%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC040+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 : n007.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 02:39:42 PM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 9 unt; 2 def)
% Number of atoms : 87 ( 45 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 93 ( 28 ~; 23 |; 28 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W ) ) ) )
| ( nil = X
& nil != W )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W ) ) ) )
| ( nil = X
& nil != W )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& nil != U
& U = W
& V = X
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl
& app(cons(sK51_skl,nil),sK52_skl) = sK49_skl
& ssList(sK52_skl)
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& nil != sK47_skl
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& nil = sK48_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl)],[f415]) ).
fof(f421,plain,
nil = sK48_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,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f430,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f430,f433]) ).
fof(f488,plain,
nil = sK50_skl,
inference(forward_demodulation,[status(thm)],[f421,f422]) ).
fof(f490,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f423,f424]) ).
fof(f491,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f490]) ).
fof(f492,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f493,plain,
( sQ1_spl
| nil != nil ),
inference(forward_demodulation,[status(thm)],[f488,f435]) ).
fof(f494,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f493]) ).
fof(f495,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,plain,
$false,
inference(sat_refutation,[status(thm)],[f436,f492,f495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC040+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 07:48:36 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.060170 seconds
% 0.11/0.41 % CPU time: 0.147341 seconds
% 0.11/0.41 % Total memory used: 62.177 MB
% 0.11/0.41 % Net memory used: 62.090 MB
%------------------------------------------------------------------------------