%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC006+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:39:33 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 12 unt; 4 def)
% Number of atoms : 125 ( 38 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 142 ( 51 ~; 47 |; 30 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 29 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( app(X2,X4) != W
| app(app(X2,X3),X4) != X
| ~ ssList(X4) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( app(X2,X4) != W
| app(app(X2,X3),X4) != X
| ~ ssList(X4) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(X2,X4) = W
& app(app(X2,X3),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( app(sK51_skl,sK53_skl) = sK49_skl
& app(app(sK51_skl,sK52_skl),sK53_skl) = sK50_skl
& ssList(sK53_skl)
& ssList(sK52_skl)
& ssList(sK51_skl)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK47_skl
| app(app(Y,Z),X1) != sK48_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_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,sK52_skl,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl),skolemize(X3,sK52_skl),skolemize(X4,sK53_skl)],[f415]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
app(app(sK51_skl,sK52_skl),sK53_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
app(sK51_skl,sK53_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f462,definition,
( sQ0_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ0_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ1_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ1_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f480,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f426]) ).
fof(f481,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f424]) ).
fof(f483,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f485,definition,
( sQ5_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ5_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f489,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f425]) ).
fof(f490,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f561,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f562,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK49_skl
| app(app(X0,X1),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f561]) ).
fof(f563,plain,
( app(sK51_skl,sK53_skl) != sK49_skl
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f562,f427]) ).
fof(f567,definition,
( sQ19_spl
<=> app(sK51_skl,sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ19_spl
| app(sK51_skl,sK53_skl) != sK49_skl ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,plain,
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f563,f462,f485,f465,f567]) ).
fof(f583,plain,
( sQ19_spl
| sK49_skl != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f428,f569]) ).
fof(f584,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f583]) ).
fof(f585,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
$false,
inference(sat_refutation,[status(thm)],[f481,f483,f490,f570,f585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC006+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 07:48:32 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % 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
% 0.25/0.58 % Elapsed time: 0.127001 seconds
% 0.25/0.58 % CPU time: 0.135031 seconds
% 0.25/0.58 % Total memory used: 13.954 MB
% 0.25/0.58 % Net memory used: 13.939 MB
%------------------------------------------------------------------------------