%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO450+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 : 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 12:25:04 PM UTC 2026
% Result : Theorem 2.18s 2.97s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 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 : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 31 ( 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f200,axiom,
! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3104,axiom,
! [Q114603,Q114604,A5] : s(cart(cart(real,Q114603),Q114604),i(s(fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604)),i(s(fun(cart(cart(real,Q114603),Q114604),fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604))),matrixu_add),s(cart(cart(real,Q114603),Q114604),i(s(fun(num,cart(cart(real,Q114603),Q114604)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,Q114603),Q114604),A5))) = s(cart(cart(real,Q114603),Q114604),A5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3108,axiom,
! [N,M,A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),B0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3135,conjecture,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3136,negated_conjecture,
~ ! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))),
inference(negated_conjecture,[status(cth)],[f3135]) ).
fof(f4153,plain,
! [X0] : s(num,i(s(fun(num,num),numeral),s(num,X0))) = s(num,X0),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f13815,plain,
! [X0,X1,X2] : s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_add),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,X0),X1),X2))) = s(cart(cart(real,X0),X1),X2),
inference(cnf_transformation,[status(thm)],[f3104]) ).
fof(f13819,plain,
! [X0,X1,X2,X3] : s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_sub),s(cart(cart(real,X0),X1),X2))),s(cart(cart(real,X0),X1),X3))) = s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_add),s(cart(cart(real,X0),X1),X2))),s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),matrixu_neg),s(cart(cart(real,X0),X1),X3))))),
inference(cnf_transformation,[status(thm)],[f3108]) ).
fof(f13846,plain,
? [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) != s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))),
inference(pre_NNF_transformation,[status(thm)],[f3136]) ).
fof(f13847,plain,
s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl))),matrixu_sub),s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(num,cart(cart(real,sK3338_skl),sK3339_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))) != s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3338_skl,sK3339_skl,sK3340_skl]),skolemize(N,sK3338_skl),skolemize(M,sK3339_skl),skolemize(A5,sK3340_skl)],[f13846]) ).
fof(f13848,plain,
s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl))),matrixu_sub),s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(num,cart(cart(real,sK3338_skl),sK3339_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))) != s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))),
inference(cnf_transformation,[status(thm)],[f13847]) ).
fof(f16381,plain,
s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl))),matrixu_sub),s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(num,cart(cart(real,sK3338_skl),sK3339_skl)),mat),s(num,u_0))))),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))) != s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))),
inference(backward_demodulation,[status(thm)],[f4153,f13848]) ).
fof(f16458,plain,
! [X0,X1,X2] : s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_add),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,u_0))))),s(cart(cart(real,X0),X1),X2))) = s(cart(cart(real,X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f4153,f13815]) ).
fof(f16827,plain,
! [X0,X1,X2] : s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_sub),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,u_0))))),s(cart(cart(real,X0),X1),X2))) = s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),matrixu_neg),s(cart(cart(real,X0),X1),X2))),
inference(paramodulation,[status(thm)],[f16458,f13819]) ).
fof(f16909,plain,
s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))) != s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl))),
inference(backward_demodulation,[status(thm)],[f16827,f16381]) ).
fof(f16945,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f16909]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO450+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n020.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sun Sep 20 16:18:34 UTC 2026
% 0.11/0.57 % CPUTime :
% 2.05/2.54 % Drodi V4.1.1
% 2.18/2.97 % Refutation found
% 2.18/2.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.18/2.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.30/3.16 % Elapsed time: 2.566028 seconds
% 3.30/3.16 % CPU time: 5.382625 seconds
% 3.30/3.16 % Total memory used: 1.414 GB
% 3.30/3.16 % Net memory used: 1.410 GB
%------------------------------------------------------------------------------