%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:40:57 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 9 unt; 1 def)
% Number of atoms : 105 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 42 ~; 38 |; 21 &)
% ( 4 <=>; 4 =>; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 29 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,conjecture,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f75,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f76,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f80,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,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))],[f81]) ).
fof(f83,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f189,plain,
! [W0] :
( ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f190,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f189]) ).
fof(f192,plain,
! [X0] :
( X0 != slcrc0
| sbrdtbr0(X0) = sz00
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f270,plain,
xk != sz00,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f302,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(f303,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f306,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f311,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f312,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f319,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f331,plain,
( sbrdtbr0(slcrc0) = sz00
| ~ aSet0(slcrc0) ),
inference(destructive_equality_resolution,[status(thm)],[f192]) ).
fof(f352,plain,
( ~ aElement0(sK0_skl(xQ))
| ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[f85,f312]) ).
fof(f353,plain,
! [X0] :
( aElement0(sK0_skl(X0))
| ~ aSet0(X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(resolution,[status(thm)],[f85,f76]) ).
fof(f355,plain,
( ~ aElement0(sK0_skl(xQ))
| xQ = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f352,f303]) ).
fof(f356,plain,
! [X0] :
( aElement0(sK0_skl(X0))
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(duplicate_literals_removal,[status(thm)],[f353]) ).
fof(f364,plain,
( xQ = slcrc0
| ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[f356,f355]) ).
fof(f365,plain,
( ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(duplicate_literals_removal,[status(thm)],[f364]) ).
fof(f366,plain,
xQ = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f365,f303]) ).
fof(f371,plain,
sbrdtbr0(slcrc0) = xk,
inference(backward_demodulation,[status(thm)],[f366,f306]) ).
fof(f439,plain,
( xk = sz00
| ~ aSet0(slcrc0) ),
inference(forward_demodulation,[status(thm)],[f371,f331]) ).
fof(f447,plain,
xk != xk,
inference(backward_demodulation,[status(thm)],[f448,f270]) ).
fof(f448,plain,
xk = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f439,f319]) ).
fof(f450,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:42:20 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.58 % Elapsed time: 0.126812 seconds
% 0.25/0.58 % CPU time: 0.128134 seconds
% 0.25/0.58 % Total memory used: 23.862 MB
% 0.25/0.58 % Net memory used: 23.832 MB
%------------------------------------------------------------------------------