%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO461+1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 : Tue May 5 04:21:22 PM UTC 2026
% Result : Theorem 22.60s 14.91s
% Output : CNFRefutation 22.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aDISTu_PASTECARTu_CANCELu_conjunct1,conjecture,
! [X1359,X1360,X1,X8,X252] : s(real,i(s(fun(prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360))),real),distance),s(prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360))),i(s(fun(cart(real,finite_sum(X1359,X1360)),prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360)))),i(s(fun(cart(real,finite_sum(X1359,X1360)),fun(cart(real,finite_sum(X1359,X1360)),prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360))))),c_),s(cart(real,finite_sum(X1359,X1360)),i(s(fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360))),i(s(fun(cart(real,X1359),fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360)))),pastecart),s(cart(real,X1359),X1))),s(cart(real,X1360),X8))))),s(cart(real,finite_sum(X1359,X1360)),i(s(fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360))),i(s(fun(cart(real,X1359),fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360)))),pastecart),s(cart(real,X1359),X1))),s(cart(real,X1360),X252))))))) = s(real,i(s(fun(prod(cart(real,X1360),cart(real,X1360)),real),distance),s(prod(cart(real,X1360),cart(real,X1360)),i(s(fun(cart(real,X1360),prod(cart(real,X1360),cart(real,X1360))),i(s(fun(cart(real,X1360),fun(cart(real,X1360),prod(cart(real,X1360),cart(real,X1360)))),c_),s(cart(real,X1360),X8))),s(cart(real,X1360),X252))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aDISTu_PASTECARTu_CANCELu_conjunct1) ).
fof(adist,axiom,
! [X1012,X1,X8] : s(real,i(s(fun(prod(cart(real,X1012),cart(real,X1012)),real),distance),s(prod(cart(real,X1012),cart(real,X1012)),i(s(fun(cart(real,X1012),prod(cart(real,X1012),cart(real,X1012))),i(s(fun(cart(real,X1012),fun(cart(real,X1012),prod(cart(real,X1012),cart(real,X1012)))),c_),s(cart(real,X1012),X1))),s(cart(real,X1012),X8))))) = s(real,i(s(fun(cart(real,X1012),real),vectoru_norm),s(cart(real,X1012),i(s(fun(cart(real,X1012),cart(real,X1012)),i(s(fun(cart(real,X1012),fun(cart(real,X1012),cart(real,X1012))),vectoru_sub),s(cart(real,X1012),X1))),s(cart(real,X1012),X8))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adist) ).
fof(aVECTORu_SUBu_REFL,axiom,
! [X975,X1] : s(cart(real,X975),i(s(fun(cart(real,X975),cart(real,X975)),i(s(fun(cart(real,X975),fun(cart(real,X975),cart(real,X975))),vectoru_sub),s(cart(real,X975),X1))),s(cart(real,X975),X1))) = s(cart(real,X975),i(s(fun(num,cart(real,X975)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aVECTORu_SUBu_REFL) ).
fof(aNUMERAL,axiom,
! [X84] : s(num,i(s(fun(num,num),numeral),s(num,X84))) = s(num,X84),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aNUMERAL) ).
fof(aNORMu_PASTECARTu_0u_conjunct1,axiom,
! [X1355,X1356,X8] : s(real,i(s(fun(cart(real,finite_sum(X1355,X1356)),real),vectoru_norm),s(cart(real,finite_sum(X1355,X1356)),i(s(fun(cart(real,X1356),cart(real,finite_sum(X1355,X1356))),i(s(fun(cart(real,X1355),fun(cart(real,X1356),cart(real,finite_sum(X1355,X1356)))),pastecart),s(cart(real,X1355),i(s(fun(num,cart(real,X1355)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,X1356),X8))))) = s(real,i(s(fun(cart(real,X1356),real),vectoru_norm),s(cart(real,X1356),X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNORMu_PASTECARTu_0u_conjunct1) ).
