%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC398+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 : n006.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 02:41:05 PM UTC 2026
% Result : Theorem 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 147 ( 38 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 183 ( 61 ~; 54 |; 51 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 54 ( 36 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,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 )
| ! [X3] :
( ssItem(X3)
=> ( memberP(V,X3)
| ~ memberP(U,X3) ) )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(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 )
| ! [X3] :
( ssItem(X3)
=> ( memberP(V,X3)
| ~ memberP(U,X3) ) )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [X3] :
( ~ memberP(V,X3)
& memberP(U,X3)
& ssItem(X3) )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(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 )
& ? [X3] :
( ~ memberP(V,X3)
& memberP(U,X3)
& ssItem(X3) )
& ? [Y] :
( ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(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 )
& ~ memberP(sK48_skl,sK52_skl)
& memberP(sK47_skl,sK52_skl)
& ssItem(sK52_skl)
& ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK49_skl
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(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,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(X3,sK52_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_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,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f429,plain,
memberP(sK47_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
~ memberP(sK48_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f465,plain,
memberP(sK49_skl,sK52_skl),
inference(forward_demodulation,[status(thm)],[f423,f429]) ).
fof(f466,plain,
~ memberP(sK50_skl,sK52_skl),
inference(forward_demodulation,[status(thm)],[f422,f430]) ).
fof(f526,plain,
! [X0] :
( ~ memberP(sK49_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK49_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f425,f271]) ).
fof(f527,plain,
! [X0] :
( ~ memberP(sK49_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f420]) ).
fof(f528,plain,
! [X0] :
( ~ memberP(sK49_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f424]) ).
fof(f529,plain,
( ~ memberP(sK49_skl,sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f528,f466]) ).
fof(f530,plain,
~ memberP(sK49_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f529,f428]) ).
fof(f535,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f530,f465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC398+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n006.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 08:21:20 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.39 % Drodi V4.1.1
% 0.15/5.42 % Refutation found
% 0.15/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.46 % Elapsed time: 0.065161 seconds
% 0.15/5.46 % CPU time: 0.195072 seconds
% 0.15/5.46 % Total memory used: 111.249 MB
% 0.15/5.46 % Net memory used: 111.052 MB
%------------------------------------------------------------------------------