TSTP Solution File: GEO460+1 by Etableau---0.67

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Etableau---0.67
% Problem  : GEO460+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s

% Computer : n014.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  : 600s
% DateTime : Sat Jul 16 04:10:08 EDT 2022

% Result   : Theorem 3.97s 4.18s
% Output   : CNFRefutation 3.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   39 (  39 unt;   0 def)
%            Number of atoms       :   39 (  38 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :   17 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  21 con; 0-2 aty)
%            Number of variables   :   51 (   2 sgn  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(aNORMu_PASTECARTu_0u_conjunct0,conjecture,
    ! [X1353,X1354,X1] : s(real,i(s(fun(cart(real,finite_sum(X1354,X1353)),real),vectoru_norm),s(cart(real,finite_sum(X1354,X1353)),i(s(fun(cart(real,X1353),cart(real,finite_sum(X1354,X1353))),i(s(fun(cart(real,X1354),fun(cart(real,X1353),cart(real,finite_sum(X1354,X1353)))),pastecart),s(cart(real,X1354),X1))),s(cart(real,X1353),i(s(fun(num,cart(real,X1353)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,X1354),real),vectoru_norm),s(cart(real,X1354),X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNORMu_PASTECARTu_0u_conjunct0) ).

fof(aNUMERAL,axiom,
    ! [X84] : s(num,i(s(fun(num,num),numeral),s(num,X84))) = s(num,X84),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aNUMERAL) ).

fof(aNORMu_PASTECART,axiom,
    ! [X1349,X1350,X1,X8] : s(real,i(s(fun(cart(real,finite_sum(X1349,X1350)),real),vectoru_norm),s(cart(real,finite_sum(X1349,X1350)),i(s(fun(cart(real,X1350),cart(real,finite_sum(X1349,X1350))),i(s(fun(cart(real,X1349),fun(cart(real,X1350),cart(real,finite_sum(X1349,X1350)))),pastecart),s(cart(real,X1349),X1))),s(cart(real,X1350),X8))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X1349),real),vectoru_norm),s(cart(real,X1349),X1))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X1350),real),vectoru_norm),s(cart(real,X1350),X8))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aNORMu_PASTECART) ).

fof(aCARDu_BOOL,axiom,
    s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aCARDu_BOOL) ).

fof(aNORMu_0,axiom,
    ! [X1015] : s(real,i(s(fun(cart(real,X1015),real),vectoru_norm),s(cart(real,X1015),i(s(fun(num,cart(real,X1015)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = 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/sandbox2/benchmark/theBenchmark.p',aNORMu_0) ).

fof(aREALu_POWu_2,axiom,
    ! [X1] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X1))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,X1))),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aREALu_POWu_2) ).

fof(aREALu_MULu_LZERO,axiom,
    ! [X1] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X1))) = 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/sandbox2/benchmark/Axioms/GEO010+0.ax',aREALu_MULu_LZERO) ).

fof(aREALu_ADDu_RID,axiom,
    ! [X1] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X1))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aREALu_ADDu_RID) ).

fof(aPOWu_2u_SQRTu_ABS,axiom,
    ! [X1] : s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X1))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X1))),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aPOWu_2u_SQRTu_ABS) ).

fof(aREALu_ABSu_NORM,axiom,
    ! [X1031,X1] : s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,X1031),real),vectoru_norm),s(cart(real,X1031),X1))))) = s(real,i(s(fun(cart(real,X1031),real),vectoru_norm),s(cart(real,X1031),X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aREALu_ABSu_NORM) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1353,X1354,X1] : s(real,i(s(fun(cart(real,finite_sum(X1354,X1353)),real),vectoru_norm),s(cart(real,finite_sum(X1354,X1353)),i(s(fun(cart(real,X1353),cart(real,finite_sum(X1354,X1353))),i(s(fun(cart(real,X1354),fun(cart(real,X1353),cart(real,finite_sum(X1354,X1353)))),pastecart),s(cart(real,X1354),X1))),s(cart(real,X1353),i(s(fun(num,cart(real,X1353)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,X1354),real),vectoru_norm),s(cart(real,X1354),X1))),
    inference(assume_negation,[status(cth)],[aNORMu_PASTECARTu_0u_conjunct0]) ).

fof(c_0_11,plain,
    ! [X2417] : s(num,i(s(fun(num,num),numeral),s(num,X2417))) = s(num,X2417),
    inference(variable_rename,[status(thm)],[aNUMERAL]) ).

fof(c_0_12,negated_conjecture,
    s(real,i(s(fun(cart(real,finite_sum(esk3847_0,esk3846_0)),real),vectoru_norm),s(cart(real,finite_sum(esk3847_0,esk3846_0)),i(s(fun(cart(real,esk3846_0),cart(real,finite_sum(esk3847_0,esk3846_0))),i(s(fun(cart(real,esk3847_0),fun(cart(real,esk3846_0),cart(real,finite_sum(esk3847_0,esk3846_0)))),pastecart),s(cart(real,esk3847_0),esk3848_0))),s(cart(real,esk3846_0),i(s(fun(num,cart(real,esk3846_0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) != s(real,i(s(fun(cart(real,esk3847_0),real),vectoru_norm),s(cart(real,esk3847_0),esk3848_0))),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_13,plain,
    ! [X16858,X16859,X16860,X16861] : s(real,i(s(fun(cart(real,finite_sum(X16858,X16859)),real),vectoru_norm),s(cart(real,finite_sum(X16858,X16859)),i(s(fun(cart(real,X16859),cart(real,finite_sum(X16858,X16859))),i(s(fun(cart(real,X16858),fun(cart(real,X16859),cart(real,finite_sum(X16858,X16859)))),pastecart),s(cart(real,X16858),X16860))),s(cart(real,X16859),X16861))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X16858),real),vectoru_norm),s(cart(real,X16858),X16860))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X16859),real),vectoru_norm),s(cart(real,X16859),X16861))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),
    inference(variable_rename,[status(thm)],[aNORMu_PASTECART]) ).

