%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC094+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 : n020.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 02:39:56 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 14 unt; 4 def)
% Number of atoms : 117 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 128 ( 50 ~; 43 |; 22 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 26 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = V
& app(app(Y,Z),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| X != W
| 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)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = V
& app(app(Y,Z),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| X != W
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != V
| app(app(Y,Z),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& X = W
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK48_skl
| app(app(Y,Z),X1) != sK47_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK50_skl = sK49_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f415]) ).
fof(f417,plain,
ssList(sK47_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,
sK50_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK48_skl
| app(app(X0,X1),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f457,plain,
sK48_skl = sK49_skl,
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f460,plain,
sK48_skl = sK47_skl,
inference(forward_demodulation,[status(thm)],[f422,f457]) ).
fof(f473,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f460,f424]) ).
fof(f475,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f477,plain,
app(nil,sK47_skl) = sK47_skl,
inference(resolution,[status(thm)],[f249,f417]) ).
fof(f480,definition,
( sQ0_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ0_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f491,plain,
! [X0] :
( app(app(nil,X0),sK47_skl) != sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f477,f473]) ).
fof(f494,definition,
! [X0] :
( sQ3_spl
<=> ( app(app(nil,X0),sK47_skl) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f495,plain,
! [X0] :
( ~ sQ3_spl
| app(app(nil,X0),sK47_skl) != sK47_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,definition,
( sQ4_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ4_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f491,f480,f494,f497]) ).
fof(f506,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f223]) ).
fof(f507,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f530,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f417]) ).
fof(f531,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f671,plain,
( ~ sQ3_spl
| app(nil,sK47_skl) != sK47_skl
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f475,f495]) ).
fof(f676,definition,
( sQ19_spl
<=> app(nil,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( sQ19_spl
| app(nil,sK47_skl) != sK47_skl ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f679,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f671,f480,f676,f494]) ).
fof(f680,plain,
( sQ19_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f477,f678]) ).
fof(f681,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f680]) ).
fof(f682,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f683,plain,
$false,
inference(sat_refutation,[status(thm)],[f500,f507,f531,f679,f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC094+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:56:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.079449 seconds
% 0.15/0.45 % CPU time: 0.196434 seconds
% 0.15/0.45 % Total memory used: 53.552 MB
% 0.15/0.45 % Net memory used: 53.220 MB
%------------------------------------------------------------------------------