TSTP Solution File: SWW179+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW179+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% 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 : 600s
% DateTime : Thu Jul 21 00:10:14 EDT 2022
% Result : Theorem 0.34s 1.53s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 36 unt; 0 def)
% Number of atoms : 130 ( 42 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 121 ( 54 ~; 45 |; 8 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 78 ( 3 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X19,X16,X17,X8] :
( class_Groups_Oab__semigroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X17,X16),X19) = c_Groups_Oplus__class_Oplus(X8,X17,c_Groups_Oplus__class_Oplus(X8,X16,X19)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(fact_add__0__iff,axiom,
! [X21,X20,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X20 = c_Groups_Oplus__class_Oplus(X8,X20,X21)
<=> X21 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__strict__increasing2,axiom,
! [X19,X16,X17,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X17)
=> ( c_Orderings_Oord__class_Oless(X8,X16,X19)
=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Oplus__class_Oplus(X8,X17,X19)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X34] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X34)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_abs__real__def,axiom,
! [X17] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X17) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17) = X17 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_abs__real__def) ).
fof(fact_less__le__not__le,axiom,
! [X10,X9,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X9,X10)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X10)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X10,X9) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_less__le__not__le) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__of__nat__1) ).
fof(fact__0960_A_060_061_Acmod_Ac_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact__0960_A_060_061_Acmod_Ac_096) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_norm__eq__zero,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_RealVector_Onorm__class_Onorm(X8,X9) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X9 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_norm__eq__zero) ).
fof(fact_real__norm__def,axiom,
! [X7] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X7) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__norm__def) ).
fof(fact_zero__less__norm__iff,axiom,
! [X9,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9))
<=> X9 != c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(c_0_18,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_19,plain,
! [X20,X21,X22,X23] :
( ~ class_Groups_Oab__semigroup__add(X23)
| c_Groups_Oplus__class_Oplus(X23,c_Groups_Oplus__class_Oplus(X23,X22,X21),X20) = c_Groups_Oplus__class_Oplus(X23,X22,c_Groups_Oplus__class_Oplus(X23,X21,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(c_0_20,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
fof(c_0_23,plain,
! [X22,X23,X24] :
( ( X23 != c_Groups_Oplus__class_Oplus(X24,X23,X22)
| X22 = c_Groups_Ozero__class_Ozero(X24)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X24) )
& ( X22 != c_Groups_Ozero__class_Ozero(X24)
| X23 = c_Groups_Oplus__class_Oplus(X24,X23,X22)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(c_0_24,plain,
! [X20,X21,X22,X23] :
( ~ class_Groups_Oordered__comm__monoid__add(X23)
| ~ c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),X22)
| ~ c_Orderings_Oord__class_Oless(X23,X21,X20)
| c_Orderings_Oord__class_Oless(X23,X21,c_Groups_Oplus__class_Oplus(X23,X22,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(c_0_25,plain,
! [X35] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X35)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
cnf(c_0_26,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( X2 = c_Groups_Oplus__class_Oplus(X1,X2,X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(c_0_30,plain,
! [X5] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(c_0_31,plain,
! [X18,X18] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = X18 ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__real__def])])])])]) ).
fof(c_0_32,plain,
! [X11,X12,X13] :
( ( c_Orderings_Oord__class_Oless__eq(X13,X12,X11)
| ~ c_Orderings_Oord__class_Oless(X13,X12,X11)
| ~ class_Orderings_Opreorder(X13) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X13,X11,X12)
| ~ c_Orderings_Oord__class_Oless(X13,X12,X11)
| ~ class_Orderings_Opreorder(X13) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X13,X12,X11)
| c_Orderings_Oord__class_Oless__eq(X13,X11,X12)
| c_Orderings_Oord__class_Oless(X13,X12,X11)
| ~ class_Orderings_Opreorder(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__le__not__le])])])]) ).
cnf(c_0_33,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
cnf(c_0_35,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]) ).
cnf(c_0_37,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = X1
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(split_conjunct,[status(thm)],[fact__0960_A_060_061_Acmod_Ac_096]) ).
cnf(c_0_43,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_44,plain,
! [X10,X11] :
( ( c_RealVector_Onorm__class_Onorm(X11,X10) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X10 = c_Groups_Ozero__class_Ozero(X11)
| ~ class_RealVector_Oreal__normed__vector(X11) )
& ( X10 != c_Groups_Ozero__class_Ozero(X11)
| c_RealVector_Onorm__class_Onorm(X11,X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X11) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(c_0_45,plain,
! [X8] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X8) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
cnf(c_0_46,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_47,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_48,plain,
! [X10,X11] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10))
| X10 != c_Groups_Ozero__class_Ozero(X11)
| ~ class_RealVector_Oreal__normed__vector(X11) )
& ( X10 = c_Groups_Ozero__class_Ozero(X11)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10))
| ~ class_RealVector_Oreal__normed__vector(X11) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
cnf(c_0_49,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_51,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_52,plain,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_54,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_46]),c_0_47])]) ).
cnf(c_0_56,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_58,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_59,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_42])]) ).
cnf(c_0_60,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_54]),c_0_53])]) ).
cnf(c_0_61,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW179+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : run_ET %s %d
% 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 : 600
% 0.13/0.34 % DateTime : Sat Jun 4 17:15:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.34/1.53 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.34/1.53 # Preprocessing time : 0.129 s
% 0.34/1.53
% 0.34/1.53 # Proof found!
