%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 02:20:17 PM UTC 2026
% Result : Theorem 0.34s 21.00s
% Output : Proof 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 4
% Syntax : Number of formulae : 83 ( 14 unt; 0 def)
% Number of atoms : 360 ( 93 equ)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 400 ( 123 ~; 185 |; 70 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f2_nnf,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [W0,W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f16,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
fof(f16_nnf,plain,
aSet0(xS),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c46,plain,
aSet0(xS),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(p298,plain,
( aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[c2,c46]) ).
fof(f18,conjecture,
( ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f18_neg,negated_conjecture,
~ ( ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [W0] :
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ~ aElementOf0(sk5,xS)
& aElementOf0(sk5,sdtpldt0(sdtmndt0(xS,xx),xx))
& ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sk4,xS)
& ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f18_nnf]) ).
cnf(c185,plain,
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(sk4,xS) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(c188,plain,
( aElementOf0(sk5,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(sk4,xS) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p246,plain,
( aElementOf0(sk4,xS)
| sk5 = xx
| aElementOf0(sk5,sdtmndt0(xS,xx))
| aElementOf0(sk4,xS) ),
inference(resolution,[status(thm)],[c185,c188]) ).
cnf(p247,plain,
( sk5 = xx
| aElementOf0(sk5,sdtmndt0(xS,xx))
| aElementOf0(sk4,xS) ),
inference(factoring,[status(thm)],[p246]) ).
cnf(c76,plain,
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p237,plain,
( aElementOf0(X0,xS)
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(factoring,[status(thm)],[c76]) ).
cnf(p239,plain,
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(factoring,[status(thm)],[p237]) ).
cnf(p248,plain,
( aElementOf0(sk5,xS)
| sk5 = xx
| aElementOf0(sk4,xS) ),
inference(resolution,[status(thm)],[p247,p239]) ).
cnf(c189,plain,
( ~ aElementOf0(sk5,xS)
| aElementOf0(sk4,xS) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p249,plain,
( aElementOf0(sk4,xS)
| sk5 = xx
| aElementOf0(sk4,xS) ),
inference(resolution,[status(thm)],[p248,c189]) ).
cnf(p250,plain,
( sk5 = xx
| aElementOf0(sk4,xS) ),
inference(factoring,[status(thm)],[p249]) ).
cnf(p300,plain,
( sk5 = xx
| aElement0(sk4) ),
inference(resolution,[status(thm)],[p298,p250]) ).
cnf(p304,plain,
( ~ aElementOf0(xx,xS)
| aElementOf0(sk4,xS)
| aElement0(sk4) ),
inference(superposition,[status(thm)],[p300,c189]) ).
fof(f17,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(f17_nnf,plain,
aElementOf0(xx,xS),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c47,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p306,plain,
( aElementOf0(sk4,xS)
| aElement0(sk4) ),
inference(resolution,[status(thm)],[p304,c47]) ).
cnf(p307,plain,
( aElement0(sk4)
| aElement0(sk4) ),
inference(resolution,[status(thm)],[p306,p298]) ).
cnf(p308,plain,
aElement0(sk4),
inference(factoring,[status(thm)],[p307]) ).
cnf(c104,plain,
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx))
| X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p265,plain,
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(factoring,[status(thm)],[c104]) ).
cnf(p270,plain,
( X0 = xx
| ~ aElement0(X0)
| X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(factoring,[status(thm)],[p265]) ).
cnf(p273,plain,
( ~ aElement0(X0)
| X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(factoring,[status(thm)],[p270]) ).
cnf(p274,plain,
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(factoring,[status(thm)],[p273]) ).
cnf(p310,plain,
( sk4 = xx
| ~ aElementOf0(sk4,xS)
| aElementOf0(sk4,sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[p308,p274]) ).
cnf(p313,plain,
( sk5 = xx
| sk4 = xx
| aElementOf0(sk4,sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[p310,p250]) ).
cnf(c160,plain,
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p275,plain,
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[c160]) ).
cnf(p279,plain,
( ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[p275]) ).
cnf(p280,plain,
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[p279]) ).
cnf(p311,plain,
( ~ aElementOf0(sk4,sdtmndt0(xS,xx))
| aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[p308,p280]) ).
cnf(p315,plain,
( aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx))
| sk5 = xx
| sk4 = xx ),
inference(resolution,[status(thm)],[p313,p311]) ).
cnf(c201,plain,
( aElementOf0(sk5,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p334,plain,
( aElementOf0(sk5,sdtpldt0(sdtmndt0(xS,xx),xx))
| sk5 = xx
| sk4 = xx ),
inference(resolution,[status(thm)],[p315,c201]) ).
cnf(c146,plain,
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p281,plain,
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[c146]) ).
cnf(p284,plain,
( X0 = xx
| X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[p281]) ).
cnf(p286,plain,
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[p284]) ).
