%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC103+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 : 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 02:39:58 PM UTC 2026
% Result : Theorem 0.15s 5.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 6 unt; 5 def)
% Number of atoms : 112 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 119 ( 41 ~; 39 |; 26 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 12 ( 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = X
& nil != W )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = X
& nil != W )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& ( nil != X
| nil = W )
& 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,
( ( ( frontsegP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| ~ neq(sK50_skl,nil) )
& ( ~ frontsegP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) )
& ( nil != sK50_skl
| nil = sK49_skl )
& 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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_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(f425,plain,
( ~ frontsegP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( neq(sK49_skl,nil)
| ~ neq(sK50_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( frontsegP(sK50_skl,sK49_skl)
| ~ neq(sK50_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f435,definition,
( sQ2_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ2_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ3_spl
<=> frontsegP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ3_spl
| ~ frontsegP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f425,f435,f438]) ).
fof(f442,definition,
( sQ4_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ4_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ5_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ5_spl
| neq(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f426,f442,f445]) ).
fof(f449,definition,
( sQ6_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ6_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f442,f449]) ).
fof(f487,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f488,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f487]) ).
fof(f489,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f495,plain,
( sQ3_spl
| ~ frontsegP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f440]) ).
fof(f500,plain,
( sQ3_spl
| ~ frontsegP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f495]) ).
fof(f502,plain,
( ~ sQ6_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f500]) ).
fof(f503,plain,
( ~ sQ6_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f506,plain,
( sQ2_spl
| ~ neq(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f422,f437]) ).
fof(f507,plain,
( sQ2_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f446]) ).
fof(f508,plain,
( sQ2_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f448,f452,f489,f503,f508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC103+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n007.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Mon Sep 21 07:53:57 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.39 % Drodi V4.1.1
% 0.15/5.41 % Refutation found
% 0.15/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.43 % Elapsed time: 0.050255 seconds
% 0.15/5.43 % CPU time: 0.130956 seconds
% 0.15/5.43 % Total memory used: 69.009 MB
% 0.15/5.43 % Net memory used: 68.912 MB
%------------------------------------------------------------------------------