%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM551+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 5 unt; 1 def)
% Number of atoms : 79 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 37 ~; 26 |; 20 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 23 !; 7 ?)
% 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(f65,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
~ ( xQ = slcrc0
| ~ ? [W0] : aElementOf0(W0,xQ) ),
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(f303,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f304,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f312,plain,
( xQ != slcrc0
& ? [W0] : aElementOf0(W0,xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f313,plain,
( xQ != slcrc0
& aElementOf0(sK15_skl,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(W0,sK15_skl)],[f312]) ).
fof(f315,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(thm)],[f313]) ).
fof(f316,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f317,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(f353,plain,
( ~ aElement0(sK0_skl(xQ))
| ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[f86,f317]) ).
fof(f354,plain,
( ~ aElement0(sK0_skl(xQ))
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f315]) ).
fof(f357,plain,
~ aElement0(sK0_skl(xQ)),
inference(forward_subsumption_resolution,[status(thm)],[f354,f304]) ).
fof(f358,plain,
! [X0] :
( ~ aElementOf0(sK0_skl(xQ),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f357,f77]) ).
fof(f359,plain,
( ~ aSet0(xQ)
| xQ = slcrc0
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f358,f86]) ).
fof(f361,plain,
( xQ = slcrc0
| ~ aSet0(xQ) ),
inference(duplicate_literals_removal,[status(thm)],[f359]) ).
fof(f362,plain,
xQ = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f361,f304]) ).
fof(f364,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f362,f315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM551+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 02:38:36 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.050693 seconds
% 0.12/0.41 % CPU time: 0.145023 seconds
% 0.12/0.41 % Total memory used: 107.842 MB
% 0.12/0.41 % Net memory used: 107.732 MB
%------------------------------------------------------------------------------