ) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
( sbrdtbr0(xP) != xk
| ( ~ aSubsetOf0(xP,xS)
& ~ aElementOf0(sK0,xS)
& aElementOf0(sK0,xP) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_65]) ).
fof(sk_m___neg,plain,
( ( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) )
& ( sbrdtbr0(xP) != xk
| ~ aElementOf0(sK0,xS) )
& ( sbrdtbr0(xP) != xk
| aElementOf0(sK0,xP) ) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_67,negated_conjecture,
( sbrdtbr0(xP) != xk
| ~ aElementOf0(sK0,xS) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_68,negated_conjecture,
( sbrdtbr0(xP) != xk
| aElementOf0(sK0,xP) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_71,plain,
( aElementOf0(A,xQ)
| ~ aElementOf0(A,sdtmndt0(xQ,xy)) ),
inference(clausify,[status(thm)],[m__2411]) ).
cnf(c_73,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(clausify,[status(thm)],[m__2411]) ).
cnf(c_74,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(clausify,[status(thm)],[m__2411]) ).
cnf(c_75,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(clausify,[status(thm)],[m__2357]) ).
cnf(c_76,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_77,plain,
( xx != A
| ~ aElement0(A)
| aElementOf0(A,xP) ),
inference(clausify,[status(thm)],[m__2357]) ).
cnf(c_78,plain,
( xx != A
| ~ aElement0(A)
| aElementOf0(A,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_76,c_77]) ).
cnf(c_81,plain,
( xx = A
| aElementOf0(A,sdtmndt0(xQ,xy))
| ~ aElementOf0(A,xP) ),
inference(clausify,[status(thm)],[m__2357]) ).
cnf(c_82,plain,
( xx = A
| aElementOf0(A,sdtmndt0(xQ,xy))
| ~ aElementOf0(A,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_76,c_81]) ).
cnf(c_85,plain,
aSet0(xP),
inference(clausify,[status(thm)],[m__2357]) ).
cnf(c_86,plain,
aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(paramod,[status(thm)],[c_76,c_85]) ).
cnf(c_88,plain,
aElementOf0(xy,xQ),
inference(clausify,[status(thm)],[m__2304]) ).
cnf(c_89,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__2304]) ).
cnf(c_90,plain,
sbrdtbr0(xQ) = xk,
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_91,plain,
xk = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_92,plain,
isFinite0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_93,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_94,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[m__2270]) ).
cnf(c_95,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(paramod,[status(thm)],[c_91,c_94]) ).
fof(m__2256,axiom,
aElementOf0(xx,xS),
file('theBenchmark.p',m__2256) ).
cnf(c_99,plain,
aElementOf0(xx,xS),
inference(clausify,[status(thm)],[m__2256]) ).
fof(nnf_59,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,X0) )
| ~ aSet0(X0) ) ) )
& ( ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X0) )
& aSet0(X0) )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X7] :
( aElementOf0(X7,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ! [X4] :
( ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X4) != xk
| ( ~ aSubsetOf0(X4,xT)
& ( ? [X6] :
( ~ aElementOf0(X6,xT)
& aElementOf0(X6,X4) )
| ~ aSet0(X4) ) ) )
& ( ( sbrdtbr0(X4) = xk
& aSubsetOf0(X4,xT)
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,X4) )
& aSet0(X4) )
| ~ aElementOf0(X4,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,xS)
& ( ? [X3] :
( ~ aElementOf0(X3,xS)
& aElementOf0(X3,X1) )
| ~ aSet0(X1) ) ) )
& ( ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,xS)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(fof_nnf,[status(thm)],[m__2227]) ).
fof(sk_m__2227_sk,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sK1,slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ( ~ aElementOf0(sK4(X0),xS)
& aElementOf0(sK4(X0),X0) )
| ~ aSet0(X0) ) ) )
& ( ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X0) )
& aSet0(X0) )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X7] :
( aElementOf0(X7,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ! [X4] :
( ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X4) != xk
| ( ~ aSubsetOf0(X4,xT)
& ( ( ~ aElementOf0(sK3(X4),xT)
& aElementOf0(sK3(X4),X4) )
| ~ aSet0(X4) ) ) )
& ( ( sbrdtbr0(X4) = xk
& aSubsetOf0(X4,xT)
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,X4) )
& aSet0(X4) )
| ~ aElementOf0(X4,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,xS)
& ( ( ~ aElementOf0(sK2(X1),xS)
& aElementOf0(sK2(X1),X1) )
| ~ aSet0(X1) ) ) )
& ( ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,xS)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK1]),skolemize(X3,sK2(X1)),skolemize(X6,sK3(X4)),skolemize(W1,sK4(X0)),skolemize(W0,sK1)],[nnf_59]) ).
