%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 01:41:10 PM UTC 2026
% Result : Theorem 0.03s 0.54s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 17 unt; 5 def)
% Number of atoms : 168 ( 58 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 193 ( 75 ~; 72 |; 33 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 52 ( 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,hypothesis,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f112,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f113,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,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))],[f114]) ).
fof(f116,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f222,plain,
! [W0] :
( ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f223,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f222]) ).
fof(f225,plain,
! [X0] :
( X0 != slcrc0
| sbrdtbr0(X0) = sz00
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f283,plain,
! [W0,W1] :
( ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f284,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f283]) ).
fof(f285,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f284]) ).
fof(f286,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( sbrdtbr0(sK10_skl(W2,W1,W0)) = W1
& aSubsetOf0(sK10_skl(W2,W1,W0),W0) )
| aElementOf0(sK10_skl(W2,W1,W0),W2) )
& ( sbrdtbr0(sK10_skl(W2,W1,W0)) != W1
| ~ aSubsetOf0(sK10_skl(W2,W1,W0),W0)
| ~ aElementOf0(sK10_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f285]) ).
fof(f289,plain,
! [X0,X1,X2,X3] :
( sbrdtbr0(X3) = X1
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f286]) ).
fof(f360,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f372,plain,
xK != sz00,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f422,plain,
aSet0(xO),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f432,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f433,plain,
xQ = slcrc0,
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f440,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f116]) ).
fof(f452,plain,
( sbrdtbr0(slcrc0) = sz00
| ~ aSet0(slcrc0) ),
inference(destructive_equality_resolution,[status(thm)],[f225]) ).
fof(f465,plain,
! [X0,X1,X2] :
( sbrdtbr0(X2) = X1
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f289]) ).
fof(f481,plain,
aSet0(xQ),
inference(forward_demodulation,[status(thm)],[f433,f440]) ).
fof(f697,definition,
( sQ35_spl
<=> aSet0(xO) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( sQ35_spl
| ~ aSet0(xO) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f778,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f422]) ).
fof(f779,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f778]) ).
fof(f2028,plain,
( sbrdtbr0(slcrc0) = sz00
| ~ aSet0(xQ) ),
inference(forward_demodulation,[status(thm)],[f433,f452]) ).
fof(f2029,plain,
( sbrdtbr0(xQ) = sz00
| ~ aSet0(xQ) ),
inference(forward_demodulation,[status(thm)],[f433,f2028]) ).
fof(f2031,plain,
sbrdtbr0(xQ) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f2029,f481]) ).
fof(f3234,definition,
( sQ435_spl
<=> aElementOf0(xK,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f3236,plain,
( sQ435_spl
| ~ aElementOf0(xK,szNzAzT0) ),
inference(component_clause,[status(thm)],[f3234]) ).
fof(f3246,plain,
( sQ435_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3236,f360]) ).
fof(f3247,plain,
sQ435_spl,
inference(contradiction_clause,[status(thm)],[f3246]) ).
fof(f3650,definition,
( sQ505_spl
<=> sbrdtbr0(xQ) = xK ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f3651,plain,
( ~ sQ505_spl
| sbrdtbr0(xQ) = xK ),
inference(component_clause,[status(thm)],[f3650]) ).
fof(f3654,plain,
( ~ sQ505_spl
| sz00 = xK ),
inference(forward_demodulation,[status(thm)],[f2031,f3651]) ).
fof(f3655,plain,
( ~ sQ505_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3654,f372]) ).
fof(f3656,plain,
~ sQ505_spl,
inference(contradiction_clause,[status(thm)],[f3655]) ).
fof(f3676,plain,
( sbrdtbr0(xQ) = xK
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[f432,f465]) ).
fof(f3685,plain,
( sQ505_spl
| ~ sQ435_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f3676,f697,f3234,f3650]) ).
fof(f3724,plain,
$false,
inference(sat_refutation,[status(thm)],[f779,f3247,f3656,f3685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:44:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.03/0.38 % Drodi V4.1.1
% 0.03/0.54 % Refutation found
% 0.03/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.55 % Elapsed time: 0.186821 seconds
% 0.03/0.55 % CPU time: 1.069806 seconds
% 0.03/0.55 % Total memory used: 128.009 MB
% 0.03/0.55 % Net memory used: 126.440 MB
%------------------------------------------------------------------------------