fof(aPASTECARTu_SUB,axiom,
! [X738,X733,X32,X100,X81,X101] : s(cart(real,finite_sum(X738,X733)),i(s(fun(cart(real,finite_sum(X738,X733)),cart(real,finite_sum(X738,X733))),i(s(fun(cart(real,finite_sum(X738,X733)),fun(cart(real,finite_sum(X738,X733)),cart(real,finite_sum(X738,X733)))),vectoru_sub),s(cart(real,finite_sum(X738,X733)),i(s(fun(cart(real,X733),cart(real,finite_sum(X738,X733))),i(s(fun(cart(real,X738),fun(cart(real,X733),cart(real,finite_sum(X738,X733)))),pastecart),s(cart(real,X738),X32))),s(cart(real,X733),X100))))),s(cart(real,finite_sum(X738,X733)),i(s(fun(cart(real,X733),cart(real,finite_sum(X738,X733))),i(s(fun(cart(real,X738),fun(cart(real,X733),cart(real,finite_sum(X738,X733)))),pastecart),s(cart(real,X738),X81))),s(cart(real,X733),X101))))) = s(cart(real,finite_sum(X738,X733)),i(s(fun(cart(real,X733),cart(real,finite_sum(X738,X733))),i(s(fun(cart(real,X738),fun(cart(real,X733),cart(real,finite_sum(X738,X733)))),pastecart),s(cart(real,X738),i(s(fun(cart(real,X738),cart(real,X738)),i(s(fun(cart(real,X738),fun(cart(real,X738),cart(real,X738))),vectoru_sub),s(cart(real,X738),X32))),s(cart(real,X738),X81))))),s(cart(real,X733),i(s(fun(cart(real,X733),cart(real,X733)),i(s(fun(cart(real,X733),fun(cart(real,X733),cart(real,X733))),vectoru_sub),s(cart(real,X733),X100))),s(cart(real,X733),X101))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPASTECARTu_SUB) ).
fof(c_0_6,negated_conjecture,
~ ! [X1359,X1360,X1,X8,X252] : s(real,i(s(fun(prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360))),real),distance),s(prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360))),i(s(fun(cart(real,finite_sum(X1359,X1360)),prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360)))),i(s(fun(cart(real,finite_sum(X1359,X1360)),fun(cart(real,finite_sum(X1359,X1360)),prod(cart(real,finite_sum(X1359,X1360)),cart(real,finite_sum(X1359,X1360))))),c_),s(cart(real,finite_sum(X1359,X1360)),i(s(fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360))),i(s(fun(cart(real,X1359),fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360)))),pastecart),s(cart(real,X1359),X1))),s(cart(real,X1360),X8))))),s(cart(real,finite_sum(X1359,X1360)),i(s(fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360))),i(s(fun(cart(real,X1359),fun(cart(real,X1360),cart(real,finite_sum(X1359,X1360)))),pastecart),s(cart(real,X1359),X1))),s(cart(real,X1360),X252))))))) = s(real,i(s(fun(prod(cart(real,X1360),cart(real,X1360)),real),distance),s(prod(cart(real,X1360),cart(real,X1360)),i(s(fun(cart(real,X1360),prod(cart(real,X1360),cart(real,X1360))),i(s(fun(cart(real,X1360),fun(cart(real,X1360),prod(cart(real,X1360),cart(real,X1360)))),c_),s(cart(real,X1360),X8))),s(cart(real,X1360),X252))))),
inference(assume_negation,[status(cth)],[aDISTu_PASTECARTu_CANCELu_conjunct1]) ).
fof(c_0_7,negated_conjecture,
s(real,i(s(fun(prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))),real),distance),s(prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0)))),i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),fun(cart(real,finite_sum(esk3846_0,esk3847_0)),prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))))),c_),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,esk3846_0),fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0)))),pastecart),s(cart(real,esk3846_0),esk3848_0))),s(cart(real,esk3847_0),esk3849_0))))),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,esk3846_0),fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0)))),pastecart),s(cart(real,esk3846_0),esk3848_0))),s(cart(real,esk3847_0),esk3850_0))))))) != s(real,i(s(fun(prod(cart(real,esk3847_0),cart(real,esk3847_0)),real),distance),s(prod(cart(real,esk3847_0),cart(real,esk3847_0)),i(s(fun(cart(real,esk3847_0),prod(cart(real,esk3847_0),cart(real,esk3847_0))),i(s(fun(cart(real,esk3847_0),fun(cart(real,esk3847_0),prod(cart(real,esk3847_0),cart(real,esk3847_0)))),c_),s(cart(real,esk3847_0),esk3849_0))),s(cart(real,esk3847_0),esk3850_0))))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X28135,X28136,X28137] : s(real,i(s(fun(prod(cart(real,X28135),cart(real,X28135)),real),distance),s(prod(cart(real,X28135),cart(real,X28135)),i(s(fun(cart(real,X28135),prod(cart(real,X28135),cart(real,X28135))),i(s(fun(cart(real,X28135),fun(cart(real,X28135),prod(cart(real,X28135),cart(real,X28135)))),c_),s(cart(real,X28135),X28136))),s(cart(real,X28135),X28137))))) = s(real,i(s(fun(cart(real,X28135),real),vectoru_norm),s(cart(real,X28135),i(s(fun(cart(real,X28135),cart(real,X28135)),i(s(fun(cart(real,X28135),fun(cart(real,X28135),cart(real,X28135))),vectoru_sub),s(cart(real,X28135),X28136))),s(cart(real,X28135),X28137))))),
inference(variable_rename,[status(thm)],[adist]) ).
