%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC406+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 02:41:07 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 106 ( 18 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 134 ( 43 ~; 37 |; 42 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 29 ( 19 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X1] :
( ssItem(X1)
=> ( memberP(V,X1)
| ~ memberP(U,X1) ) )
| ? [Y] :
( ( ( ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Z,Y)
| ~ memberP(X,Z) ) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| 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)
=> ( ! [X1] :
( ssItem(X1)
=> ( memberP(V,X1)
| ~ memberP(U,X1) ) )
| ? [Y] :
( ( ( ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Z,Y)
| ~ memberP(X,Z) ) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X1] :
( ~ memberP(V,X1)
& memberP(U,X1)
& ssItem(X1) )
& ! [Y] :
( ( ( ( ! [Z] :
( ~ leq(Z,Y)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y) )
| ~ memberP(W,Y) )
& ( ~ memberP(X,Y)
| ? [Z] :
( Y != Z
& leq(Z,Y)
& memberP(X,Z)
& ssItem(Z) )
| memberP(W,Y) ) )
| ~ ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ~ memberP(sK48_skl,sK52_skl)
& memberP(sK47_skl,sK52_skl)
& ssItem(sK52_skl)
& ! [Y] :
( ( ( ( ! [Z] :
( ~ leq(Z,Y)
| ~ memberP(sK50_skl,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(sK50_skl,Y) )
| ~ memberP(sK49_skl,Y) )
& ( ~ memberP(sK50_skl,Y)
| ( Y != sK51_skl(Y)
& leq(sK51_skl(Y),Y)
& memberP(sK50_skl,sK51_skl(Y))
& ssItem(sK51_skl(Y)) )
| memberP(sK49_skl,Y) ) )
| ~ ssItem(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,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl(Y)),skolemize(X1,sK52_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(f427,plain,
! [X0] :
( memberP(sK50_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
memberP(sK47_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
~ memberP(sK48_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f468,plain,
! [X0] :
( memberP(sK50_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f469,plain,
! [X0] :
( memberP(sK48_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f468]) ).
fof(f470,plain,
( ~ memberP(sK47_skl,sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f469,f431]) ).
fof(f471,plain,
~ memberP(sK47_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f470,f429]) ).
fof(f486,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f471,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:22:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.049498 seconds
% 0.10/0.42 % CPU time: 0.124290 seconds
% 0.10/0.42 % Total memory used: 62.374 MB
% 0.10/0.42 % Net memory used: 62.285 MB
%------------------------------------------------------------------------------