TSTP Solution File: SWW224+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.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 00:10:20 EDT 2022
% Result : Theorem 0.40s 23.58s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 45
% Syntax : Number of formulae : 171 ( 71 unt; 0 def)
% Number of atoms : 385 ( 87 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 388 ( 174 ~; 154 |; 13 &)
% ( 8 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 271 ( 6 sgn 160 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_order__le__less__trans,axiom,
! [X13,X14,X12,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X12,X14)
=> ( c_Orderings_Oord__class_Oless(X7,X14,X13)
=> c_Orderings_Oord__class_Oless(X7,X12,X13) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X13,X14,X12,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X12,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X14,X13)
=> c_Orderings_Oord__class_Oless(X7,X12,X13) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__less__le__trans) ).
fof(conj_0,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_order__less__irrefl,axiom,
! [X12,X7] :
( class_Orderings_Opreorder(X7)
=> ~ c_Orderings_Oord__class_Oless(X7,X12,X12) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__less__irrefl) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X18,X5,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X5,X18)
<=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X5,X18),c_Groups_Ozero__class_Ozero(X7)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__iff__diff__less__0) ).
fof(fact_leI,axiom,
! [X14,X12,X7] :
( class_Orderings_Olinorder(X7)
=> ( ~ c_Orderings_Oord__class_Oless(X7,X12,X14)
=> c_Orderings_Oord__class_Oless__eq(X7,X14,X12) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_leI) ).
fof(fact_positive__add,axiom,
! [X14,X12] :
( c_RealDef_Opositive(X12)
=> ( c_RealDef_Opositive(X14)
=> c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X14)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_positive__add) ).
fof(fact_double__zero__sym,axiom,
! [X5,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,X5,X5)
<=> X5 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_double__zero__sym) ).
fof(fact_positive__zero,axiom,
~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_positive__zero) ).
fof(fact_less__real__def,axiom,
! [X16,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16)
<=> c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X16,X6)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__real__def) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_1) ).
fof(fact_real__norm__def,axiom,
! [X31] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X31) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X31),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_real__norm__def) ).
fof(fact_abs__minus__commute,axiom,
! [X8,X9,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8)) = c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X8,X9)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__minus__commute) ).
fof(fact_order__less__asym,axiom,
! [X14,X12,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X12,X14)
=> ~ c_Orderings_Oord__class_Oless(X7,X14,X12) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__less__asym) ).
fof(fact_less__eq__real__def,axiom,
! [X16,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X16)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16)
| X6 = X16 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__eq__real__def) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(conj_2,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_2) ).
fof(fact_abs__of__nonneg,axiom,
! [X9,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
=> c_Groups_Oabs__class_Oabs(X7,X9) = X9 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__of__nonneg) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(fact_abs__of__pos,axiom,
! [X9,X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X9)
=> c_Groups_Oabs__class_Oabs(X7,X9) = X9 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__of__pos) ).
fof(fact_add__right__cancel,axiom,
! [X17,X5,X18,X7] :
( class_Groups_Ocancel__semigroup__add(X7)
=> ( c_Groups_Oplus__class_Oplus(X7,X18,X5) = c_Groups_Oplus__class_Oplus(X7,X17,X5)
<=> X18 = X17 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__right__cancel) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X9,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X9) = X9 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_diff__add__cancel,axiom,
! [X8,X9,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8),X8) = X9 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_diff__add__cancel) ).
fof(fact_add__diff__cancel,axiom,
! [X8,X9,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X9,X8),X8) = X9 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__diff__cancel) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X11,X9,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X9,X11) = c_Groups_Oplus__class_Oplus(X7,X11,X9) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_norm__minus__commute,axiom,
! [X8,X9,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8)) = c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X8,X9)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__minus__commute) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_add__0__iff,axiom,
! [X5,X18,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( X18 = c_Groups_Oplus__class_Oplus(X7,X18,X5)
<=> X5 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__0__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.mepo_128.in',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X14,X12,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( X12 != X14
=> ( ~ c_Orderings_Oord__class_Oless(X7,X12,X14)
=> c_Orderings_Oord__class_Oless(X7,X14,X12) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_linorder__neqE__linordered__idom) ).
fof(fact_less__le__not__le,axiom,
! [X16,X6,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless(X7,X6,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(X7,X6,X16)
& ~ c_Orderings_Oord__class_Oless__eq(X7,X16,X6) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__le__not__le) ).