fof(sk_m__2227,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sK1,slbdtsldtrb0(xS,xk))
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aSubsetOf0(VAR_0,xS) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aElementOf0(sK4(VAR_0),xS)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK4(VAR_0),VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( sbrdtbr0(VAR_0) = xk
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSubsetOf0(VAR_0,xS)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,xS)
| ~ aElementOf0(VAR_1,VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSet0(VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aSubsetOf0(VAR_0,xT) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aElementOf0(sK3(VAR_0),xT)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK3(VAR_0),VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( sbrdtbr0(VAR_0) = xk
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& ! [VAR_0] :
( aSubsetOf0(VAR_0,xT)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,xT)
| ~ aElementOf0(VAR_1,VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& ! [VAR_0] :
( aSet0(VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aSubsetOf0(VAR_0,xS) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aElementOf0(sK2(VAR_0),xS)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK2(VAR_0),VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( sbrdtbr0(VAR_0) = xk
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSubsetOf0(VAR_0,xS)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,xS)
| ~ aElementOf0(VAR_1,VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSet0(VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[status(thm)],[sk_m__2227_sk]) ).
cnf(c_102,plain,
aElementOf0(sK1,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_103,plain,
aElementOf0(sK1,slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(paramod,[status(thm)],[c_91,c_102]) ).
cnf(c_110,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_45509,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_91,c_110]) ).
cnf(c_45510,plain,
( sbrdtbr0(A) = sbrdtbr0(xQ)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_91,c_45509]) ).
cnf(c_111,plain,
( sbrdtbr0(xQ) = sbrdtbr0(A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(copy,[status(thm)],[c_45510]) ).
cnf(c_114,plain,
( aElementOf0(B,xS)
| ~ aElementOf0(B,A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_115,plain,
( aElementOf0(B,xS)
| ~ aElementOf0(B,A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_91,c_114]) ).
cnf(c_152,plain,
aSet0(xS),
inference(clausify,[status(thm)],[m__2202_02]) ).
cnf(c_204,plain,
( sbrdtbr0(A) = szszuzczcdt0(sbrdtbr0(sdtmndt0(A,B)))
| ~ aElementOf0(B,A)
| ~ isFinite0(A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardDiff]) ).
cnf(c_205,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(A,B))) = sbrdtbr0(A)
| ~ aElementOf0(B,A)
| ~ isFinite0(A)
| ~ aSet0(A) ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_232,plain,
( isFinite0(sdtmndt0(B,A))
| ~ isFinite0(B)
| ~ aSet0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mFDiffSet]) ).
cnf(c_233,plain,
( isFinite0(sdtpldt0(B,A))
| ~ isFinite0(B)
| ~ aSet0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mFConsSet]) ).
cnf(c_236,plain,
( sdtmndt0(sdtpldt0(B,A),A) = B
| aElementOf0(A,B)
| ~ aSet0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDiffCons]) ).
cnf(c_275,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_45511,negated_conjecture,
( sbrdtbr0(xP) != xk
| aElementOf0(sK0,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_76,c_68]) ).
cnf(c_45512,negated_conjecture,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk
| aElementOf0(sK0,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_76,c_45511]) ).
cnf(c_276,negated_conjecture,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != sbrdtbr0(xQ)
| aElementOf0(sK0,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_91,c_45512]) ).
cnf(c_45513,negated_conjecture,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk
| ~ aElementOf0(sK0,xS) ),
inference(paramod,[status(thm)],[c_76,c_67]) ).
cnf(c_277,negated_conjecture,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != sbrdtbr0(xQ)
| ~ aElementOf0(sK0,xS) ),
inference(paramod,[status(thm)],[c_91,c_45513]) ).
cnf(c_309,plain,
sbrdtbr0(xQ) = sbrdtbr0(sK1),
inference(resolve,[status(thm)],[c_111,c_103]) ).
cnf(c_316,negated_conjecture,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != sbrdtbr0(sK1)
| ~ aElementOf0(sK0,xS) ),
inference(paramod,[status(thm)],[c_309,c_277]) ).
cnf(c_317,negated_conjecture,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != sbrdtbr0(sK1)
| aElementOf0(sK0,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_309,c_276]) ).
cnf(c_334,plain,
( aElementOf0(B,xS)
| ~ aElementOf0(B,A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(sK1))) ),
inference(paramod,[status(thm)],[c_309,c_115]) ).
cnf(c_341,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,sbrdtbr0(sK1))),
inference(paramod,[status(thm)],[c_309,c_95]) ).
cnf(c_45514,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xQ)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_205,c_88]) ).
cnf(c_45515,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(sK1)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(paramod,[status(thm)],[c_309,c_45514]) ).
