%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC189+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 02:40:20 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 14 unt; 5 def)
% Number of atoms : 132 ( 33 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 138 ( 42 ~; 41 |; 34 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 44 ( 28 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( X3 = X4
| app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) != U ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = W
& Y != Z
& ssList(X2) )
& ssList(X1) )
& ssItem(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)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( X3 = X4
| app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) != U ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = W
& Y != Z
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( X3 != X4
& app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) = U
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != W
| Y = Z
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(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,
( sK51_skl != sK52_skl
& app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_skl)
& ssItem(sK51_skl)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != sK49_skl
| Y = Z
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(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,sK54_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X3,sK51_skl),skolemize(X4,sK52_skl),skolemize(X5,sK53_skl),skolemize(X6,sK54_skl)],[f415]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
! [X0,X1,X2,X3] :
( app(app(app(X2,cons(X0,nil)),cons(X1,nil)),X3) != sK49_skl
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
sK51_skl != sK52_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f486,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f422,f428]) ).
fof(f487,plain,
( sK51_skl = sK52_skl
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f423,f486]) ).
fof(f489,definition,
( sQ4_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( sQ4_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,definition,
( sQ5_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ5_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,definition,
( sQ6_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ6_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,definition,
( sQ7_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ7_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ8_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( ~ sQ8_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f487,f489,f492,f495,f498,f501]) ).
fof(f509,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f429]) ).
fof(f510,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f427]) ).
fof(f512,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f426]) ).
fof(f514,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f424]) ).
fof(f516,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f517,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f425]) ).
fof(f518,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
$false,
inference(sat_refutation,[status(thm)],[f504,f510,f512,f514,f516,f518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC189+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 08:08:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % 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: 0.062196 seconds
% 0.13/0.42 % CPU time: 0.165833 seconds
% 0.13/0.42 % Total memory used: 110.733 MB
% 0.13/0.42 % Net memory used: 110.563 MB
%------------------------------------------------------------------------------