%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM631+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 01:41:16 PM UTC 2026
% Result : Theorem 23.85s 3.57s
% Output : CNFRefutation 23.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 25 unt; 0 def)
% Number of atoms : 222 ( 74 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 237 ( 72 ~; 67 |; 82 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 13 con; 0-2 aty)
% Number of variables : 46 ( 45 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )
& aSet0(W1) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
( xp = szmzizndt0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,hypothesis,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,hypothesis,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,hypothesis,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(W0,xP) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f117,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f183,plain,
! [W0] :
( ! [W1] :
( sdtpldt0(sdtmndt0(W0,W1),W1) = W0
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f184,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f550,plain,
( ! [W0] :
( ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( sdtlseqdt0(sdtlpdtrp0(xe,W0),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f555,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
fof(f556,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ? [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(W2,W1) ) ) ) )
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f557,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ aElementOf0(sK32_skl(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(sK32_skl(W1,W0),W1) ) ) )
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(W2,sK32_skl(W1,W0))],[f556]) ).
fof(f562,plain,
! [X0,X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f557]) ).
fof(f606,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f99]) ).
fof(f607,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f606]) ).
fof(f626,plain,
( xp = szmzizndt0(xQ)
& ! [W0] :
( sdtlseqdt0(xp,W0)
| ~ aElementOf0(W0,xQ) )
& aElementOf0(xp,xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f103]) ).
fof(f627,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[status(thm)],[f626]) ).
fof(f629,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[status(thm)],[f626]) ).
fof(f630,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(pre_NNF_transformation,[status(thm)],[f104]) ).
fof(f631,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( ( W0 = szmzizndt0(xQ)
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ( ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,xP) ) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(NNF_transformation,[status(thm)],[f630]) ).
fof(f632,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( W0 = szmzizndt0(xQ)
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ! [W0] :
( ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,xP) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(miniscoping,[status(thm)],[f631]) ).
fof(f633,plain,
aSet0(xP),
inference(cnf_transformation,[status(thm)],[f632]) ).
fof(f639,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[status(thm)],[f632]) ).
fof(f650,plain,
sbrdtbr0(xP) = xk,
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f653,plain,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f655,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f656,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f658,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f113]) ).
fof(f660,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[status(thm)],[f658]) ).
fof(f675,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(W0,xP) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f116]) ).
fof(f676,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [W0] :
( ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn))
& ~ aElementOf0(W0,xP) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(W0,xP) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn)) ) ),
inference(NNF_transformation,[status(thm)],[f675]) ).
fof(f677,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn))
& ~ aElementOf0(W0,xP) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& ! [W0] :
( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(W0,xP) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn)) ) ),
inference(miniscoping,[status(thm)],[f676]) ).
fof(f684,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[status(thm)],[f677]) ).
fof(f685,plain,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f1225,plain,
! [X0] :
( sdtpldt0(sdtmndt0(xQ,X0),X0) = xQ
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[status(thm)],[f184,f607]) ).
fof(f1246,plain,
sdtpldt0(sdtmndt0(xQ,xp),xp) = xQ,
inference(resolution,[status(thm)],[f1225,f627]) ).
fof(f1900,plain,
sdtpldt0(xP,xp) = xQ,
inference(backward_demodulation,[status(thm)],[f1901,f1246]) ).
fof(f1901,plain,
xP = sdtmndt0(xQ,xp),
inference(forward_demodulation,[status(thm)],[f629,f639]) ).
fof(f1925,plain,
sdtlpdtrp0(xc,xQ) != szDzizrdt0(xd),
inference(backward_demodulation,[status(thm)],[f653,f685]) ).
fof(f8652,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[status(thm)],[f555,f655]) ).
fof(f8661,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[status(thm)],[f656,f8652]) ).
fof(f9805,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,xp)) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(forward_demodulation,[status(thm)],[f8661,f684]) ).
fof(f9806,plain,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(forward_demodulation,[status(thm)],[f1900,f9805]) ).
fof(f9809,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,xQ)
| sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f9806,f562]) ).
fof(f9822,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,xQ)
| xk != xk
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f650,f9809]) ).
fof(f9823,plain,
( szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ)
| xk != xk
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f653,f9822]) ).
fof(f9824,plain,
( szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(trivial_equality_resolution,[status(thm)],[f9823]) ).
fof(f9825,plain,
( szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f9824,f655]) ).
fof(f10106,plain,
( szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(forward_subsumption_resolution,[status(thm)],[f9825,f633]) ).
fof(f10107,plain,
szDzizrdt0(xd) = sdtlpdtrp0(xc,xQ),
inference(resolution,[status(thm)],[f10106,f660]) ).
fof(f10111,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10107,f1925]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM631+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 02:45:27 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.41 % Drodi V4.1.1
% 23.85/3.57 % Refutation found
% 23.85/3.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.85/3.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.35/3.65 % Elapsed time: 3.266208 seconds
% 1.35/3.65 % CPU time: 24.947052 seconds
% 1.35/3.65 % Total memory used: 251.303 MB
% 1.35/3.65 % Net memory used: 241.058 MB
%------------------------------------------------------------------------------