%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO460+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:28:18 PM UTC 2026
% Result : Theorem 9.90s 2.94s
% Output : CNFRefutation 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 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 : 27 ( 27 usr; 22 con; 0-2 aty)
% Number of variables : 61 ( 2 sgn 36 !; 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(aDOTu_SQUAREu_NORM,axiom,
! [X1043,X1] : s(real,i(s(fun(cart(real,X1043),real),i(s(fun(cart(real,X1043),fun(cart(real,X1043),real)),dot),s(cart(real,X1043),X1))),s(cart(real,X1043),X1))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X1043),real),vectoru_norm),s(cart(real,X1043),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))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aDOTu_SQUAREu_NORM) ).
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(aEXPu_2,axiom,
! [X84] : s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X84))),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(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X84))),s(num,X84))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aEXPu_2) ).
fof(aMULTu_0,axiom,
! [X85] : s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X85))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aMULTu_0) ).
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(aREALu_OFu_NUMu_POW,axiom,
! [X1,X84] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X1))))),s(num,X84))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X1))),s(num,X84))))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aREALu_OFu_NUMu_POW) ).
fof(avectoru_norm,axiom,
! [X1011,X1] : s(real,i(s(fun(cart(real,X1011),real),vectoru_norm),s(cart(real,X1011),X1))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(cart(real,X1011),real),i(s(fun(cart(real,X1011),fun(cart(real,X1011),real)),dot),s(cart(real,X1011),X1))),s(cart(real,X1011),X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',avectoru_norm) ).
fof(c_0_11,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_12,plain,
! [X1598] : s(num,i(s(fun(num,num),numeral),s(num,X1598))) = s(num,X1598),
inference(variable_rename,[status(thm)],[aNUMERAL]) ).
fof(c_0_13,negated_conjecture,
s(real,i(s(fun(cart(real,finite_sum(esk2_0,esk1_0)),real),vectoru_norm),s(cart(real,finite_sum(esk2_0,esk1_0)),i(s(fun(cart(real,esk1_0),cart(real,finite_sum(esk2_0,esk1_0))),i(s(fun(cart(real,esk2_0),fun(cart(real,esk1_0),cart(real,finite_sum(esk2_0,esk1_0)))),pastecart),s(cart(real,esk2_0),esk3_0))),s(cart(real,esk1_0),i(s(fun(num,cart(real,esk1_0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) != s(real,i(s(fun(cart(real,esk2_0),real),vectoru_norm),s(cart(real,esk2_0),esk3_0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_14,plain,
! [X1835,X1836,X1837,X1838] : s(real,i(s(fun(cart(real,finite_sum(X1835,X1836)),real),vectoru_norm),s(cart(real,finite_sum(X1835,X1836)),i(s(fun(cart(real,X1836),cart(real,finite_sum(X1835,X1836))),i(s(fun(cart(real,X1835),fun(cart(real,X1836),cart(real,finite_sum(X1835,X1836)))),pastecart),s(cart(real,X1835),X1837))),s(cart(real,X1836),X1838))))) = 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,X1835),real),vectoru_norm),s(cart(real,X1835),X1837))))),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,X1836),real),vectoru_norm),s(cart(real,X1836),X1838))))),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_15,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_16,plain,
s(num,i(s(fun(num,num),numeral),s(num,X1))) = s(num,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X1529,X1530] : s(real,i(s(fun(cart(real,X1529),real),i(s(fun(cart(real,X1529),fun(cart(real,X1529),real)),dot),s(cart(real,X1529),X1530))),s(cart(real,X1529),X1530))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,X1529),real),vectoru_norm),s(cart(real,X1529),X1530))))),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)],[aDOTu_SQUAREu_NORM]) ).
fof(c_0_18,plain,
! [X1456] : s(real,i(s(fun(cart(real,X1456),real),vectoru_norm),s(cart(real,X1456),i(s(fun(num,cart(real,X1456)),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_19,plain,
! [X9191] : s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X9191))),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(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X9191))),s(num,X9191))),
inference(variable_rename,[status(thm)],[aEXPu_2]) ).
fof(c_0_20,plain,
! [X6999] : s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X6999))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(variable_rename,[status(thm)],[aMULTu_0]) ).
fof(c_0_21,plain,
! [X3633] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X3633))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,X3633),
inference(variable_rename,[status(thm)],[aREALu_ADDu_RID]) ).
cnf(c_0_22,negated_conjecture,
s(real,i(s(fun(cart(real,finite_sum(esk2_0,esk1_0)),real),vectoru_norm),s(cart(real,finite_sum(esk2_0,esk1_0)),i(s(fun(cart(real,esk1_0),cart(real,finite_sum(esk2_0,esk1_0))),i(s(fun(cart(real,esk2_0),fun(cart(real,esk1_0),cart(real,finite_sum(esk2_0,esk1_0)))),pastecart),s(cart(real,esk2_0),esk3_0))),s(cart(real,esk1_0),i(s(fun(num,cart(real,esk1_0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) != s(real,i(s(fun(cart(real,esk2_0),real),vectoru_norm),s(cart(real,esk2_0),esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,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_14]) ).
