%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM560+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:41:00 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 7 unt; 2 def)
% Number of atoms : 172 ( 24 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 228 ( 90 ~; 93 |; 35 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 73 ( 69 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,definition,
! [W0,W1] :
( ( aElement0(W1)
& aFunction0(W0) )
=> ! [W2] :
( W2 = sdtlbdtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
( aElement0(xy)
& aFunction0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,conjecture,
aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f94,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f95,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f97,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f96]) ).
fof(f100,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f278,plain,
! [W0] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f279,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f282,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtlbdtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) ) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f283,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| aElementOf0(W3,W2) )
& ( sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0))
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtlbdtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0))
| aElementOf0(W3,W2) )
& ( ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtlbdtrb0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(NNF_transformation,[status(thm)],[f282]) ).
fof(f284,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| aElementOf0(W3,W2) )
& ( sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0))
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtlbdtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0))
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtlbdtrb0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(miniscoping,[status(thm)],[f283]) ).
fof(f285,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( sdtlpdtrp0(W0,sK12_skl(W2,W1,W0)) = W1
& aElementOf0(sK12_skl(W2,W1,W0),szDzozmdt0(W0)) )
| aElementOf0(sK12_skl(W2,W1,W0),W2) )
& ( sdtlpdtrp0(W0,sK12_skl(W2,W1,W0)) != W1
| ~ aElementOf0(sK12_skl(W2,W1,W0),szDzozmdt0(W0))
| ~ aElementOf0(sK12_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtlbdtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sdtlpdtrp0(W0,W3) != W1
| ~ aElementOf0(W3,szDzozmdt0(W0))
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtlbdtrb0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(W3,sK12_skl(W2,W1,W0))],[f284]) ).
fof(f286,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtlbdtrb0(X0,X1)
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f287,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,szDzozmdt0(X0))
| ~ aElementOf0(X3,X2)
| X2 != sdtlbdtrb0(X0,X1)
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f293,plain,
aFunction0(xF),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f294,plain,
aElement0(xy),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f295,plain,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f329,plain,
! [X0,X1] :
( aSet0(sdtlbdtrb0(X0,X1))
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f286]) ).
fof(f330,plain,
! [X0,X1,X2] :
( aElementOf0(X2,szDzozmdt0(X0))
| ~ aElementOf0(X2,sdtlbdtrb0(X0,X1))
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f287]) ).
fof(f343,plain,
! [X0,X1] :
( aElementOf0(X1,szDzozmdt0(xF))
| ~ aElementOf0(X1,sdtlbdtrb0(xF,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f330,f293]) ).
fof(f360,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X0,szDzozmdt0(xF)),sdtlbdtrb0(xF,X1))
| ~ aElement0(X1)
| ~ aSet0(X0)
| aSubsetOf0(X0,szDzozmdt0(xF))
| ~ aSet0(szDzozmdt0(xF)) ),
inference(resolution,[status(thm)],[f101,f343]) ).
fof(f373,plain,
! [X0] :
( ~ aSet0(sdtlbdtrb0(xF,X0))
| aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF))
| ~ aSet0(szDzozmdt0(xF))
| ~ aElement0(X0)
| ~ aSet0(sdtlbdtrb0(xF,X0))
| aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF))
| ~ aSet0(szDzozmdt0(xF)) ),
inference(resolution,[status(thm)],[f360,f100]) ).
fof(f374,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aSet0(sdtlbdtrb0(xF,X0))
| aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF))
| ~ aSet0(szDzozmdt0(xF)) ),
inference(duplicate_literals_removal,[status(thm)],[f373]) ).
fof(f375,plain,
! [X0] :
( ~ aFunction0(xF)
| ~ aElement0(X0)
| ~ aSet0(sdtlbdtrb0(xF,X0))
| aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF)) ),
inference(resolution,[status(thm)],[f374,f279]) ).
fof(f377,plain,
! [X0] :
( ~ aFunction0(xF)
| ~ aElement0(X0)
| aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF)) ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f329]) ).
fof(f378,plain,
! [X0] :
( ~ aElement0(X0)
| aSubsetOf0(sdtlbdtrb0(xF,X0),szDzozmdt0(xF)) ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f293]) ).
fof(f380,plain,
aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(resolution,[status(thm)],[f378,f294]) ).
fof(f383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f380,f295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM560+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:46:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.042787 seconds
% 0.14/0.41 % CPU time: 0.094590 seconds
% 0.14/0.41 % Total memory used: 20.215 MB
% 0.14/0.41 % Net memory used: 20.178 MB
%------------------------------------------------------------------------------