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.mepo_128.in',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_add__le__imp__le__right,axiom,
! [X8,X11,X9,X7] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X9,X11),c_Groups_Oplus__class_Oplus(X7,X8,X11))
=> c_Orderings_Oord__class_Oless__eq(X7,X9,X8) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__le__imp__le__right) ).
fof(fact_norm__not__less__zero,axiom,
! [X12,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__not__less__zero) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(fact_abs__diff__less__iff,axiom,
! [X4,X5,X6,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)),X4)
<=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X5,X4),X6)
& c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Oplus__class_Oplus(X7,X5,X4)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__diff__less__iff) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(fact_add__strict__increasing2,axiom,
! [X11,X8,X9,X7] :
( class_Groups_Oordered__comm__monoid__add(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
=> ( c_Orderings_Oord__class_Oless(X7,X8,X11)
=> c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Oplus__class_Oplus(X7,X9,X11)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__strict__increasing2) ).
fof(fact_norm__ge__zero,axiom,
! [X12,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X12)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__ge__zero) ).
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.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(c_0_45,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ c_Orderings_Oord__class_Oless__eq(X18,X17,X16)
| ~ c_Orderings_Oord__class_Oless(X18,X16,X15)
| c_Orderings_Oord__class_Oless(X18,X17,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(c_0_46,plain,
! [X15,X16,X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ c_Orderings_Oord__class_Oless(X18,X17,X16)
| ~ c_Orderings_Oord__class_Oless__eq(X18,X16,X15)
| c_Orderings_Oord__class_Oless(X18,X17,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
cnf(c_0_47,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_49,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_50,plain,
! [X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_Orderings_Oord__class_Oless(X14,X13,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__irrefl])])]) ).
cnf(c_0_51,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_52,plain,
! [X19,X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless(X21,X20,X19)
| c_Orderings_Oord__class_Oless(X21,c_Groups_Ominus__class_Ominus(X21,X20,X19),c_Groups_Ozero__class_Ozero(X21))
| ~ class_Groups_Oordered__ab__group__add(X21) )
& ( ~ c_Orderings_Oord__class_Oless(X21,c_Groups_Ominus__class_Ominus(X21,X20,X19),c_Groups_Ozero__class_Ozero(X21))
| c_Orderings_Oord__class_Oless(X21,X20,X19)
| ~ class_Groups_Oordered__ab__group__add(X21) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(c_0_53,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Oord__class_Oless(X17,X16,X15)
| c_Orderings_Oord__class_Oless__eq(X17,X15,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_leI])])]) ).
fof(c_0_54,plain,
! [X15,X16] :
( ~ c_RealDef_Opositive(X16)
| ~ c_RealDef_Opositive(X15)
| c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__add])]) ).
fof(c_0_55,plain,
! [X8,X9] :
( ( c_Groups_Ozero__class_Ozero(X9) != c_Groups_Oplus__class_Oplus(X9,X8,X8)
| X8 = c_Groups_Ozero__class_Ozero(X9)
| ~ class_Groups_Olinordered__ab__group__add(X9) )
& ( X8 != c_Groups_Ozero__class_Ozero(X9)
| c_Groups_Ozero__class_Ozero(X9) = c_Groups_Oplus__class_Oplus(X9,X8,X8)
| ~ class_Groups_Olinordered__ab__group__add(X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(c_0_56,plain,
~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[fact_positive__zero]) ).
