%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC009+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 : n010.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 02:39:34 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 13 unt; 5 def)
% Number of atoms : 199 ( 66 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 250 ( 94 ~; 85 |; 55 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 46 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = 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 )
| ! [X2] :
( ssList(X2)
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( lt(X5,X3)
& app(X6,cons(X5,nil)) = W
& ssList(X6) )
& ssItem(X5) )
& app(cons(X3,nil),X4) = X2
& ssList(X4) )
& ssItem(X3) )
| ~ strictorderedP(W)
| app(W,X2) != X ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| 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 )
| ! [X2] :
( ssList(X2)
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( lt(X5,X3)
& app(X6,cons(X5,nil)) = W
& ssList(X6) )
& ssItem(X5) )
& app(cons(X3,nil),X4) = X2
& ssList(X4) )
& ssItem(X3) )
| ~ strictorderedP(W)
| app(W,X2) != X ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ lt(X5,X3)
| app(X6,cons(X5,nil)) != W
| ~ ssList(X6) )
| ~ ssItem(X5) )
| app(cons(X3,nil),X4) != X2
| ~ ssList(X4) )
| ~ ssItem(X3) )
& strictorderedP(W)
& app(W,X2) = X
& ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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 )
& ? [X2] :
( ! [X3] :
( ! [X5] :
( ~ lt(X5,X3)
| ! [X6] :
( app(X6,cons(X5,nil)) != W
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ! [X4] :
( app(cons(X3,nil),X4) != X2
| ~ ssList(X4) )
| ~ ssItem(X3) )
& strictorderedP(W)
& app(W,X2) = X
& ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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 )
& ! [X3] :
( ! [X5] :
( ~ lt(X5,X3)
| ! [X6] :
( app(X6,cons(X5,nil)) != sK49_skl
| ~ ssList(X6) )
| ~ ssItem(X5) )
| ! [X4] :
( app(cons(X3,nil),X4) != sK51_skl
| ~ ssList(X4) )
| ~ ssItem(X3) )
& strictorderedP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_skl
& ssList(sK51_skl)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK47_skl
| app(app(Y,Z),X1) != sK48_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& 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(X2,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,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f481,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f482,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK49_skl
| app(app(X0,X1),X2) != sK50_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f481]) ).
fof(f483,plain,
! [X0] :
( app(sK49_skl,X0) != sK49_skl
| app(sK50_skl,X0) != sK50_skl
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f426,f482]) ).
fof(f484,definition,
( sQ2_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ2_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,definition,
( sQ3_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ3_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,definition,
! [X0] :
( sQ4_spl
<=> ( app(sK49_skl,X0) != sK49_skl
| app(sK50_skl,X0) != sK50_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f491,plain,
! [X0] :
( ~ sQ4_spl
| app(sK49_skl,X0) != sK49_skl
| app(sK50_skl,X0) != sK50_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f483,f484,f487,f490]) ).
fof(f502,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f425]) ).
fof(f503,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f504,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f420]) ).
fof(f505,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f519,plain,
( ~ sQ4_spl
| app(sK50_skl,nil) != sK50_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f389,f491]) ).
fof(f520,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ10_spl
<=> app(sK50_skl,nil) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ10_spl
| app(sK50_skl,nil) != sK50_skl ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f519,f484,f520,f523,f490]) ).
fof(f527,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f223]) ).
fof(f528,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ10_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f525,f389]) ).
fof(f530,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f421]) ).
fof(f531,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
$false,
inference(sat_refutation,[status(thm)],[f493,f503,f505,f526,f528,f531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC009+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 07:49:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.063494 seconds
% 0.11/0.45 % CPU time: 0.161879 seconds
% 0.11/0.45 % Total memory used: 93.349 MB
% 0.11/0.45 % Net memory used: 93.209 MB
%------------------------------------------------------------------------------