fof(c_0_9,plain,
! [X28015,X28016] : s(cart(real,X28015),i(s(fun(cart(real,X28015),cart(real,X28015)),i(s(fun(cart(real,X28015),fun(cart(real,X28015),cart(real,X28015))),vectoru_sub),s(cart(real,X28015),X28016))),s(cart(real,X28015),X28016))) = s(cart(real,X28015),i(s(fun(num,cart(real,X28015)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
inference(variable_rename,[status(thm)],[aVECTORu_SUBu_REFL]) ).
fof(c_0_10,plain,
! [X16063] : s(num,i(s(fun(num,num),numeral),s(num,X16063))) = s(num,X16063),
inference(variable_rename,[status(thm)],[aNUMERAL]) ).
fof(c_0_11,plain,
! [X30519,X30520,X30521] : s(real,i(s(fun(cart(real,finite_sum(X30519,X30520)),real),vectoru_norm),s(cart(real,finite_sum(X30519,X30520)),i(s(fun(cart(real,X30520),cart(real,finite_sum(X30519,X30520))),i(s(fun(cart(real,X30519),fun(cart(real,X30520),cart(real,finite_sum(X30519,X30520)))),pastecart),s(cart(real,X30519),i(s(fun(num,cart(real,X30519)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,X30520),X30521))))) = s(real,i(s(fun(cart(real,X30520),real),vectoru_norm),s(cart(real,X30520),X30521))),
inference(variable_rename,[status(thm)],[aNORMu_PASTECARTu_0u_conjunct1]) ).
cnf(c_0_12,negated_conjecture,
s(real,i(s(fun(prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))),real),distance),s(prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0)))),i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),fun(cart(real,finite_sum(esk3846_0,esk3847_0)),prod(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))))),c_),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,esk3846_0),fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0)))),pastecart),s(cart(real,esk3846_0),esk3848_0))),s(cart(real,esk3847_0),esk3849_0))))),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,esk3846_0),fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0)))),pastecart),s(cart(real,esk3846_0),esk3848_0))),s(cart(real,esk3847_0),esk3850_0))))))) != s(real,i(s(fun(prod(cart(real,esk3847_0),cart(real,esk3847_0)),real),distance),s(prod(cart(real,esk3847_0),cart(real,esk3847_0)),i(s(fun(cart(real,esk3847_0),prod(cart(real,esk3847_0),cart(real,esk3847_0))),i(s(fun(cart(real,esk3847_0),fun(cart(real,esk3847_0),prod(cart(real,esk3847_0),cart(real,esk3847_0)))),c_),s(cart(real,esk3847_0),esk3849_0))),s(cart(real,esk3847_0),esk3850_0))))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
s(real,i(s(fun(prod(cart(real,X1),cart(real,X1)),real),distance),s(prod(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),prod(cart(real,X1),cart(real,X1))),i(s(fun(cart(real,X1),fun(cart(real,X1),prod(cart(real,X1),cart(real,X1)))),c_),s(cart(real,X1),X2))),s(cart(real,X1),X3))))) = s(real,i(s(fun(cart(real,X1),real),vectoru_norm),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),X2))),s(cart(real,X1),X3))))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X30463,X30464,X30465,X30466,X30467,X30468] : s(cart(real,finite_sum(X30463,X30464)),i(s(fun(cart(real,finite_sum(X30463,X30464)),cart(real,finite_sum(X30463,X30464))),i(s(fun(cart(real,finite_sum(X30463,X30464)),fun(cart(real,finite_sum(X30463,X30464)),cart(real,finite_sum(X30463,X30464)))),vectoru_sub),s(cart(real,finite_sum(X30463,X30464)),i(s(fun(cart(real,X30464),cart(real,finite_sum(X30463,X30464))),i(s(fun(cart(real,X30463),fun(cart(real,X30464),cart(real,finite_sum(X30463,X30464)))),pastecart),s(cart(real,X30463),X30465))),s(cart(real,X30464),X30466))))),s(cart(real,finite_sum(X30463,X30464)),i(s(fun(cart(real,X30464),cart(real,finite_sum(X30463,X30464))),i(s(fun(cart(real,X30463),fun(cart(real,X30464),cart(real,finite_sum(X30463,X30464)))),pastecart),s(cart(real,X30463),X30467))),s(cart(real,X30464),X30468))))) = s(cart(real,finite_sum(X30463,X30464)),i(s(fun(cart(real,X30464),cart(real,finite_sum(X30463,X30464))),i(s(fun(cart(real,X30463),fun(cart(real,X30464),cart(real,finite_sum(X30463,X30464)))),pastecart),s(cart(real,X30463),i(s(fun(cart(real,X30463),cart(real,X30463)),i(s(fun(cart(real,X30463),fun(cart(real,X30463),cart(real,X30463))),vectoru_sub),s(cart(real,X30463),X30465))),s(cart(real,X30463),X30467))))),s(cart(real,X30464),i(s(fun(cart(real,X30464),cart(real,X30464)),i(s(fun(cart(real,X30464),fun(cart(real,X30464),cart(real,X30464))),vectoru_sub),s(cart(real,X30464),X30466))),s(cart(real,X30464),X30468))))),
inference(variable_rename,[status(thm)],[aPASTECARTu_SUB]) ).