fof(c_0_57,plain,
! [X17,X18,X17,X18] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
| c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X17,X18)) )
& ( ~ c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X17,X18))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__real__def])])])]) ).
cnf(c_0_58,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_59,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_60,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_61,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_m) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_48]),c_0_49])]) ).
cnf(c_0_62,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_64,plain,
! [X32] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X32) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X32),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_65,plain,
! [X10,X11,X12] :
( ~ class_Groups_Oordered__ab__group__add__abs(X12)
| c_Groups_Oabs__class_Oabs(X12,c_Groups_Ominus__class_Ominus(X12,X11,X10)) = c_Groups_Oabs__class_Oabs(X12,c_Groups_Ominus__class_Ominus(X12,X10,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
fof(c_0_66,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| ~ c_Orderings_Oord__class_Oless(X17,X16,X15)
| ~ c_Orderings_Oord__class_Oless(X17,X15,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__asym])])]) ).
fof(c_0_67,plain,
! [X17,X18,X17,X18] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
| X18 = X17 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17) )
& ( X18 != X17
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])])]) ).
cnf(c_0_68,plain,
( c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
| ~ c_RealDef_Opositive(X2)
| ~ c_RealDef_Opositive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_69,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
cnf(c_0_71,plain,
~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,plain,
( c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_73,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_74,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(assume_negation,[status(cth)],[conj_2]) ).
fof(c_0_75,plain,
! [X10,X11] :
( ~ class_Groups_Oordered__ab__group__add__abs(X11)
| ~ c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Ozero__class_Ozero(X11),X10)
| c_Groups_Oabs__class_Oabs(X11,X10) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
cnf(c_0_76,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_49])]) ).
cnf(c_0_77,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3))
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_78,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).
cnf(c_0_79,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_80,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_64]) ).
cnf(c_0_81,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_82,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c_0_83,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_84,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_85,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_RealDef_Opositive(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]),c_0_71]) ).
cnf(c_0_86,hypothesis,
c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_87,plain,
! [X10,X11] :
( ~ class_Groups_Oordered__ab__group__add__abs(X11)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ozero__class_Ozero(X11),X10)
| c_Groups_Oabs__class_Oabs(X11,X10) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(c_0_88,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_89,plain,
! [X19,X20,X21,X22] :
( ( c_Groups_Oplus__class_Oplus(X22,X21,X20) != c_Groups_Oplus__class_Oplus(X22,X19,X20)
| X21 = X19
| ~ class_Groups_Ocancel__semigroup__add(X22) )
& ( X21 != X19
| c_Groups_Oplus__class_Oplus(X22,X21,X20) = c_Groups_Oplus__class_Oplus(X22,X19,X20)
| ~ class_Groups_Ocancel__semigroup__add(X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(c_0_90,plain,
! [X10,X11] :
( ~ class_Rings_Ocomm__semiring__1(X11)
| c_Groups_Oplus__class_Oplus(X11,c_Groups_Ozero__class_Ozero(X11),X10) = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(c_0_91,plain,
! [X10,X11,X12] :
( ~ class_Groups_Ogroup__add(X12)
| c_Groups_Oplus__class_Oplus(X12,c_Groups_Ominus__class_Ominus(X12,X11,X10),X10) = X11 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
cnf(c_0_92,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_93,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79])]) ).
cnf(c_0_94,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_80]),c_0_82])]) ).
cnf(c_0_95,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_73]),c_0_49])]) ).
cnf(c_0_96,plain,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_84]),c_0_78])]) ).
