TSTP Solution File: GEO461+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GEO461+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:08:58 EDT 2023
% Result : Theorem 12.47s 2.82s
% Output : CNFRefutation 13.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 23 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 7 |; 4 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 16 con; 0-2 aty)
% Number of variables : 77 (; 72 !; 5 ?)
% 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(f2890,axiom,
! [Q104658,X] : s(real,i(s(fun(prod(cart(real,Q104658),cart(real,Q104658)),real),distance),s(prod(cart(real,Q104658),cart(real,Q104658)),i(s(fun(cart(real,Q104658),prod(cart(real,Q104658),cart(real,Q104658))),i(s(fun(cart(real,Q104658),fun(cart(real,Q104658),prod(cart(real,Q104658),cart(real,Q104658)))),c_),s(cart(real,Q104658),X))),s(cart(real,Q104658),X))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2895,axiom,
! [Q104818,X,Y] :
( s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q104818),X) = s(cart(real,Q104818),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2907,axiom,
! [Q105385,X] :
( s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),X))),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X)))
& s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q105385),X))))) = s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3279,axiom,
! [M,N,X1,Y1,X2,Y2] : s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X1))),s(cart(real,N),Y1))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X2))),s(cart(real,N),Y2))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),X1))),s(cart(real,M),X2))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),Y1))),s(cart(real,N),Y2))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3291,axiom,
! [Q121236,Q121234,Y] : s(real,i(s(fun(cart(real,finite_sum(Q121236,Q121234)),real),vectoru_norm),s(cart(real,finite_sum(Q121236,Q121234)),i(s(fun(cart(real,Q121234),cart(real,finite_sum(Q121236,Q121234))),i(s(fun(cart(real,Q121236),fun(cart(real,Q121234),cart(real,finite_sum(Q121236,Q121234)))),pastecart),s(cart(real,Q121236),i(s(fun(num,cart(real,Q121236)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q121234),Y))))) = s(real,i(s(fun(cart(real,Q121234),real),vectoru_norm),s(cart(real,Q121234),Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3293,conjecture,
! [Q121316,Q121317,X,Y,YI_] : s(real,i(s(fun(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),real),distance),s(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317)))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))))),c_),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),Y))))),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),YI_))))))) = s(real,i(s(fun(prod(cart(real,Q121317),cart(real,Q121317)),real),distance),s(prod(cart(real,Q121317),cart(real,Q121317)),i(s(fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317))),i(s(fun(cart(real,Q121317),fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317)))),c_),s(cart(real,Q121317),Y))),s(cart(real,Q121317),YI_))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3294,negated_conjecture,
~ ! [Q121316,Q121317,X,Y,YI_] : s(real,i(s(fun(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),real),distance),s(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317)))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))))),c_),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),Y))))),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),YI_))))))) = s(real,i(s(fun(prod(cart(real,Q121317),cart(real,Q121317)),real),distance),s(prod(cart(real,Q121317),cart(real,Q121317)),i(s(fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317))),i(s(fun(cart(real,Q121317),fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317)))),c_),s(cart(real,Q121317),Y))),s(cart(real,Q121317),YI_))))),
inference(negated_conjecture,[status(cth)],[f3293]) ).
fof(f13019,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(esa)],[f2817]) ).
fof(f13211,plain,
! [X0,X1] : 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),X1))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
inference(cnf_transformation,[status(esa)],[f2890]) ).
fof(f13216,plain,
! [Q104818,X,Y] :
( ( s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,Q104818),X) = s(cart(real,Q104818),Y) )
& ( s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,Q104818),X) != s(cart(real,Q104818),Y) ) ),
inference(NNF_transformation,[status(esa)],[f2895]) ).
fof(f13217,plain,
( ! [Q104818,X,Y] :
( s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,Q104818),X) = s(cart(real,Q104818),Y) )
& ! [Q104818,X,Y] :
( s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,Q104818),X) != s(cart(real,Q104818),Y) ) ),
inference(miniscoping,[status(esa)],[f13216]) ).
