%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO452+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:25:04 PM UTC 2026
% Result : Theorem 2.24s 7.88s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 19 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 2 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 25 ( 21 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3176,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3177,conjecture,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3178,negated_conjecture,
~ ! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) ),
inference(negated_conjecture,[status(cth)],[f3177]) ).
fof(f13984,plain,
! [N,M,F0] :
( ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))
| ~ p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) ),
inference(pre_NNF_transformation,[status(thm)],[f3176]) ).
fof(f13985,plain,
! [X0,X1,X2,X3] :
( s(cart(real,X1),i(s(fun(cart(real,X0),cart(real,X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(real,X0),cart(real,X1))),matrixu_vectoru_mul),s(cart(cart(real,X0),X1),i(s(fun(fun(cart(real,X0),cart(real,X1)),cart(cart(real,X0),X1)),matrix),s(fun(cart(real,X0),cart(real,X1)),X2))))),s(cart(real,X0),X3))) = s(cart(real,X1),i(s(fun(cart(real,X0),cart(real,X1)),X2),s(cart(real,X0),X3)))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),cart(real,X1)),bool),linear),s(fun(cart(real,X0),cart(real,X1)),X2)))) ),
inference(cnf_transformation,[status(thm)],[f13984]) ).
fof(f13986,plain,
? [N,M,F0] :
( ? [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) != s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X)))
& p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) ),
inference(pre_NNF_transformation,[status(thm)],[f3178]) ).
fof(f13987,plain,
( s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl),s(cart(real,sK3367_skl),sK3369_skl))) != s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),i(s(fun(cart(cart(real,sK3367_skl),sK3366_skl),fun(cart(real,sK3367_skl),cart(real,sK3366_skl))),matrixu_vectoru_mul),s(cart(cart(real,sK3367_skl),sK3366_skl),i(s(fun(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),cart(cart(real,sK3367_skl),sK3366_skl)),matrix),s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl))))),s(cart(real,sK3367_skl),sK3369_skl)))
& p(s(bool,i(s(fun(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),bool),linear),s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3366_skl,sK3367_skl,sK3368_skl,sK3369_skl]),skolemize(N,sK3366_skl),skolemize(M,sK3367_skl),skolemize(F0,sK3368_skl),skolemize(X,sK3369_skl)],[f13986]) ).
fof(f13988,plain,
p(s(bool,i(s(fun(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),bool),linear),s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl)))),
inference(cnf_transformation,[status(thm)],[f13987]) ).
fof(f13989,plain,
s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl),s(cart(real,sK3367_skl),sK3369_skl))) != s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),i(s(fun(cart(cart(real,sK3367_skl),sK3366_skl),fun(cart(real,sK3367_skl),cart(real,sK3366_skl))),matrixu_vectoru_mul),s(cart(cart(real,sK3367_skl),sK3366_skl),i(s(fun(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),cart(cart(real,sK3367_skl),sK3366_skl)),matrix),s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl))))),s(cart(real,sK3367_skl),sK3369_skl))),
inference(cnf_transformation,[status(thm)],[f13987]) ).
fof(f19556,plain,
! [X0] : s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),i(s(fun(cart(cart(real,sK3367_skl),sK3366_skl),fun(cart(real,sK3367_skl),cart(real,sK3366_skl))),matrixu_vectoru_mul),s(cart(cart(real,sK3367_skl),sK3366_skl),i(s(fun(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),cart(cart(real,sK3367_skl),sK3366_skl)),matrix),s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl))))),s(cart(real,sK3367_skl),X0))) = s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl),s(cart(real,sK3367_skl),X0))),
inference(resolution,[status(thm)],[f13985,f13988]) ).
fof(f20156,plain,
s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl),s(cart(real,sK3367_skl),sK3369_skl))) != s(cart(real,sK3366_skl),i(s(fun(cart(real,sK3367_skl),cart(real,sK3366_skl)),sK3368_skl),s(cart(real,sK3367_skl),sK3369_skl))),
inference(backward_demodulation,[status(thm)],[f19556,f13989]) ).
fof(f20218,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f20156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO452+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 16:18:57 UTC 2026
% 0.10/5.38 % CPUTime :
% 2.05/7.36 % Drodi V4.1.1
% 2.24/7.88 % Refutation found
% 2.24/7.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.24/7.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.71/8.08 % Elapsed time: 2.670177 seconds
% 4.71/8.08 % CPU time: 6.274739 seconds
% 4.71/8.08 % Total memory used: 1.442 GB
% 4.71/8.08 % Net memory used: 1.439 GB
%------------------------------------------------------------------------------