%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM551+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 : n002.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 01:40:58 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 6 unt; 4 def)
% Number of atoms : 85 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 37 ~; 33 |; 12 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,conjecture,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f76,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f77,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f81,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,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))],[f82]) ).
fof(f86,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f276,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f279,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f280,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f281,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
fof(f317,plain,
( ~ aElement0(sK0_skl(xQ))
| ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[f86,f281]) ).
fof(f325,definition,
( sQ2_spl
<=> xQ = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( ~ sQ2_spl
| xQ = slcrc0 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,definition,
( sQ3_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ3_spl
| ~ aSet0(xQ) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ4_spl
<=> aElement0(sK0_skl(xQ)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ4_spl
| ~ aElement0(sK0_skl(xQ)) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f317,f325,f328,f331]) ).
fof(f353,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f276]) ).
fof(f354,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f359,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f279]) ).
fof(f360,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f362,plain,
! [X0] :
( sQ4_spl
| ~ aElementOf0(sK0_skl(xQ),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f333,f77]) ).
fof(f363,plain,
( sQ4_spl
| ~ aSet0(xQ)
| xQ = slcrc0
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f362,f86]) ).
fof(f364,plain,
( sQ4_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f363,f328,f325,f331]) ).
fof(f365,plain,
$false,
inference(sat_refutation,[status(thm)],[f334,f354,f360,f364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:41:46 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.057564 seconds
% 0.12/0.42 % CPU time: 0.176308 seconds
% 0.12/0.42 % Total memory used: 106.382 MB
% 0.12/0.42 % Net memory used: 106.267 MB
%------------------------------------------------------------------------------