cnf(c_0_24,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_15,c_0_16]) ).
cnf(c_0_25,plain,
s(real,i(s(fun(cart(real,X1),real),i(s(fun(cart(real,X1),fun(cart(real,X1),real)),dot),s(cart(real,X1),X2))),s(cart(real,X1),X2))) = 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),X2))))),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_17]) ).
cnf(c_0_26,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_18]) ).
fof(c_0_27,plain,
! [X9253,X9254] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X9253))))),s(num,X9254))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X9253))),s(num,X9254))))),
inference(variable_rename,[status(thm)],[aREALu_OFu_NUMu_POW]) ).
cnf(c_0_28,plain,
s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,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(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X1))),s(num,X1))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X1))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,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_21]) ).
fof(c_0_31,plain,
! [X6185,X6186] : s(real,i(s(fun(cart(real,X6185),real),vectoru_norm),s(cart(real,X6185),X6186))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(cart(real,X6185),real),i(s(fun(cart(real,X6185),fun(cart(real,X6185),real)),dot),s(cart(real,X6185),X6186))),s(cart(real,X6185),X6186))))),
inference(variable_rename,[status(thm)],[avectoru_norm]) ).
cnf(c_0_32,negated_conjecture,
s(real,i(s(fun(cart(real,finite_sum(esk2_0,esk1_0)),real),vectoru_norm),s(cart(real,finite_sum(esk2_0,esk1_0)),i(s(fun(cart(real,esk1_0),cart(real,finite_sum(esk2_0,esk1_0))),i(s(fun(cart(real,esk2_0),fun(cart(real,esk1_0),cart(real,finite_sum(esk2_0,esk1_0)))),pastecart),s(cart(real,esk2_0),esk3_0))),s(cart(real,esk1_0),i(s(fun(num,cart(real,esk1_0)),vec),s(num,u_0))))))) != s(real,i(s(fun(cart(real,esk2_0),real),vectoru_norm),s(cart(real,esk2_0),esk3_0))),
inference(rw,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_33,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_23,c_0_16]),c_0_24]),c_0_16]),c_0_24]) ).
cnf(c_0_34,plain,
s(real,i(s(fun(cart(real,X1),real),i(s(fun(cart(real,X1),fun(cart(real,X1),real)),dot),s(cart(real,X1),X2))),s(cart(real,X1),X2))) = 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),X2))))),s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16]),c_0_24]) ).
cnf(c_0_35,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_26,c_0_16]),c_0_16]) ).
cnf(c_0_36,plain,
s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X1))))),s(num,X2))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X1))),s(num,X2))))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X1))),s(num,i(s(fun(fun(bool,bool),num),card),s(fun(bool,bool),univ))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X1))),s(num,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_16]),c_0_24]) ).
cnf(c_0_38,plain,
s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X1))),s(num,u_0))) = s(num,u_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_16]),c_0_16]) ).
cnf(c_0_39,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_30,c_0_16]) ).
cnf(c_0_40,plain,
s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),X2))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(cart(real,X1),real),i(s(fun(cart(real,X1),fun(cart(real,X1),real)),dot),s(cart(real,X1),X2))),s(cart(real,X1),X2))))),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,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)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO460+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 16:24:05 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.90/2.94 % Version: 3.5.1
% 9.90/2.94 % Preprocessing class: FMLMSMSLSSSNFFN.
% 9.90/2.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.90/2.94 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 9.90/2.94 % Starting new_bool_3 with 600s (2) cores
% 9.90/2.94 % Starting new_bool_1 with 600s (2) cores
% 9.90/2.94 % Starting sh5l with 300s (1) cores
% 9.90/2.94 % new_bool_1 with pid 3025690 completed with status 0
% 9.90/2.94 % Result found by new_bool_1
% 9.90/2.94 % Preprocessing class: FMLMSMSLSSSNFFN.
% 9.90/2.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.90/2.94 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 9.90/2.94 % Starting new_bool_3 with 600s (2) cores
% 9.90/2.94 % Starting new_bool_1 with 600s (2) cores
% 9.90/2.94 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.90/2.94 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.90/2.94 % Search class: FGHSM-SMLM33-DFFFFFNN
% 9.90/2.94 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 9.90/2.94 % Starting SubtermCWHack with 55s (1) cores
% 9.90/2.94 % Starting new_bool_1 with 61s (1) cores
% 9.90/2.94 % new_bool_1 with pid 3025693 completed with status 0
% 9.90/2.94 % Result found by new_bool_1
% 9.90/2.94 % Preprocessing class: FMLMSMSLSSSNFFN.