cnf(c_0_14,plain,
    s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),
    inference(split_conjunct,[status(thm)],[aCARDu_BOOL]) ).

cnf(c_0_15,plain,
    s(num,i(s(fun(num,num),numeral),s(num,X1))) = s(num,X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X14543] : s(real,i(s(fun(cart(real,X14543),real),vectoru_norm),s(cart(real,X14543),i(s(fun(num,cart(real,X14543)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
    inference(variable_rename,[status(thm)],[aNORMu_0]) ).

fof(c_0_17,plain,
    ! [X4979] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X4979))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X4979))),s(real,X4979))),
    inference(variable_rename,[status(thm)],[aREALu_POWu_2]) ).

fof(c_0_18,plain,
    ! [X4914] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X4914))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
    inference(variable_rename,[status(thm)],[aREALu_MULu_LZERO]) ).

fof(c_0_19,plain,
    ! [X4897] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X4897))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,X4897),
    inference(variable_rename,[status(thm)],[aREALu_ADDu_RID]) ).

fof(c_0_20,plain,
    ! [X14252] : s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X14252))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X14252))),
    inference(variable_rename,[status(thm)],[aPOWu_2u_SQRTu_ABS]) ).

cnf(c_0_21,negated_conjecture,
    s(real,i(s(fun(cart(real,finite_sum(esk3847_0,esk3846_0)),real),vectoru_norm),s(cart(real,finite_sum(esk3847_0,esk3846_0)),i(s(fun(cart(real,esk3846_0),cart(real,finite_sum(esk3847_0,esk3846_0))),i(s(fun(cart(real,esk3847_0),fun(cart(real,esk3846_0),cart(real,finite_sum(esk3847_0,esk3846_0)))),pastecart),s(cart(real,esk3847_0),esk3848_0))),s(cart(real,esk3846_0),i(s(fun(num,cart(real,esk3846_0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) != s(real,i(s(fun(cart(real,esk3847_0),real),vectoru_norm),s(cart(real,esk3847_0),esk3848_0))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,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),X3))),s(cart(real,X2),X4))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),X3))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X2),real),vectoru_norm),s(cart(real,X2),X4))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,plain,
    s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_24,plain,
    s(real,i(s(fun(cart(real,X1),real),vectoru_norm),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(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X1))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,X1))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X1))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,plain,
    s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X1))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X1))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X1))),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_29,plain,
    ! [X14591,X14592] : s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,X14591),real),vectoru_norm),s(cart(real,X14591),X14592))))) = s(real,i(s(fun(cart(real,X14591),real),vectoru_norm),s(cart(real,X14591),X14592))),
    inference(variable_rename,[status(thm)],[aREALu_ABSu_NORM]) ).

cnf(c_0_30,negated_conjecture,
    s(real,i(s(fun(cart(real,finite_sum(esk3847_0,esk3846_0)),real),vectoru_norm),s(cart(real,finite_sum(esk3847_0,esk3846_0)),i(s(fun(cart(real,esk3846_0),cart(real,finite_sum(esk3847_0,esk3846_0))),i(s(fun(cart(real,esk3847_0),fun(cart(real,esk3846_0),cart(real,finite_sum(esk3847_0,esk3846_0)))),pastecart),s(cart(real,esk3847_0),esk3848_0))),s(cart(real,esk3846_0),i(s(fun(num,cart(real,esk3846_0)),vec),s(num,u_0))))))) != s(real,i(s(fun(cart(real,esk3847_0),real),vectoru_norm),s(cart(real,esk3847_0),esk3848_0))),
    inference(rw,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_31,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),X3))),s(cart(real,X2),X4))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),X3))))),s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X2),real),vectoru_norm),s(cart(real,X2),X4))))),s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_15]),c_0_23]),c_0_15]),c_0_23]) ).

cnf(c_0_32,plain,
    s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,u_0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_15]),c_0_15]) ).

cnf(c_0_33,plain,
    s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X1))),s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_15]),c_0_23]) ).

cnf(c_0_34,plain,
    s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,X1))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15]),c_0_15]) ).

cnf(c_0_35,plain,
    s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X1))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))) = s(real,X1),
    inference(rw,[status(thm)],[c_0_27,c_0_15]) ).

cnf(c_0_36,plain,
    s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X1))),s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15]),c_0_23]) ).

cnf(c_0_37,plain,
    s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),X2))))) = s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),X2))),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO460+1 : TPTP v8.1.0. Released v7.0.0.
% 0.06/0.13  % Command  : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.13/0.34  % Computer : n014.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  : 600
% 0.13/0.34  % DateTime : Fri Jun 17 22:11:49 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 3.97/4.18  # No SInE strategy applied
% 3.97/4.18  # Auto-Mode selected heuristic C07_19_nc_SAT001_MinMin_rr
% 3.97/4.18  # and selection function SelectMaxLComplexAvoidPosPred.
% 3.97/4.18  #
% 3.97/4.18  # Presaturation interreduction done
% 3.97/4.18  
% 3.97/4.18  # Proof found!
% 3.97/4.18  # SZS status Theorem
% 3.97/4.18  # SZS output start CNFRefutation
% See solution above
% 3.97/4.19  # Training examples: 0 positive, 0 negative
%------------------------------------------------------------------------------