%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM561+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 : n007.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 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 9 unt; 1 def)
% Number of atoms : 108 ( 24 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 137 ( 54 ~; 53 |; 22 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-4 aty)
% Number of variables : 56 ( 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2] :
( W2 = sdtlcdtrc0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) ) )
& aSet0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,hypothesis,
aFunction0(xF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f107,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f108,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f281,plain,
! [W0] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f282,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f298,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( W2 = sdtlcdtrc0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) ) )
& aSet0(W2) ) )
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f299,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ( ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) )
| aElementOf0(W3,W2) )
& ( ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) )
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtlcdtrc0(W0,W1) )
& ( ( ! [W3] :
( ( ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) )
| aElementOf0(W3,W2) )
& ( ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtlcdtrc0(W0,W1) ) )
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(NNF_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ? [W3] :
( ( ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) )
| aElementOf0(W3,W2) )
& ( ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) )
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtlcdtrc0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) )
| aElementOf0(W3,W2) )
& ! [W3] :
( ? [W4] :
( sdtlpdtrp0(W0,W4) = W3
& aElementOf0(W4,W1) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtlcdtrc0(W0,W1) ) )
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(miniscoping,[status(thm)],[f299]) ).
fof(f301,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ( ( ( sdtlpdtrp0(W0,sK15_skl(W2,W1,W0)) = sK14_skl(W2,W1,W0)
& aElementOf0(sK15_skl(W2,W1,W0),W1) )
| aElementOf0(sK14_skl(W2,W1,W0),W2) )
& ( ! [W4] :
( sdtlpdtrp0(W0,W4) != sK14_skl(W2,W1,W0)
| ~ aElementOf0(W4,W1) )
| ~ aElementOf0(sK14_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtlcdtrc0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4] :
( sdtlpdtrp0(W0,W4) != W3
| ~ aElementOf0(W4,W1) )
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sdtlpdtrp0(W0,sK13_skl(W3,W2,W1,W0)) = W3
& aElementOf0(sK13_skl(W3,W2,W1,W0),W1) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtlcdtrc0(W0,W1) ) )
| ~ aSubsetOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(W4,sK13_skl(W3,W2,W1,W0)),skolemize(W3,sK14_skl(W2,W1,W0)),skolemize(W4,sK15_skl(W2,W1,W0))],[f300]) ).
fof(f305,plain,
! [X0,X1,X2,X3,X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1)
| aElementOf0(X3,X2)
| X2 != sdtlcdtrc0(X0,X1)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f309,plain,
aFunction0(xF),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f310,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f311,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f352,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(sdtlpdtrp0(X0,X2),sdtlcdtrc0(X0,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f305]) ).
fof(f358,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aFunction0(X0)
| ~ aSet0(szDzozmdt0(X0)) ),
inference(resolution,[status(thm)],[f108,f352]) ).
fof(f359,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aFunction0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f282]) ).
fof(f360,plain,
( ~ aElementOf0(xx,szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(resolution,[status(thm)],[f359,f311]) ).
fof(f361,plain,
~ aElementOf0(xx,szDzozmdt0(xF)),
inference(forward_subsumption_resolution,[status(thm)],[f360,f309]) ).
fof(f362,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f361,f310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM561+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n007.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 02:38:26 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.15/5.42 % Refutation found
% 0.15/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.45 % Elapsed time: 0.060388 seconds
% 0.15/5.45 % CPU time: 0.160013 seconds
% 0.15/5.45 % Total memory used: 107.328 MB
% 0.15/5.45 % Net memory used: 107.220 MB
%------------------------------------------------------------------------------