%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC082+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 : n003.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 02:39:53 PM UTC 2026
% Result : Theorem 0.14s 5.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 6 unt; 5 def)
% Number of atoms : 130 ( 18 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 156 ( 57 ~; 50 |; 34 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 22 ( 15 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssList(Z)
=> ( ~ segmentP(W,Z)
| ~ segmentP(X,Z)
| ~ neq(Z,nil) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
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)
& ! [Z] :
( ssList(Z)
=> ( ~ segmentP(W,Z)
| ~ segmentP(X,Z)
| ~ neq(Z,nil) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Z] :
( segmentP(W,Z)
& segmentP(X,Z)
& neq(Z,nil)
& ssList(Z) ) )
& ( nil != X
| nil = W )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( segmentP(sK49_skl,sK51_skl)
& segmentP(sK50_skl,sK51_skl)
& neq(sK51_skl,nil)
& ssList(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil)
& 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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_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,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| neq(sK51_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| segmentP(sK50_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| segmentP(sK49_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f437,definition,
( sQ2_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f440,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f437,f440]) ).
fof(f444,definition,
( sQ4_spl
<=> neq(sK51_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ4_spl
| neq(sK51_skl,nil) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f444,f440]) ).
fof(f448,definition,
( sQ5_spl
<=> segmentP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f428,f448,f440]) ).
fof(f452,definition,
( sQ6_spl
<=> segmentP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f429,f452,f440]) ).
fof(f489,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f496,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f424]) ).
fof(f497,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f496]) ).
fof(f499,plain,
( ~ sQ4_spl
| ~ segmentP(sK49_skl,sK51_skl)
| ~ segmentP(sK50_skl,sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f497,f445]) ).
fof(f511,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f499,f437,f448,f452,f444]) ).
fof(f523,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f489]) ).
fof(f524,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f447,f451,f455,f511,f524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.57 % Computer : n003.cluster.edu
% 0.10/5.57 % Model : x86_64 x86_64
% 0.10/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.57 % Memory : 8046.5625MB
% 0.10/5.57 % OS : Linux 6.8.0-71-generic
% 0.10/5.57 % CPULimit : 300
% 0.10/5.57 % WCLimit : 300
% 0.10/5.57 % DateTime : Mon Sep 21 07:56:07 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.59 % Drodi V4.1.1
% 0.14/5.61 % Refutation found
% 0.14/5.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.64 % Elapsed time: 0.055837 seconds
% 0.14/5.64 % CPU time: 0.135314 seconds
% 0.14/5.64 % Total memory used: 72.518 MB
% 0.14/5.64 % Net memory used: 72.438 MB
%------------------------------------------------------------------------------