%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC213+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 02:40:25 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 161 ( 60 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 201 ( 67 ~; 57 |; 61 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 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 : 62 ( 38 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
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 )
| neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = W
& ssList(X6) )
& app(cons(X4,nil),X5) = Z
& ssList(X5) )
& ssItem(X4) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X1,nil),X3) = W
& ssList(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(app(Y,W),Z) != X ) ) )
| ~ neq(V,nil)
| 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 )
| neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = W
& ssList(X6) )
& app(cons(X4,nil),X5) = Z
& ssList(X5) )
& ssItem(X4) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X1,nil),X3) = W
& ssList(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(app(Y,W),Z) != X ) ) )
| ~ neq(V,nil)
| 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(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ neq(U,nil)
& ? [Y] :
( ? [Z] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != W
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != Z
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( app(cons(X1,nil),X3) != W
| ~ ssList(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& neq(V,nil)
& 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 )
& ~ neq(U,nil)
& ? [Y] :
( ? [Z] :
( ! [X4] :
( ! [X6] :
( app(X6,cons(X4,nil)) != W
| ~ ssList(X6) )
| ! [X5] :
( app(cons(X4,nil),X5) != Z
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X1] :
( ! [X3] :
( app(cons(X1,nil),X3) != W
| ~ ssList(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& neq(V,nil)
& 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 )
& ~ neq(sK47_skl,nil)
& ! [X4] :
( ! [X6] :
( app(X6,cons(X4,nil)) != sK49_skl
| ~ ssList(X6) )
| ! [X5] :
( app(cons(X4,nil),X5) != sK52_skl
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X1] :
( ! [X3] :
( app(cons(X1,nil),X3) != sK49_skl
| ~ ssList(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != sK51_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(sK49_skl)
& app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_skl)
& neq(sK48_skl,nil)
& 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(Z,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,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,plain,
~ neq(sK47_skl,nil),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f466,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f467,plain,
~ neq(sK49_skl,nil),
inference(forward_demodulation,[status(thm)],[f423,f431]) ).
fof(f470,plain,
( sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f220,f467]) ).
fof(f473,plain,
( sK49_skl = nil
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f420]) ).
fof(f476,plain,
( nil != nil
| nil = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f482,f432]) ).
fof(f478,plain,
~ neq(nil,nil),
inference(backward_demodulation,[status(thm)],[f482,f467]) ).
fof(f482,plain,
sK49_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f473,f223]) ).
fof(f483,plain,
nil = sK50_skl,
inference(trivial_equality_resolution,[status(thm)],[f476]) ).
fof(f484,plain,
neq(nil,nil),
inference(backward_demodulation,[status(thm)],[f483,f466]) ).
fof(f490,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f484,f478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 08:04:57 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.059778 seconds
% 0.13/0.42 % CPU time: 0.157866 seconds
% 0.13/0.42 % Total memory used: 83.114 MB
% 0.13/0.42 % Net memory used: 82.999 MB
%------------------------------------------------------------------------------