% 0.34/1.53 # SZS status Theorem
% 0.34/1.53 # SZS output start CNFRefutation
% See solution above
% 0.34/1.53 # Proof object total steps : 63
% 0.34/1.53 # Proof object clause steps : 33
% 0.34/1.53 # Proof object formula steps : 30
% 0.34/1.53 # Proof object conjectures : 11
% 0.34/1.53 # Proof object clause conjectures : 8
% 0.34/1.53 # Proof object formula conjectures : 3
% 0.34/1.53 # Proof object initial clauses used : 18
% 0.34/1.53 # Proof object initial formulas used : 18
% 0.34/1.53 # Proof object generating inferences : 14
% 0.34/1.53 # Proof object simplifying inferences : 12
% 0.34/1.53 # Training examples: 0 positive, 0 negative
% 0.34/1.53 # Parsed axioms : 1275
% 0.34/1.53 # Removed by relevancy pruning/SinE : 0
% 0.34/1.53 # Initial clauses : 1761
% 0.34/1.53 # Removed in clause preprocessing : 50
% 0.34/1.53 # Initial clauses in saturation : 1711
% 0.34/1.53 # Processed clauses : 2321
% 0.34/1.53 # ...of these trivial : 41
% 0.34/1.53 # ...subsumed : 599
% 0.34/1.53 # ...remaining for further processing : 1681
% 0.34/1.53 # Other redundant clauses eliminated : 215
% 0.34/1.53 # Clauses deleted for lack of memory : 0
% 0.34/1.53 # Backward-subsumed : 19
% 0.34/1.53 # Backward-rewritten : 17
% 0.34/1.53 # Generated clauses : 49375
% 0.34/1.53 # ...of the previous two non-trivial : 45875
% 0.34/1.53 # Contextual simplify-reflections : 47
% 0.34/1.53 # Paramodulations : 49109
% 0.34/1.53 # Factorizations : 10
% 0.34/1.53 # Equation resolutions : 256
% 0.34/1.53 # Current number of processed clauses : 1608
% 0.34/1.53 # Positive orientable unit clauses : 329
% 0.34/1.53 # Positive unorientable unit clauses: 11
% 0.34/1.53 # Negative unit clauses : 60
% 0.34/1.53 # Non-unit-clauses : 1208
% 0.34/1.53 # Current number of unprocessed clauses: 44716
% 0.34/1.53 # ...number of literals in the above : 145530
% 0.34/1.53 # Current number of archived formulas : 0
% 0.34/1.53 # Current number of archived clauses : 37
% 0.34/1.53 # Clause-clause subsumption calls (NU) : 128841
% 0.34/1.53 # Rec. Clause-clause subsumption calls : 85049
% 0.34/1.53 # Non-unit clause-clause subsumptions : 296
% 0.34/1.53 # Unit Clause-clause subsumption calls : 4736
% 0.34/1.53 # Rewrite failures with RHS unbound : 0
% 0.34/1.53 # BW rewrite match attempts : 1233
% 0.34/1.53 # BW rewrite match successes : 125
% 0.34/1.53 # Condensation attempts : 0
% 0.34/1.53 # Condensation successes : 0
% 0.34/1.53 # Termbank termtop insertions : 1248665
% 0.34/1.53
% 0.34/1.53 # -------------------------------------------------
% 0.34/1.53 # User time : 0.729 s
% 0.34/1.53 # System time : 0.029 s
% 0.34/1.53 # Total time : 0.758 s
% 0.34/1.53 # Maximum resident set size: 51064 pages
% 0.34/23.52 eprover: CPU time limit exceeded, terminating
% 0.34/23.53 eprover: CPU time limit exceeded, terminating
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55 eprover: No such file or directory
% 0.34/23.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.56 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.59 eprover: No such file or directory
% 0.34/23.60 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.60 eprover: No such file or directory
% 0.34/23.60 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.60 eprover: No such file or directory
% 0.34/23.61 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.61 eprover: No such file or directory
% 0.34/23.61 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.61 eprover: No such file or directory
% 0.34/23.62 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.62 eprover: No such file or directory
%------------------------------------------------------------------------------