cnf(c_0_97,hypothesis,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_98,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_99,plain,
! [X10,X11,X12] :
( ~ class_Groups_Ogroup__add(X12)
| c_Groups_Ominus__class_Ominus(X12,c_Groups_Oplus__class_Oplus(X12,X11,X10),X10) = X11 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(c_0_100,plain,
! [X12,X13,X14] :
( ~ class_Rings_Ocomm__semiring__1(X14)
| c_Groups_Oplus__class_Oplus(X14,X13,X12) = c_Groups_Oplus__class_Oplus(X14,X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
cnf(c_0_101,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
fof(c_0_102,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__vector(X12)
| c_RealVector_Onorm__class_Onorm(X12,c_Groups_Ominus__class_Ominus(X12,X11,X10)) = c_RealVector_Onorm__class_Onorm(X12,c_Groups_Ominus__class_Ominus(X12,X10,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
cnf(c_0_103,plain,
( X2 = X3
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_104,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_105,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_106,hypothesis,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_80]),c_0_94]),c_0_82])]) ).
cnf(c_0_107,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(c_0_108,plain,
! [X19,X20,X21] :
( ( X20 != c_Groups_Oplus__class_Oplus(X21,X20,X19)
| X19 = c_Groups_Ozero__class_Ozero(X21)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21) )
& ( X19 != c_Groups_Ozero__class_Ozero(X21)
| X20 = c_Groups_Oplus__class_Oplus(X21,X20,X19)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
cnf(c_0_109,hypothesis,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_110,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Orderings_Olinorder(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_63]) ).
cnf(c_0_111,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_112,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_113,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
inference(rw,[status(thm)],[c_0_101,c_0_80]) ).
cnf(c_0_114,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_115,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_116,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) != X3
| ~ class_Rings_Ocomm__semiring__1(X2)
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_117,hypothesis,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)),v_m) = v_x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).
cnf(c_0_118,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_119,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
fof(c_0_120,plain,
! [X15,X16,X17] :
( ~ class_Rings_Olinordered__idom(X17)
| X16 = X15
| c_Orderings_Oord__class_Oless(X17,X16,X15)
| c_Orderings_Oord__class_Oless(X17,X15,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom])])]) ).
fof(c_0_121,plain,
! [X17,X18,X19] :
( ( c_Orderings_Oord__class_Oless__eq(X19,X18,X17)
| ~ c_Orderings_Oord__class_Oless(X19,X18,X17)
| ~ class_Orderings_Opreorder(X19) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X19,X17,X18)
| ~ c_Orderings_Oord__class_Oless(X19,X18,X17)
| ~ class_Orderings_Opreorder(X19) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X19,X18,X17)
| c_Orderings_Oord__class_Oless__eq(X19,X17,X18)
| c_Orderings_Oord__class_Oless(X19,X18,X17)
| ~ class_Orderings_Opreorder(X19) ) ),
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_122,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_108]) ).
cnf(c_0_123,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_124,plain,
! [X12,X13,X14,X15] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
| ~ c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Oplus__class_Oplus(X15,X14,X13),c_Groups_Oplus__class_Oplus(X15,X12,X13))
| c_Orderings_Oord__class_Oless__eq(X15,X14,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(c_0_125,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero])])]) ).
cnf(c_0_126,hypothesis,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_80]),c_0_79]),c_0_82])]),c_0_94]) ).
cnf(c_0_127,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = X3
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_128,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)),v_e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_129,hypothesis,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| v_x != v_m ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119])]) ).
cnf(c_0_130,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X3 = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_131,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_132,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_121]) ).
cnf(c_0_133,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_e ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_122]),c_0_123])]) ).
cnf(c_0_134,hypothesis,
c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)),
inference(spm,[status(thm)],[c_0_72,c_0_59]) ).