fof(f13218,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(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,X0),X1) = s(cart(real,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f13217]) ).
fof(f13250,plain,
( ! [Q105385,X] : s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),X))),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X)))
& ! [Q105385,X] : s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q105385),X))))) = s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X))) ),
inference(miniscoping,[status(esa)],[f2907]) ).
fof(f13251,plain,
! [X0,X1] : 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),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1))),
inference(cnf_transformation,[status(esa)],[f13250]) ).
fof(f14352,plain,
! [X0,X1,X2,X3,X4,X5] : s(cart(real,finite_sum(X0,X1)),i(s(fun(cart(real,finite_sum(X0,X1)),cart(real,finite_sum(X0,X1))),i(s(fun(cart(real,finite_sum(X0,X1)),fun(cart(real,finite_sum(X0,X1)),cart(real,finite_sum(X0,X1)))),vectoru_sub),s(cart(real,finite_sum(X0,X1)),i(s(fun(cart(real,X1),cart(real,finite_sum(X0,X1))),i(s(fun(cart(real,X0),fun(cart(real,X1),cart(real,finite_sum(X0,X1)))),pastecart),s(cart(real,X0),X2))),s(cart(real,X1),X3))))),s(cart(real,finite_sum(X0,X1)),i(s(fun(cart(real,X1),cart(real,finite_sum(X0,X1))),i(s(fun(cart(real,X0),fun(cart(real,X1),cart(real,finite_sum(X0,X1)))),pastecart),s(cart(real,X0),X4))),s(cart(real,X1),X5))))) = s(cart(real,finite_sum(X0,X1)),i(s(fun(cart(real,X1),cart(real,finite_sum(X0,X1))),i(s(fun(cart(real,X0),fun(cart(real,X1),cart(real,finite_sum(X0,X1)))),pastecart),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),X4))))),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_sub),s(cart(real,X1),X3))),s(cart(real,X1),X5))))),
inference(cnf_transformation,[status(esa)],[f3279]) ).
fof(f14373,plain,
! [X0,X1,X2] : s(real,i(s(fun(cart(real,finite_sum(X0,X1)),real),vectoru_norm),s(cart(real,finite_sum(X0,X1)),i(s(fun(cart(real,X1),cart(real,finite_sum(X0,X1))),i(s(fun(cart(real,X0),fun(cart(real,X1),cart(real,finite_sum(X0,X1)))),pastecart),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,X1),X2))))) = s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),X2))),
inference(cnf_transformation,[status(esa)],[f3291]) ).
fof(f14375,plain,
? [Q121316,Q121317,X,Y,YI_] : s(real,i(s(fun(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),real),distance),s(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317)))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))))),c_),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),Y))))),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),YI_))))))) != s(real,i(s(fun(prod(cart(real,Q121317),cart(real,Q121317)),real),distance),s(prod(cart(real,Q121317),cart(real,Q121317)),i(s(fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317))),i(s(fun(cart(real,Q121317),fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317)))),c_),s(cart(real,Q121317),Y))),s(cart(real,Q121317),YI_))))),
inference(pre_NNF_transformation,[status(esa)],[f3294]) ).
fof(f14376,plain,
s(real,i(s(fun(prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),real),distance),s(prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450)))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),fun(cart(real,finite_sum(sk0_3449,sk0_3450)),prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))))),c_),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3452))))),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3453))))))) != s(real,i(s(fun(prod(cart(real,sk0_3450),cart(real,sk0_3450)),real),distance),s(prod(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),prod(cart(real,sk0_3450),cart(real,sk0_3450))),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),prod(cart(real,sk0_3450),cart(real,sk0_3450)))),c_),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(skolemization,[status(esa)],[f14375]) ).
fof(f14377,plain,
s(real,i(s(fun(prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),real),distance),s(prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450)))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),fun(cart(real,finite_sum(sk0_3449,sk0_3450)),prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))))),c_),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3452))))),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3453))))))) != s(real,i(s(fun(prod(cart(real,sk0_3450),cart(real,sk0_3450)),real),distance),s(prod(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),prod(cart(real,sk0_3450),cart(real,sk0_3450))),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),prod(cart(real,sk0_3450),cart(real,sk0_3450)))),c_),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(cnf_transformation,[status(esa)],[f14376]) ).
