%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO443+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:25:03 PM UTC 2026
% Result : Theorem 187.71s 24.77s
% Output : CNFRefutation 40.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 21 ( 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2817,axiom,
! [Q100698,X,Y] : s(real,i(s(fun(prod(cart(real,Q100698),cart(real,Q100698)),real),distance),s(prod(cart(real,Q100698),cart(real,Q100698)),i(s(fun(cart(real,Q100698),prod(cart(real,Q100698),cart(real,Q100698))),i(s(fun(cart(real,Q100698),fun(cart(real,Q100698),prod(cart(real,Q100698),cart(real,Q100698)))),c_),s(cart(real,Q100698),X))),s(cart(real,Q100698),Y))))) = s(real,i(s(fun(cart(real,Q100698),real),vectoru_norm),s(cart(real,Q100698),i(s(fun(cart(real,Q100698),cart(real,Q100698)),i(s(fun(cart(real,Q100698),fun(cart(real,Q100698),cart(real,Q100698))),vectoru_sub),s(cart(real,Q100698),X))),s(cart(real,Q100698),Y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2848,axiom,
! [Q102210,X,Y] : s(real,i(s(fun(cart(real,Q102210),real),vectoru_norm),s(cart(real,Q102210),i(s(fun(cart(real,Q102210),cart(real,Q102210)),i(s(fun(cart(real,Q102210),fun(cart(real,Q102210),cart(real,Q102210))),vectoru_sub),s(cart(real,Q102210),X))),s(cart(real,Q102210),Y))))) = s(real,i(s(fun(cart(real,Q102210),real),vectoru_norm),s(cart(real,Q102210),i(s(fun(cart(real,Q102210),cart(real,Q102210)),i(s(fun(cart(real,Q102210),fun(cart(real,Q102210),cart(real,Q102210))),vectoru_sub),s(cart(real,Q102210),Y))),s(cart(real,Q102210),X))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2891,conjecture,
! [Q104680,X,Y] : s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),X))),s(cart(real,Q104680),Y))))) = s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),Y))),s(cart(real,Q104680),X))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2892,negated_conjecture,
~ ! [Q104680,X,Y] : s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),X))),s(cart(real,Q104680),Y))))) = s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),Y))),s(cart(real,Q104680),X))))),
inference(negated_conjecture,[status(cth)],[f2891]) ).
fof(f12617,plain,
! [X0,X1,X2] : s(real,i(s(fun(prod(cart(real,X0),cart(real,X0)),real),distance),s(prod(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),prod(cart(real,X0),cart(real,X0))),i(s(fun(cart(real,X0),fun(cart(real,X0),prod(cart(real,X0),cart(real,X0)))),c_),s(cart(real,X0),X1))),s(cart(real,X0),X2))))) = s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_sub),s(cart(real,X0),X1))),s(cart(real,X0),X2))))),
inference(cnf_transformation,[status(thm)],[f2817]) ).
fof(f12692,plain,
! [X0,X1,X2] : s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_sub),s(cart(real,X0),X1))),s(cart(real,X0),X2))))) = s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_sub),s(cart(real,X0),X2))),s(cart(real,X0),X1))))),
inference(cnf_transformation,[status(thm)],[f2848]) ).
fof(f12810,plain,
? [Q104680,X,Y] : s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),X))),s(cart(real,Q104680),Y))))) != s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),Y))),s(cart(real,Q104680),X))))),
inference(pre_NNF_transformation,[status(thm)],[f2892]) ).
fof(f12811,plain,
s(real,i(s(fun(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),real),distance),s(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl))),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl)))),c_),s(cart(real,sK2957_skl),sK2958_skl))),s(cart(real,sK2957_skl),sK2959_skl))))) != s(real,i(s(fun(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),real),distance),s(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl))),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl)))),c_),s(cart(real,sK2957_skl),sK2959_skl))),s(cart(real,sK2957_skl),sK2958_skl))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2957_skl,sK2958_skl,sK2959_skl]),skolemize(Q104680,sK2957_skl),skolemize(X,sK2958_skl),skolemize(Y,sK2959_skl)],[f12810]) ).
fof(f12812,plain,
s(real,i(s(fun(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),real),distance),s(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl))),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl)))),c_),s(cart(real,sK2957_skl),sK2958_skl))),s(cart(real,sK2957_skl),sK2959_skl))))) != s(real,i(s(fun(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),real),distance),s(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl))),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl)))),c_),s(cart(real,sK2957_skl),sK2959_skl))),s(cart(real,sK2957_skl),sK2958_skl))))),
inference(cnf_transformation,[status(thm)],[f12811]) ).
fof(f20393,plain,
s(real,i(s(fun(cart(real,sK2957_skl),real),vectoru_norm),s(cart(real,sK2957_skl),i(s(fun(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),cart(real,sK2957_skl))),vectoru_sub),s(cart(real,sK2957_skl),sK2958_skl))),s(cart(real,sK2957_skl),sK2959_skl))))) != s(real,i(s(fun(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),real),distance),s(prod(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl))),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),prod(cart(real,sK2957_skl),cart(real,sK2957_skl)))),c_),s(cart(real,sK2957_skl),sK2959_skl))),s(cart(real,sK2957_skl),sK2958_skl))))),
inference(forward_demodulation,[status(thm)],[f12617,f12812]) ).
fof(f20394,plain,
s(real,i(s(fun(cart(real,sK2957_skl),real),vectoru_norm),s(cart(real,sK2957_skl),i(s(fun(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),cart(real,sK2957_skl))),vectoru_sub),s(cart(real,sK2957_skl),sK2958_skl))),s(cart(real,sK2957_skl),sK2959_skl))))) != s(real,i(s(fun(cart(real,sK2957_skl),real),vectoru_norm),s(cart(real,sK2957_skl),i(s(fun(cart(real,sK2957_skl),cart(real,sK2957_skl)),i(s(fun(cart(real,sK2957_skl),fun(cart(real,sK2957_skl),cart(real,sK2957_skl))),vectoru_sub),s(cart(real,sK2957_skl),sK2959_skl))),s(cart(real,sK2957_skl),sK2958_skl))))),
inference(forward_demodulation,[status(thm)],[f12617,f20393]) ).
fof(f20395,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20394,f12692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO443+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 16:11:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.89/1.14 % Drodi V4.1.1
% 187.71/24.77 % Refutation found
% 187.71/24.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 187.71/24.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.48/25.10 % Elapsed time: 24.707493 seconds
% 6.48/25.10 % CPU time: 189.442664 seconds
% 6.48/25.10 % Total memory used: 2.185 GB
% 6.48/25.10 % Net memory used: 2.172 GB
%------------------------------------------------------------------------------