%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC372+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 : n016.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 0.03s 0.40s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 18 unt; 6 def)
% Number of atoms : 222 ( 49 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 261 ( 94 ~; 89 |; 57 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 48 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| segmentP(V,U)
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| 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)
=> ( ( nil = W
& nil != X )
| segmentP(V,U)
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ segmentP(V,U)
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ segmentP(V,U)
& ? [Y] :
( ! [Z] :
( ! [X2] :
( ~ lt(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( nil != sK49_skl
| nil = sK50_skl )
& ~ segmentP(sK48_skl,sK47_skl)
& ! [Z] :
( ! [X2] :
( ~ lt(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != sK49_skl
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_skl
& ssList(sK51_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,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f428,plain,
~ segmentP(sK48_skl,sK47_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f480,definition,
( sQ3_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ3_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,definition,
( sQ4_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ4_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f487,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f420]) ).
fof(f488,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
~ segmentP(sK48_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f423,f428]) ).
fof(f490,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f424]) ).
fof(f491,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f492,plain,
~ segmentP(sK50_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f422,f489]) ).
fof(f504,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f509,definition,
( sQ7_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ7_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f516,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f223]) ).
fof(f517,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f534,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f504,f443]) ).
fof(f535,definition,
! [X0] :
( sQ11_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f536,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f534,f535,f483,f512]) ).
fof(f539,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f504,f536]) ).
fof(f552,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f421]) ).
fof(f553,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f625,plain,
( ~ sQ11_spl
| ~ ssList(sK51_skl)
| segmentP(app(sK49_skl,sK51_skl),sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f425,f539]) ).
fof(f630,definition,
( sQ22_spl
<=> segmentP(app(sK49_skl,sK51_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ22_spl
| segmentP(app(sK49_skl,sK51_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| sQ22_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f625,f509,f630,f480,f535]) ).
fof(f635,plain,
( ~ sQ22_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f631]) ).
fof(f636,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f635,f492]) ).
fof(f637,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f638,plain,
$false,
inference(sat_refutation,[status(thm)],[f488,f491,f517,f538,f553,f633,f637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC372+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:24:08 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.38 % Drodi V4.1.1
% 0.03/0.40 % Refutation found
% 0.03/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.43 % Elapsed time: 0.068148 seconds
% 0.03/0.43 % CPU time: 0.217822 seconds
% 0.03/0.43 % Total memory used: 80.224 MB
% 0.03/0.43 % Net memory used: 80.069 MB
%------------------------------------------------------------------------------