%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM549+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 : n004.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 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 9 unt; 1 def)
% Number of atoms : 96 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 41 ~; 37 |; 15 &)
% ( 4 <=>; 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; 6 con; 0-1 aty)
% Number of variables : 32 ( 27 !; 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(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
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,conjecture,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('/export/starexec/sandbox/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(f275,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f277,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f278,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f279,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f286,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f298,plain,
( sbrdtbr0(slcrc0) = sz00
| ~ aSet0(slcrc0) ),
inference(destructive_equality_resolution,[status(thm)],[f192]) ).
fof(f316,plain,
( ~ aElement0(sK0_skl(xQ))
| ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[f85,f279]) ).
fof(f317,plain,
! [X0] :
( aElement0(sK0_skl(X0))
| ~ aSet0(X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(resolution,[status(thm)],[f85,f76]) ).
fof(f318,plain,
( ~ aElement0(sK0_skl(xQ))
| xQ = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f275]) ).
fof(f319,plain,
! [X0] :
( aElement0(sK0_skl(X0))
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(duplicate_literals_removal,[status(thm)],[f317]) ).
fof(f331,plain,
( xQ = slcrc0
| ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[f319,f318]) ).
fof(f332,plain,
( ~ aSet0(xQ)
| xQ = slcrc0 ),
inference(duplicate_literals_removal,[status(thm)],[f331]) ).
fof(f333,plain,
xQ = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f332,f275]) ).
fof(f338,plain,
sbrdtbr0(slcrc0) = xk,
inference(backward_demodulation,[status(thm)],[f333,f277]) ).
fof(f389,plain,
( xk = sz00
| ~ aSet0(slcrc0) ),
inference(forward_demodulation,[status(thm)],[f338,f298]) ).
fof(f398,plain,
sz00 != sz00,
inference(backward_demodulation,[status(thm)],[f399,f270]) ).
fof(f399,plain,
xk = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f389,f286]) ).
fof(f401,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM549+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n004.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 02:39:04 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.52 % Elapsed time: 0.090064 seconds
% 0.17/0.52 % CPU time: 0.115179 seconds
% 0.17/0.52 % Total memory used: 17.115 MB
% 0.17/0.52 % Net memory used: 17.083 MB
%------------------------------------------------------------------------------