cnf(c_45516,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(sK1)
| ~ isFinite0(xQ) ),
inference(resolve,[status(thm)],[c_93,c_45515]) ).
cnf(c_354,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(sK1),
inference(resolve,[status(thm)],[c_92,c_45516]) ).
cnf(c_45517,plain,
( isFinite0(sdtmndt0(xQ,A))
| ~ aSet0(xQ)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_232,c_92]) ).
cnf(c_399,plain,
( isFinite0(sdtmndt0(xQ,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_93,c_45517]) ).
cnf(c_45518,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_275,c_99]) ).
cnf(c_483,plain,
aElement0(xx),
inference(resolve,[status(thm)],[c_152,c_45518]) ).
cnf(c_523,plain,
( sdtmndt0(sdtpldt0(A,xx),xx) = A
| aElementOf0(xx,A)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_483,c_236]) ).
cnf(c_45519,plain,
( xx != xx
| aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(resolve,[status(thm)],[c_483,c_78]) ).
cnf(c_524,plain,
aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(copy,[status(thm)],[c_45519]) ).
cnf(c_1585,plain,
isFinite0(sdtmndt0(xQ,xy)),
inference(resolve,[status(thm)],[c_399,c_89]) ).
cnf(c_45520,plain,
( isFinite0(sdtpldt0(sdtmndt0(xQ,xy),A))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_1585,c_233]) ).
cnf(c_1646,plain,
( isFinite0(sdtpldt0(sdtmndt0(xQ,xy),A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_73,c_45520]) ).
cnf(c_45521,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ isFinite0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(resolve,[status(thm)],[c_524,c_205]) ).
cnf(c_4774,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ isFinite0(sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(resolve,[status(thm)],[c_86,c_45521]) ).
cnf(c_45522,plain,
( sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx) = sdtmndt0(xQ,xy)
| aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(resolve,[status(thm)],[c_523,c_73]) ).
cnf(c_9954,plain,
sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx) = sdtmndt0(xQ,xy),
inference(resolve,[status(thm)],[c_74,c_45522]) ).
cnf(c_45523,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ isFinite0(sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_9954,c_4774]) ).
cnf(c_45524,plain,
( sbrdtbr0(sK1) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ isFinite0(sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_354,c_45523]) ).
cnf(c_9955,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = sbrdtbr0(sK1)
| ~ isFinite0(sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(copy,[status(thm)],[c_45524]) ).
cnf(c_17512,plain,
isFinite0(sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(resolve,[status(thm)],[c_1646,c_483]) ).
cnf(c_17520,plain,
sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = sbrdtbr0(sK1),
inference(resolve,[status(thm)],[c_17512,c_9955]) ).
cnf(c_45525,negated_conjecture,
( sbrdtbr0(sK1) != sbrdtbr0(sK1)
| aElementOf0(sK0,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(paramod,[status(thm)],[c_17520,c_317]) ).
cnf(c_17521,negated_conjecture,
aElementOf0(sK0,sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(copy,[status(thm)],[c_45525]) ).
cnf(c_45526,negated_conjecture,
( sbrdtbr0(sK1) != sbrdtbr0(sK1)
| ~ aElementOf0(sK0,xS) ),
inference(paramod,[status(thm)],[c_17520,c_316]) ).
cnf(c_17522,negated_conjecture,
~ aElementOf0(sK0,xS),
inference(copy,[status(thm)],[c_45526]) ).
cnf(c_17705,plain,
( xx = sK0
| aElementOf0(sK0,sdtmndt0(xQ,xy)) ),
inference(resolve,[status(thm)],[c_17521,c_82]) ).
cnf(c_42299,plain,
( aElementOf0(sK0,xQ)
| xx = sK0 ),
inference(resolve,[status(thm)],[c_17705,c_71]) ).
cnf(c_45527,plain,
( aElementOf0(sK0,xS)
| ~ aElementOf0(xQ,slbdtsldtrb0(xS,sbrdtbr0(sK1)))
| xx = sK0 ),
inference(resolve,[status(thm)],[c_42299,c_334]) ).
cnf(c_45528,plain,
( aElementOf0(sK0,xS)
| xx = sK0 ),
inference(resolve,[status(thm)],[c_341,c_45527]) ).
cnf(c_42302,negated_conjecture,
xx = sK0,
inference(resolve,[status(thm)],[c_17522,c_45528]) ).
cnf(c_45529,plain,
aElementOf0(sK0,xS),
inference(paramod,[status(thm)],[c_42302,c_99]) ).
cnf(c_45508,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17522,c_45529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Sat Sep 26 03:13:00 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/5.32 % Process 3755496 was started by sandbox on n012,
% 0.04/5.32 % Sat Sep 26 03:13:00 2026
% 0.04/5.32 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/5.33
% 0.04/5.33 % From the command line: assign(max_seconds, 300).