% 9.90/2.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.90/2.94 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 9.90/2.94 % Starting new_bool_3 with 600s (2) cores
% 9.90/2.94 % Starting new_bool_1 with 600s (2) cores
% 9.90/2.94 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.90/2.94 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.90/2.94 % Search class: FGHSM-SMLM33-DFFFFFNN
% 9.90/2.94 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 9.90/2.94 % Starting SubtermCWHack with 55s (1) cores
% 9.90/2.94 % Starting new_bool_1 with 61s (1) cores
% 9.90/2.94 % Preprocessing time : 0.555 s
% 9.90/2.94 % Presaturation interreduction done
% 9.90/2.94
% 9.90/2.94 % Proof found!
% 9.90/2.94 % SZS status Theorem
% 9.90/2.94 % SZS output start CNFRefutation
% See solution above
% 9.90/2.94 % Parsed axioms : 3290
% 9.90/2.94 % Removed by relevancy pruning/SinE : 1531
% 9.90/2.94 % Initial clauses : 4934
% 9.90/2.94 % Removed in clause preprocessing : 223
% 9.90/2.94 % Initial clauses in saturation : 4711
% 9.90/2.94 % Processed clauses : 2183
% 9.90/2.94 % ...of these trivial : 93
% 9.90/2.94 % ...subsumed : 165
% 9.90/2.94 % ...remaining for further processing : 1925
% 9.90/2.94 % Other redundant clauses eliminated : 0
% 9.90/2.94 % Clauses deleted for lack of memory : 0
% 9.90/2.94 % Backward-subsumed : 3
% 9.90/2.94 % Backward-rewritten : 53
% 9.90/2.94 % Generated clauses : 0
% 9.90/2.94 % ...of the previous two non-redundant : 19
% 9.90/2.94 % ...aggressively subsumed : 0
% 9.90/2.94 % Contextual simplify-reflections : 16
% 9.90/2.94 % Paramodulations : 0
% 9.90/2.94 % Factorizations : 0
% 9.90/2.94 % NegExts : 0
% 9.90/2.94 % Equation resolutions : 0
% 9.90/2.94 % Disequality decompositions : 0
% 9.90/2.94 % Total rewrite steps : 1948
% 9.90/2.94 % ...of those cached : 1490
% 9.90/2.94 % Propositional unsat checks : 0
% 9.90/2.94 % Propositional check models : 0
% 9.90/2.94 % Propositional check unsatisfiable : 0
% 9.90/2.94 % Propositional clauses : 0
% 9.90/2.94 % Propositional clauses after purity: 0
% 9.90/2.94 % Propositional unsat core size : 0
% 9.90/2.94 % Propositional preprocessing time : 0.000
% 9.90/2.94 % Propositional encoding time : 0.000
% 9.90/2.94 % Propositional solver time : 0.000
% 9.90/2.94 % Success case prop preproc time : 0.000
% 9.90/2.94 % Success case prop encoding time : 0.000
% 9.90/2.94 % Success case prop solver time : 0.000
% 9.90/2.94 % Current number of processed clauses : 1869
% 9.90/2.94 % Positive orientable unit clauses : 431
% 9.90/2.94 % Positive unorientable unit clauses: 25
% 9.90/2.94 % Negative unit clauses : 13
% 9.90/2.94 % Non-unit-clauses : 1400
% 9.90/2.94 % Current number of unprocessed clauses: 2547
% 9.90/2.94 % ...number of literals in the above : 17867
% 9.90/2.94 % Current number of archived formulas : 0
% 9.90/2.94 % Current number of archived clauses : 56
% 9.90/2.94 % Clause-clause subsumption calls (NU) : 250750
% 9.90/2.94 % Rec. Clause-clause subsumption calls : 128139
% 9.90/2.94 % Non-unit clause-clause subsumptions : 161
% 9.90/2.94 % Unit Clause-clause subsumption calls : 96
% 9.90/2.94 % Rewrite failures with RHS unbound : 12
% 9.90/2.94 % BW rewrite match attempts : 134830
% 9.90/2.94 % BW rewrite match successes : 229
% 9.90/2.94 % Condensation attempts : 0
% 9.90/2.94 % Condensation successes : 0
% 9.90/2.94 % Termbank termtop insertions : 2721479
% 9.90/2.94 % Search garbage collected termcells : 127320
% 9.90/2.94
% 9.90/2.94 % -------------------------------------------------
% 9.90/2.94 % User time : 1.839 s
% 9.90/2.94 % System time : 0.108 s
% 9.90/2.94 % Total time : 1.947 s
% 9.90/2.94 % Maximum resident set size: 36720 pages
% 9.90/2.94
% 9.90/2.94 % -------------------------------------------------
% 9.90/2.94 % User time : 3.690 s
% 9.90/2.94 % System time : 0.219 s
% 9.90/2.94 % Total time : 3.909 s
% 9.90/2.94 % Maximum resident set size: 14848 pages
% 9.90/2.94 % E exiting
%------------------------------------------------------------------------------