fof(f17093,plain,
s(real,i(s(fun(prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),real),distance),s(prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450)))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),fun(cart(real,finite_sum(sk0_3449,sk0_3450)),prod(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))))),c_),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3452))))),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3453))))))) != s(real,i(s(fun(cart(real,sk0_3450),real),vectoru_norm),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(backward_demodulation,[status(thm)],[f13019,f14377]) ).
fof(f17094,plain,
s(real,i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),real),vectoru_norm),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),fun(cart(real,finite_sum(sk0_3449,sk0_3450)),cart(real,finite_sum(sk0_3449,sk0_3450)))),vectoru_sub),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3452))))),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3450),sk0_3453))))))) != s(real,i(s(fun(cart(real,sk0_3450),real),vectoru_norm),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(forward_demodulation,[status(thm)],[f13019,f17093]) ).
fof(f17131,plain,
! [X0,X1] : 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),X1))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
inference(forward_demodulation,[status(thm)],[f13019,f13211]) ).
fof(f17639,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(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,X0),X1) = s(cart(real,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f13019,f13218]) ).
fof(f17916,plain,
! [X0,X1] : 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),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1))),
inference(forward_demodulation,[status(thm)],[f13019,f13251]) ).
fof(f17953,plain,
! [X0,X1] :
( s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,X0),X1) = s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ),
inference(paramodulation,[status(thm)],[f17916,f17639]) ).
fof(f18095,plain,
! [X0,X1] : 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),X1))) = s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
inference(resolution,[status(thm)],[f17953,f17131]) ).
fof(f20786,plain,
s(real,i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),real),vectoru_norm),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),i(s(fun(cart(real,sk0_3449),cart(real,sk0_3449)),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3449),cart(real,sk0_3449))),vectoru_sub),s(cart(real,sk0_3449),sk0_3451))),s(cart(real,sk0_3449),sk0_3451))))),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))))) != s(real,i(s(fun(cart(real,sk0_3450),real),vectoru_norm),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(backward_demodulation,[status(thm)],[f14352,f17094]) ).
fof(f21699,plain,
s(real,i(s(fun(cart(real,finite_sum(sk0_3449,sk0_3450)),real),vectoru_norm),s(cart(real,finite_sum(sk0_3449,sk0_3450)),i(s(fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450))),i(s(fun(cart(real,sk0_3449),fun(cart(real,sk0_3450),cart(real,finite_sum(sk0_3449,sk0_3450)))),pastecart),s(cart(real,sk0_3449),i(s(fun(num,cart(real,sk0_3449)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))))) != s(real,i(s(fun(cart(real,sk0_3450),real),vectoru_norm),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(backward_demodulation,[status(thm)],[f18095,f20786]) ).
fof(f21700,plain,
s(real,i(s(fun(cart(real,sk0_3450),real),vectoru_norm),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))) != s(real,i(s(fun(cart(real,sk0_3450),real),vectoru_norm),s(cart(real,sk0_3450),i(s(fun(cart(real,sk0_3450),cart(real,sk0_3450)),i(s(fun(cart(real,sk0_3450),fun(cart(real,sk0_3450),cart(real,sk0_3450))),vectoru_sub),s(cart(real,sk0_3450),sk0_3452))),s(cart(real,sk0_3450),sk0_3453))))),
inference(forward_demodulation,[status(thm)],[f14373,f21699]) ).
fof(f21701,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f21700]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO461+1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 12:04:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.09/1.32 % Drodi V3.5.1
% 12.47/2.82 % Refutation found
% 12.47/2.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.47/2.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.59/2.98 % Elapsed time: 2.614400 seconds
% 13.59/2.98 % CPU time: 13.229668 seconds
% 13.59/2.98 % Memory used: 1.476 GB
%------------------------------------------------------------------------------