cnf(c_0_15,plain,
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),X2))),s(cart(real,X1),X2))) = s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
s(num,i(s(fun(num,num),numeral),s(num,X1))) = s(num,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
s(real,i(s(fun(cart(real,finite_sum(X1,X2)),real),vectoru_norm),s(cart(real,finite_sum(X1,X2)),i(s(fun(cart(real,X2),cart(real,finite_sum(X1,X2))),i(s(fun(cart(real,X1),fun(cart(real,X2),cart(real,finite_sum(X1,X2)))),pastecart),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,X2),X3))))) = s(real,i(s(fun(cart(real,X2),real),vectoru_norm),s(cart(real,X2),X3))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
s(real,i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),real),vectoru_norm),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,finite_sum(esk3846_0,esk3847_0)),fun(cart(real,finite_sum(esk3846_0,esk3847_0)),cart(real,finite_sum(esk3846_0,esk3847_0)))),vectoru_sub),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,esk3846_0),fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0)))),pastecart),s(cart(real,esk3846_0),esk3848_0))),s(cart(real,esk3847_0),esk3849_0))))),s(cart(real,finite_sum(esk3846_0,esk3847_0)),i(s(fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0))),i(s(fun(cart(real,esk3846_0),fun(cart(real,esk3847_0),cart(real,finite_sum(esk3846_0,esk3847_0)))),pastecart),s(cart(real,esk3846_0),esk3848_0))),s(cart(real,esk3847_0),esk3850_0))))))) != s(real,i(s(fun(cart(real,esk3847_0),real),vectoru_norm),s(cart(real,esk3847_0),i(s(fun(cart(real,esk3847_0),cart(real,esk3847_0)),i(s(fun(cart(real,esk3847_0),fun(cart(real,esk3847_0),cart(real,esk3847_0))),vectoru_sub),s(cart(real,esk3847_0),esk3849_0))),s(cart(real,esk3847_0),esk3850_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_19,plain,
s(cart(real,finite_sum(X1,X2)),i(s(fun(cart(real,finite_sum(X1,X2)),cart(real,finite_sum(X1,X2))),i(s(fun(cart(real,finite_sum(X1,X2)),fun(cart(real,finite_sum(X1,X2)),cart(real,finite_sum(X1,X2)))),vectoru_sub),s(cart(real,finite_sum(X1,X2)),i(s(fun(cart(real,X2),cart(real,finite_sum(X1,X2))),i(s(fun(cart(real,X1),fun(cart(real,X2),cart(real,finite_sum(X1,X2)))),pastecart),s(cart(real,X1),X3))),s(cart(real,X2),X4))))),s(cart(real,finite_sum(X1,X2)),i(s(fun(cart(real,X2),cart(real,finite_sum(X1,X2))),i(s(fun(cart(real,X1),fun(cart(real,X2),cart(real,finite_sum(X1,X2)))),pastecart),s(cart(real,X1),X5))),s(cart(real,X2),X6))))) = s(cart(real,finite_sum(X1,X2)),i(s(fun(cart(real,X2),cart(real,finite_sum(X1,X2))),i(s(fun(cart(real,X1),fun(cart(real,X2),cart(real,finite_sum(X1,X2)))),pastecart),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))))),s(cart(real,X2),i(s(fun(cart(real,X2),cart(real,X2)),i(s(fun(cart(real,X2),fun(cart(real,X2),cart(real,X2))),vectoru_sub),s(cart(real,X2),X4))),s(cart(real,X2),X6))))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
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),X2))),s(cart(real,X1),X2))) = s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,u_0))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
s(real,i(s(fun(cart(real,finite_sum(X1,X2)),real),vectoru_norm),s(cart(real,finite_sum(X1,X2)),i(s(fun(cart(real,X2),cart(real,finite_sum(X1,X2))),i(s(fun(cart(real,X1),fun(cart(real,X2),cart(real,finite_sum(X1,X2)))),pastecart),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,u_0))))),s(cart(real,X2),X3))))) = s(real,i(s(fun(cart(real,X2),real),vectoru_norm),s(cart(real,X2),X3))),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO461+1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:58:18 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 22.60/14.91 % Version : CSE_E---1.7
% 22.60/14.91 % Problem : theBenchmark.p
% 22.60/14.91 % SZS status Theorem for theBenchmark.p
% 22.60/14.91 % SZS output start CNFRefutation
% See solution above
% 22.60/14.95 % Total time : 12.509s
%------------------------------------------------------------------------------