%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC369+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 : n009.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 02:40:58 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 13 unt; 6 def)
% Number of atoms : 136 ( 29 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 142 ( 53 ~; 47 |; 23 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 24 ( 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| segmentP(V,U)
| 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)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| segmentP(V,U)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( nil != X
| nil = W )
& ~ segmentP(V,U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ( segmentP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| ~ neq(sK50_skl,nil) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ~ segmentP(sK48_skl,sK47_skl)
& 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(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
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,
~ segmentP(sK48_skl,sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( segmentP(sK50_skl,sK49_skl)
| ~ neq(sK50_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f427,f430]) ).
fof(f434,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f441,definition,
( sQ4_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ4_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f434,f441]) ).
fof(f478,plain,
~ segmentP(sK50_skl,sK47_skl),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f479,plain,
~ segmentP(sK50_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f422,f478]) ).
fof(f481,plain,
! [X0] :
( ~ sQ0_spl
| segmentP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f428,f323]) ).
fof(f482,plain,
( ~ sQ0_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f481,f479]) ).
fof(f483,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f420]) ).
fof(f484,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f497,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f505,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f223]) ).
fof(f506,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
( sQ2_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f220,f436]) ).
fof(f510,definition,
( sQ9_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ9_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f507,f510,f497,f430,f434]) ).
fof(f514,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f420]) ).
fof(f515,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f479]) ).
fof(f517,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f518,plain,
$false,
inference(sat_refutation,[status(thm)],[f433,f444,f484,f506,f513,f515,f517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC369+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 08:19:13 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.048650 seconds
% 0.12/0.41 % CPU time: 0.086309 seconds
% 0.12/0.41 % Total memory used: 20.773 MB
% 0.12/0.41 % Net memory used: 20.745 MB
%------------------------------------------------------------------------------