%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM540+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 : n018.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 01:40:55 PM UTC 2026
% Result : Theorem 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 11 unt; 2 def)
% Number of atoms : 132 ( 24 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 161 ( 63 ~; 60 |; 30 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,definition,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,conjecture,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
slbdtrb0(sz00) != slcrc0,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f64,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f65,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
( ! [W0] :
( aElementOf0(sK0_skl(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f66]) ).
fof(f70,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f132,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f148,plain,
! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f149,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f206,plain,
! [W0] :
( ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f207,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ( ( ! [W2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f206]) ).
fof(f208,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ! [W1] :
( ( ! [W2] :
( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f209,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtlseqdt0(szszuzczcdt0(sK8_skl(W1,W0)),W0)
& aElementOf0(sK8_skl(W1,W0),szNzAzT0) )
| aElementOf0(sK8_skl(W1,W0),W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(sK8_skl(W1,W0)),W0)
| ~ aElementOf0(sK8_skl(W1,W0),szNzAzT0)
| ~ aElementOf0(sK8_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ! [W1] :
( ( ! [W2] :
( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W2,sK8_skl(W1,W0))],[f208]) ).
fof(f210,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f211,plain,
! [X0,X1,X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f212,plain,
! [X0,X1,X2] :
( sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f219,plain,
slbdtrb0(sz00) != slcrc0,
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f243,plain,
! [X0] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f210]) ).
fof(f244,plain,
! [X0,X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f211]) ).
fof(f245,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f212]) ).
fof(f261,plain,
aSet0(slbdtrb0(sz00)),
inference(resolution,[status(thm)],[f243,f132]) ).
fof(f263,plain,
( aElementOf0(sK0_skl(slbdtrb0(sz00)),slbdtrb0(sz00))
| slbdtrb0(sz00) = slcrc0 ),
inference(resolution,[status(thm)],[f261,f70]) ).
fof(f264,plain,
aElementOf0(sK0_skl(slbdtrb0(sz00)),slbdtrb0(sz00)),
inference(forward_subsumption_resolution,[status(thm)],[f263,f219]) ).
fof(f275,plain,
( sdtlseqdt0(szszuzczcdt0(sK0_skl(slbdtrb0(sz00))),sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolution,[status(thm)],[f264,f245]) ).
fof(f276,plain,
( aElementOf0(sK0_skl(slbdtrb0(sz00)),szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolution,[status(thm)],[f264,f244]) ).
fof(f278,plain,
sdtlseqdt0(szszuzczcdt0(sK0_skl(slbdtrb0(sz00))),sz00),
inference(forward_subsumption_resolution,[status(thm)],[f275,f132]) ).
fof(f279,plain,
aElementOf0(sK0_skl(slbdtrb0(sz00)),szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[f276,f132]) ).
fof(f281,plain,
~ aElementOf0(sK0_skl(slbdtrb0(sz00)),szNzAzT0),
inference(resolution,[status(thm)],[f278,f149]) ).
fof(f331,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f281,f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM540+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n018.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 02:40:28 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.19/0.43 % Drodi V4.1.1
% 0.19/0.44 % Refutation found
% 0.19/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.51 % Elapsed time: 0.086464 seconds
% 0.19/0.51 % CPU time: 0.111520 seconds
% 0.19/0.51 % Total memory used: 8.168 MB
% 0.19/0.51 % Net memory used: 8.148 MB
%------------------------------------------------------------------------------