%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO443+1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 04:20:45 PM UTC 2026
% Result : Theorem 18.64s 12.57s
% Output : CNFRefutation 18.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 24 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aDISTu_SYM,conjecture,
! [X1049,X1,X8] : s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X1))),s(cart(real,X1049),X8))))) = s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X8))),s(cart(real,X1049),X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aDISTu_SYM) ).
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/sandbox2/benchmark/theBenchmark.p',adist) ).
fof(aNORMu_SUB,axiom,
! [X1018,X1,X8] : s(real,i(s(fun(cart(real,X1018),real),vectoru_norm),s(cart(real,X1018),i(s(fun(cart(real,X1018),cart(real,X1018)),i(s(fun(cart(real,X1018),fun(cart(real,X1018),cart(real,X1018))),vectoru_sub),s(cart(real,X1018),X1))),s(cart(real,X1018),X8))))) = s(real,i(s(fun(cart(real,X1018),real),vectoru_norm),s(cart(real,X1018),i(s(fun(cart(real,X1018),cart(real,X1018)),i(s(fun(cart(real,X1018),fun(cart(real,X1018),cart(real,X1018))),vectoru_sub),s(cart(real,X1018),X8))),s(cart(real,X1018),X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNORMu_SUB) ).
fof(c_0_3,negated_conjecture,
~ ! [X1049,X1,X8] : s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X1))),s(cart(real,X1049),X8))))) = s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X8))),s(cart(real,X1049),X1))))),
inference(assume_negation,[status(cth)],[aDISTu_SYM]) ).
fof(c_0_4,negated_conjecture,
s(real,i(s(fun(prod(cart(real,esk3350_0),cart(real,esk3350_0)),real),distance),s(prod(cart(real,esk3350_0),cart(real,esk3350_0)),i(s(fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0))),i(s(fun(cart(real,esk3350_0),fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0)))),c_),s(cart(real,esk3350_0),esk3351_0))),s(cart(real,esk3350_0),esk3352_0))))) != s(real,i(s(fun(prod(cart(real,esk3350_0),cart(real,esk3350_0)),real),distance),s(prod(cart(real,esk3350_0),cart(real,esk3350_0)),i(s(fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0))),i(s(fun(cart(real,esk3350_0),fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0)))),c_),s(cart(real,esk3350_0),esk3352_0))),s(cart(real,esk3350_0),esk3351_0))))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X25753,X25754,X25755] : s(real,i(s(fun(prod(cart(real,X25753),cart(real,X25753)),real),distance),s(prod(cart(real,X25753),cart(real,X25753)),i(s(fun(cart(real,X25753),prod(cart(real,X25753),cart(real,X25753))),i(s(fun(cart(real,X25753),fun(cart(real,X25753),prod(cart(real,X25753),cart(real,X25753)))),c_),s(cart(real,X25753),X25754))),s(cart(real,X25753),X25755))))) = s(real,i(s(fun(cart(real,X25753),real),vectoru_norm),s(cart(real,X25753),i(s(fun(cart(real,X25753),cart(real,X25753)),i(s(fun(cart(real,X25753),fun(cart(real,X25753),cart(real,X25753))),vectoru_sub),s(cart(real,X25753),X25754))),s(cart(real,X25753),X25755))))),
inference(variable_rename,[status(thm)],[adist]) ).
fof(c_0_6,plain,
! [X25812,X25813,X25814] : s(real,i(s(fun(cart(real,X25812),real),vectoru_norm),s(cart(real,X25812),i(s(fun(cart(real,X25812),cart(real,X25812)),i(s(fun(cart(real,X25812),fun(cart(real,X25812),cart(real,X25812))),vectoru_sub),s(cart(real,X25812),X25813))),s(cart(real,X25812),X25814))))) = s(real,i(s(fun(cart(real,X25812),real),vectoru_norm),s(cart(real,X25812),i(s(fun(cart(real,X25812),cart(real,X25812)),i(s(fun(cart(real,X25812),fun(cart(real,X25812),cart(real,X25812))),vectoru_sub),s(cart(real,X25812),X25814))),s(cart(real,X25812),X25813))))),
inference(variable_rename,[status(thm)],[aNORMu_SUB]) ).
cnf(c_0_7,negated_conjecture,
s(real,i(s(fun(prod(cart(real,esk3350_0),cart(real,esk3350_0)),real),distance),s(prod(cart(real,esk3350_0),cart(real,esk3350_0)),i(s(fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0))),i(s(fun(cart(real,esk3350_0),fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0)))),c_),s(cart(real,esk3350_0),esk3351_0))),s(cart(real,esk3350_0),esk3352_0))))) != s(real,i(s(fun(prod(cart(real,esk3350_0),cart(real,esk3350_0)),real),distance),s(prod(cart(real,esk3350_0),cart(real,esk3350_0)),i(s(fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0))),i(s(fun(cart(real,esk3350_0),fun(cart(real,esk3350_0),prod(cart(real,esk3350_0),cart(real,esk3350_0)))),c_),s(cart(real,esk3350_0),esk3352_0))),s(cart(real,esk3350_0),esk3351_0))))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,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_5]) ).
cnf(c_0_9,plain,
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))))) = 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),X3))),s(cart(real,X1),X2))))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO443+1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % 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 17:54:43 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 18.64/12.57 % Version : CSE_E---1.7
% 18.64/12.57 % Problem : theBenchmark.p
% 18.64/12.57 % SZS status Theorem for theBenchmark.p
% 18.64/12.57 % SZS output start CNFRefutation
% See solution above
% 18.74/12.61 % Total time : 10.255s
%------------------------------------------------------------------------------