% 65.88/14.98
% 65.88/14.98 % given #500 (T,wt=6): 755 sdtlseqdt0(f1(szNzAzT0),szszuzczcdt0(f1(szNzAzT0))). [resolve(469,a,218,a)].
% 65.88/14.98
% 65.88/14.98 % given #1000 (F,wt=6): 5771 slbdtrb0(sbrdtbr0(c1)) != slbdtrb0(sz00). [resolve(5707,a,208,a),rewrite([660(4)]),flip(b),unit_del(a,319)].
% 65.88/14.98
% 65.88/14.98 % given #1500 (T,wt=5): 10810 aElement0(sbrdtbr0(sdtpldt0(xQ,xy))). [resolve(10716,a,213,a)].
% 65.88/14.98
% 65.88/14.98 % given #2000 (F,wt=7): 13991 sdtmndt0(sdtmndt0(xS,xx),xx) != xS. [resolve(13924,a,1394,a)].
% 65.88/14.98
% 65.88/14.98 % given #2500 (T,wt=7): 13918 isCountable0(sdtpldt0(szNzAzT0,sbrdtbr0(sdtmndt0(szNzAzT0,xx)))). [resolve(13899,a,402,a)].
% 65.88/14.98
% 65.88/14.98 % given #3000 (F,wt=8): 17663 sdtmndt0(sdtpldt0(xQ,sz00),f1(szNzAzT0)) != szNzAzT0. [resolve(17633,a,11761,a)].
% 65.88/14.98
% 65.88/14.98 % given #3500 (T,wt=6): 19655 isFinite0(sdtmndt0(slbdtrb0(sbrdtbr0(c1)),xy)). [resolve(5715,a,89,a)].
% 65.88/14.98
% 65.88/14.98 % given #4000 (F,wt=9): 21268 sdtmndt0(slbdtrb0(f9(sz00,szNzAzT0)),f1(xQ)) != xS. [resolve(21252,a,16916,a)].
% 65.88/14.98
% 65.88/14.98 % given #4500 (A,wt=18): 984 -aSet0(A) | slbdtsldtrb0(A,f9(sz00,szNzAzT0)) != B | -aElementOf0(C,B) | f9(sz00,szNzAzT0) = sbrdtbr0(C). [resolve(464,a,162,b),flip(d)].
% 65.88/14.98
% 65.88/14.98 % given #5000 (T,wt=6): 25719 isFinite0(sdtmndt0(sdtpldt0(xQ,xy),xy)). [resolve(10719,a,89,a)].
% 65.88/14.98
% 65.88/14.98 % given #5500 (F,wt=8): 27567 szszuzczcdt0(sbrdtbr0(sdtpldt0(c1,sbrdtbr0(xT)))) != sz00. [resolve(27503,a,227,a)].
% 65.88/14.98
% 65.88/14.98 % given #6000 (T,wt=7): 29616 isFinite0(sdtmndt0(sdtpldt0(c1,xx),szszuzczcdt0(sz00))). [resolve(13062,a,678,a)].
% 65.88/14.98
% 65.88/14.98 % given #6500 (F,wt=10): 24700 slbdtsldtrb0(sdtpldt0(szNzAzT0,xx),szszuzczcdt0(sbrdtbr0(c1))) != slbdtrb0(sz00). [resolve(1027,a,13191,a),unit_del(a,13195)].
% 65.88/14.98
% 65.88/14.98 % given #7000 (T,wt=8): 15404 isFinite0(slbdtsldtrb0(f6(c1,szszuzczcdt0(sz00)),sbrdtbr0(c1))). [resolve(668,b,2997,a),unit_del(a,2995)].
% 65.88/14.98
% 65.88/14.98 % given #7500 (F,wt=7): 37845 sdtmndt0(sdtmndt0(xT,xx),xy) != xT. [resolve(37422,a,14054,a)].
% 65.88/14.98
% 65.88/14.98 % given #8000 (T,wt=8): 16854 sdtmndt0(szNzAzT0,szszuzczcdt0(sz00)) != A | aSet0(A). [resolve(724,a,231,a)].
% 65.88/14.98
% 65.88/14.98 % SZS status Theorem for theBenchmark
% 65.88/14.98
% 65.88/14.98 % Proof 1 at 7.71 (+ 1.85) seconds.
% 65.88/14.98 % Length of proof is 73.
% 65.88/14.98 % Level of proof is 12.
% 65.88/14.98 % Maximum clause weight is 22.000.
% 65.88/14.98 % Given clauses 8159.
% 65.88/14.98
% 65.88/14.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------