%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC217+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 : n014.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 0.18s 5.49s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 13 unt; 6 def)
% Number of atoms : 144 ( 36 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 157 ( 58 ~; 50 |; 27 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 24 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| ( nil = X
& nil != W )
| neq(U,nil)
| ~ neq(V,nil)
| 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(X,nil)
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| ( nil = X
& nil != W )
| neq(U,nil)
| ~ 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(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& ~ neq(U,nil)
& 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,
( ( ~ neq(sK50_skl,nil)
| ( memberP(sK50_skl,sK51_skl)
& cons(sK51_skl,nil) = sK49_skl
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ~ neq(sK47_skl,nil)
& 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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
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(f423,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
~ neq(sK47_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| cons(sK51_skl,nil) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f436,definition,
( sQ2_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f439,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f436,f439]) ).
fof(f443,definition,
( sQ4_spl
<=> cons(sK51_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ4_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f443,f439]) ).
fof(f484,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f486,plain,
~ neq(sK49_skl,nil),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f500,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f441,f484]) ).
fof(f501,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f500]) ).
fof(f524,definition,
( sQ9_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( sQ9_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f534,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f538,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f419]) ).
fof(f539,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f543,plain,
( ~ sQ4_spl
| sK49_skl != nil
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f444,f225]) ).
fof(f551,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f543,f534,f436,f429,f443]) ).
fof(f552,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f223]) ).
fof(f553,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f556,plain,
( sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f220,f486]) ).
fof(f559,plain,
( sQ0_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f556,f524,f534,f429]) ).
fof(f560,plain,
$false,
inference(sat_refutation,[status(thm)],[f442,f446,f501,f539,f551,f553,f559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC217+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n014.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Mon Sep 21 08:05:40 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 0.18/5.49 % Refutation found
% 0.18/5.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.59 % Elapsed time: 0.117918 seconds
% 0.23/5.59 % CPU time: 0.121799 seconds
% 0.23/5.59 % Total memory used: 7.002 MB
% 0.23/5.59 % Net memory used: 6.997 MB
%------------------------------------------------------------------------------