%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC185+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 : n001.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 02:40:18 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 113 ( 21 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 143 ( 53 ~; 42 |; 34 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 26 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ~ memberP(X4,X2)
& ~ memberP(X3,X2) )
| app(app(X3,cons(X2,nil)),X4) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& 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)
=> ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ~ memberP(X4,X2)
& ~ memberP(X3,X2) )
| app(app(X3,cons(X2,nil)),X4) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( memberP(X4,X2)
| memberP(X3,X2) )
& app(app(X3,cons(X2,nil)),X4) = U
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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(sK53_skl,sK51_skl)
| memberP(sK52_skl,sK51_skl) )
& app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl
& ssList(sK53_skl)
& ssList(sK52_skl)
& ssItem(sK51_skl)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != sK49_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl),skolemize(X3,sK52_skl),skolemize(X4,sK53_skl)],[f415]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( memberP(sK53_skl,sK51_skl)
| memberP(sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f463,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f422,f428]) ).
fof(f464,plain,
( ~ memberP(sK52_skl,sK51_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f423,f463]) ).
fof(f466,plain,
( ~ memberP(sK52_skl,sK51_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f425]) ).
fof(f469,plain,
( ~ memberP(sK53_skl,sK51_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f424,f463]) ).
fof(f471,plain,
( ~ memberP(sK53_skl,sK51_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f425]) ).
fof(f478,plain,
( ~ memberP(sK52_skl,sK51_skl)
| ~ ssList(sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f426]) ).
fof(f479,plain,
( ~ memberP(sK53_skl,sK51_skl)
| ~ ssList(sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f426]) ).
fof(f480,plain,
( memberP(sK52_skl,sK51_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f479,f429]) ).
fof(f481,plain,
memberP(sK52_skl,sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f480,f427]) ).
fof(f482,plain,
~ ssList(sK53_skl),
inference(backward_subsumption_resolution,[status(thm)],[f478,f481]) ).
fof(f483,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f482,f427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC185+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 08:08:14 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.51 % Elapsed time: 0.069031 seconds
% 0.18/0.51 % CPU time: 0.171932 seconds
% 0.18/0.51 % Total memory used: 62.185 MB
% 0.18/0.51 % Net memory used: 62.096 MB
%------------------------------------------------------------------------------