%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC218+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 : n026.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 02:40:26 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 19 unt; 0 def)
% Number of atoms : 194 ( 71 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 214 ( 84 ~; 74 |; 27 &)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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 : 60 ( 53 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ! [X1] :
( ssItem(X1)
=> app(app(Y,cons(X1,nil)),Z) != W )
| app(Y,Z) != X ) ) )
| 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)
=> ( neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ! [X1] :
( ssItem(X1)
=> app(app(Y,cons(X1,nil)),Z) != W )
| app(Y,Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
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] :
( ~ neq(U,nil)
& ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(Y,cons(X1,nil)),Z) = W
& ssItem(X1) )
& app(Y,Z) = X
& 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,
( ~ neq(sK47_skl,nil)
& app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl) = sK49_skl
& ssItem(sK53_skl)
& app(sK51_skl,sK52_skl) = sK50_skl
& ssList(sK52_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,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl)],[f415]) ).
fof(f417,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
app(sK51_skl,sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssItem(sK53_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
~ neq(sK47_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f463,plain,
app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl) = sK47_skl,
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f465,plain,
( sK47_skl = nil
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f220,f428]) ).
fof(f468,plain,
( sK47_skl = nil
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f417]) ).
fof(f469,plain,
app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl) = nil,
inference(backward_demodulation,[status(thm)],[f474,f463]) ).
fof(f474,plain,
sK47_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f468,f223]) ).
fof(f493,plain,
( nil = sK52_skl
| ~ ssList(sK52_skl)
| ~ ssList(app(sK51_skl,cons(sK53_skl,nil))) ),
inference(resolution,[status(thm)],[f385,f469]) ).
fof(f499,plain,
( nil = sK52_skl
| ~ ssList(app(sK51_skl,cons(sK53_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f424]) ).
fof(f505,plain,
( nil = app(sK51_skl,cons(sK53_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssList(app(sK51_skl,cons(sK53_skl,nil))) ),
inference(resolution,[status(thm)],[f386,f469]) ).
fof(f511,plain,
( nil = app(sK51_skl,cons(sK53_skl,nil))
| ~ ssList(app(sK51_skl,cons(sK53_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f424]) ).
fof(f517,plain,
( ~ ssList(cons(sK53_skl,nil))
| ~ ssList(sK51_skl)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f499,f245]) ).
fof(f518,plain,
( ~ ssList(cons(sK53_skl,nil))
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f423]) ).
fof(f538,plain,
( ~ ssItem(sK53_skl)
| ~ ssList(nil)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f518,f222]) ).
fof(f539,plain,
( ~ ssItem(sK53_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f223]) ).
fof(f544,plain,
app(sK51_skl,nil) = sK50_skl,
inference(backward_demodulation,[status(thm)],[f546,f425]) ).
fof(f546,plain,
nil = sK52_skl,
inference(forward_subsumption_resolution,[status(thm)],[f539,f426]) ).
fof(f547,plain,
( sK50_skl = sK51_skl
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f544,f389]) ).
fof(f553,plain,
sK50_skl = sK51_skl,
inference(forward_subsumption_resolution,[status(thm)],[f547,f423]) ).
fof(f644,plain,
( nil = app(sK51_skl,cons(sK53_skl,nil))
| ~ ssList(app(sK50_skl,cons(sK53_skl,nil))) ),
inference(forward_demodulation,[status(thm)],[f553,f511]) ).
fof(f645,plain,
( nil = app(sK50_skl,cons(sK53_skl,nil))
| ~ ssList(app(sK50_skl,cons(sK53_skl,nil))) ),
inference(forward_demodulation,[status(thm)],[f553,f644]) ).
fof(f646,plain,
( ~ ssList(cons(sK53_skl,nil))
| ~ ssList(sK50_skl)
| nil = app(sK50_skl,cons(sK53_skl,nil)) ),
inference(resolution,[status(thm)],[f645,f245]) ).
fof(f647,plain,
( ~ ssList(cons(sK53_skl,nil))
| nil = app(sK50_skl,cons(sK53_skl,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f420]) ).
fof(f677,plain,
( nil = cons(sK53_skl,nil)
| ~ ssList(cons(sK53_skl,nil))
| ~ ssList(sK50_skl)
| ~ ssList(cons(sK53_skl,nil)) ),
inference(resolution,[status(thm)],[f647,f385]) ).
fof(f680,plain,
( nil = cons(sK53_skl,nil)
| ~ ssList(sK50_skl)
| ~ ssList(cons(sK53_skl,nil)) ),
inference(duplicate_literals_removal,[status(thm)],[f677]) ).
fof(f681,plain,
( nil = cons(sK53_skl,nil)
| ~ ssList(cons(sK53_skl,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f680,f420]) ).
fof(f778,plain,
( ~ ssItem(sK53_skl)
| ~ ssList(nil)
| nil = cons(sK53_skl,nil) ),
inference(resolution,[status(thm)],[f681,f222]) ).
fof(f779,plain,
( ~ ssItem(sK53_skl)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f235]) ).
fof(f781,plain,
~ ssItem(sK53_skl),
inference(forward_subsumption_resolution,[status(thm)],[f779,f223]) ).
fof(f782,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f426,f781]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 08:08:07 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.57 % Elapsed time: 0.124897 seconds
% 0.26/0.57 % CPU time: 0.212333 seconds
% 0.26/0.57 % Total memory used: 42.418 MB
% 0.26/0.57 % Net memory used: 42.297 MB
%------------------------------------------------------------------------------