%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC408+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:41:07 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 91 ( 16 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 105 ( 37 ~; 33 |; 20 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 25 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Y] :
( ssItem(Y)
=> ( memberP(U,Y)
| ~ memberP(V,Y) ) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Y] :
( ssItem(Y)
=> ( memberP(U,Y)
| ~ memberP(V,Y) ) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ~ memberP(U,Y)
& memberP(V,Y)
& ssItem(Y) )
& U = W
& V = X
& app(X,X) = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ~ memberP(sK47_skl,sK51_skl)
& memberP(sK48_skl,sK51_skl)
& ssItem(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& app(sK50_skl,sK50_skl) = sK49_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f415]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
app(sK50_skl,sK50_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
memberP(sK48_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
~ memberP(sK47_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f459,plain,
memberP(sK50_skl,sK51_skl),
inference(forward_demodulation,[status(thm)],[f422,f425]) ).
fof(f461,plain,
app(sK50_skl,sK50_skl) = sK47_skl,
inference(forward_demodulation,[status(thm)],[f423,f421]) ).
fof(f479,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f461,f271]) ).
fof(f480,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK50_skl)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f479]) ).
fof(f481,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f420]) ).
fof(f485,plain,
( ~ memberP(sK50_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f481,f426]) ).
fof(f487,plain,
~ memberP(sK50_skl,sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f485,f424]) ).
fof(f488,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f487,f459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC408+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:22:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.064875 seconds
% 0.13/0.44 % CPU time: 0.178729 seconds
% 0.13/0.44 % Total memory used: 110.574 MB
% 0.13/0.44 % Net memory used: 110.416 MB
%------------------------------------------------------------------------------