cnf(p336,plain,
( sk5 = xx
| aElementOf0(sk5,sdtmndt0(xS,xx))
| sk5 = xx
| sk4 = xx ),
inference(resolution,[status(thm)],[p334,p286]) ).
cnf(p337,plain,
( aElementOf0(sk5,sdtmndt0(xS,xx))
| sk5 = xx
| sk4 = xx ),
inference(factoring,[status(thm)],[p336]) ).
cnf(p338,plain,
( aElementOf0(sk5,xS)
| sk5 = xx
| sk4 = xx ),
inference(resolution,[status(thm)],[p337,p239]) ).
cnf(c202,plain,
( ~ aElementOf0(sk5,xS)
| ~ aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p333,plain,
( ~ aElementOf0(sk5,xS)
| sk5 = xx
| sk4 = xx ),
inference(resolution,[status(thm)],[p315,c202]) ).
cnf(p339,plain,
( sk5 = xx
| sk4 = xx
| sk5 = xx
| sk4 = xx ),
inference(resolution,[status(thm)],[p338,p333]) ).
cnf(p340,plain,
( sk5 = xx
| sk5 = xx
| sk4 = xx ),
inference(factoring,[status(thm)],[p339]) ).
cnf(p342,plain,
( sk5 = xx
| sk4 = xx ),
inference(factoring,[status(thm)],[p340]) ).
cnf(p343,plain,
( ~ aElementOf0(xx,xS)
| aElementOf0(sk4,xS)
| sk4 = xx ),
inference(superposition,[status(thm)],[p342,c189]) ).
cnf(p346,plain,
( aElementOf0(sk4,xS)
| sk4 = xx ),
inference(resolution,[status(thm)],[p343,c47]) ).
cnf(p347,plain,
( sk4 = xx
| aElementOf0(sk4,sdtmndt0(xS,xx))
| sk4 = xx ),
inference(resolution,[status(thm)],[p346,p310]) ).
cnf(p349,plain,
( aElementOf0(sk4,sdtmndt0(xS,xx))
| sk4 = xx ),
inference(factoring,[status(thm)],[p347]) ).
cnf(p350,plain,
( aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx))
| sk4 = xx ),
inference(resolution,[status(thm)],[p349,p311]) ).
cnf(p351,plain,
( ~ aElementOf0(sk5,xS)
| sk4 = xx ),
inference(resolution,[status(thm)],[p350,c202]) ).
cnf(p353,plain,
( ~ aElementOf0(xx,xS)
| sk4 = xx
| sk4 = xx ),
inference(superposition,[status(thm)],[p342,p351]) ).
cnf(p354,plain,
( ~ aElementOf0(xx,xS)
| sk4 = xx ),
inference(factoring,[status(thm)],[p353]) ).
cnf(p355,plain,
sk4 = xx,
inference(resolution,[status(thm)],[p354,c47]) ).
cnf(p356,plain,
( aElementOf0(sk5,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(demodulation,[status(thm)],[p355,c201]) ).
cnf(c174,plain,
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p258,plain,
( X0 != xx
| ~ aElement0(X0)
| X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[c174]) ).
cnf(p262,plain,
( ~ aElement0(X0)
| X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[p258]) ).
cnf(p263,plain,
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(factoring,[status(thm)],[p262]) ).
cnf(p309,plain,
( sk4 != xx
| aElementOf0(sk4,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[p308,p263]) ).
cnf(p359,plain,
( xx != xx
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(demodulation,[status(thm)],[p355,p309]) ).
cnf(p360,plain,
aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(equality_resolution,[status(thm)],[p359]) ).
cnf(p362,plain,
aElementOf0(sk5,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(resolution,[status(thm)],[p356,p360]) ).
cnf(p363,plain,
( sk5 = xx
| aElementOf0(sk5,sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[p362,p286]) ).
cnf(p364,plain,
( aElementOf0(sk5,xS)
| sk5 = xx ),
inference(resolution,[status(thm)],[p363,p239]) ).
cnf(p357,plain,
( ~ aElementOf0(sk5,xS)
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(demodulation,[status(thm)],[p355,c202]) ).
cnf(p361,plain,
~ aElementOf0(sk5,xS),
inference(resolution,[status(thm)],[p360,p357]) ).
cnf(p365,plain,
sk5 = xx,
inference(resolution,[status(thm)],[p364,p361]) ).
cnf(p366,plain,
~ aElementOf0(xx,xS),
inference(demodulation,[status(thm)],[p365,p361]) ).
cnf(p367,plain,
$false,
inference(resolution,[status(thm)],[p366,c47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/20.44 % CPULimit : 300
% 0.09/20.44 % WCLimit : 300
% 0.09/20.44 % DateTime : Thu Sep 24 04:32:43 UTC 2026
% 0.09/20.45 % CPUTime :
% 0.09/20.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.34/21.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/21.00 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------