fof(c_0_135,plain,
! [X8,X9,X10,X11] :
( ( c_Orderings_Oord__class_Oless(X11,c_Groups_Ominus__class_Ominus(X11,X9,X8),X10)
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oabs__class_Oabs(X11,c_Groups_Ominus__class_Ominus(X11,X10,X9)),X8)
| ~ class_Rings_Olinordered__idom(X11) )
& ( c_Orderings_Oord__class_Oless(X11,X10,c_Groups_Oplus__class_Oplus(X11,X9,X8))
| ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oabs__class_Oabs(X11,c_Groups_Ominus__class_Ominus(X11,X10,X9)),X8)
| ~ class_Rings_Olinordered__idom(X11) )
& ( ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ominus__class_Ominus(X11,X9,X8),X10)
| ~ c_Orderings_Oord__class_Oless(X11,X10,c_Groups_Oplus__class_Oplus(X11,X9,X8))
| c_Orderings_Oord__class_Oless(X11,c_Groups_Oabs__class_Oabs(X11,c_Groups_Ominus__class_Ominus(X11,X10,X9)),X8)
| ~ class_Rings_Olinordered__idom(X11) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).
cnf(c_0_136,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_137,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_138,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_139,hypothesis,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))) = v_e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_118]),c_0_107])]) ).
cnf(c_0_140,negated_conjecture,
( v_x != v_m
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_141,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_142,hypothesis,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_49]),c_0_48])]) ).
cnf(c_0_143,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_59]),c_0_49])]) ).
cnf(c_0_144,hypothesis,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_85,c_0_134]) ).
cnf(c_0_145,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_146,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
| ~ class_Groups_Ogroup__add(X1)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(spm,[status(thm)],[c_0_136,c_0_105]) ).
cnf(c_0_147,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(spm,[status(thm)],[c_0_137,c_0_59]) ).
cnf(c_0_148,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(c_0_149,plain,
! [X12,X13,X14,X15] :
( ~ class_Groups_Oordered__comm__monoid__add(X15)
| ~ c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15),X14)
| ~ c_Orderings_Oord__class_Oless(X15,X13,X12)
| c_Orderings_Oord__class_Oless(X15,X13,c_Groups_Oplus__class_Oplus(X15,X14,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(c_0_150,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X14,X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
cnf(c_0_151,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_115])]) ).
cnf(c_0_152,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| v_x != v_m ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_153,hypothesis,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_96]),c_0_144]) ).
cnf(c_0_154,plain,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = X3
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_84]),c_0_80]),c_0_131])]) ).
cnf(c_0_155,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_e),v_m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_107]),c_0_148])]) ).
cnf(c_0_156,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_149]) ).
cnf(c_0_157,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_158,hypothesis,
( v_x = v_m
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,v_x) ),
inference(spm,[status(thm)],[c_0_76,c_0_141]) ).
cnf(c_0_159,negated_conjecture,
v_x != v_m,
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_160,hypothesis,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_110]),c_0_80]),c_0_79]),c_0_82])]),c_0_94]) ).
cnf(c_0_161,negated_conjecture,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_e) = v_m
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x,v_e)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_154]),c_0_155])]) ).
cnf(c_0_162,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_156,c_0_112]) ).
cnf(c_0_163,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_164,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_139]),c_0_115])]) ).
cnf(c_0_165,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,v_x),
inference(sr,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_166,hypothesis,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))),v_x) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_160]),c_0_107])]) ).
cnf(c_0_167,hypothesis,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_144,c_0_160]) ).
cnf(c_0_168,negated_conjecture,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_e) = v_m,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]),c_0_118]),c_0_164]),c_0_165])]) ).
cnf(c_0_169,hypothesis,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) != v_x,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_166]),c_0_118]),c_0_119])]),c_0_167]) ).
cnf(c_0_170,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_168]),c_0_107])]),c_0_169]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.10 % Command : run_ET %s %d
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sat Jun 4 10:19:32 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.40/23.42 eprover: CPU time limit exceeded, terminating
% 0.40/23.43 eprover: CPU time limit exceeded, terminating
% 0.40/23.43 eprover: CPU time limit exceeded, terminating
% 0.40/23.58 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.40/23.58 # Preprocessing time : 0.094 s
% 0.40/23.58
% 0.40/23.58 # Proof found!
% 0.40/23.58 # SZS status Theorem
% 0.40/23.58 # SZS output start CNFRefutation
% See solution above
% 0.40/23.58 # Proof object total steps : 171
% 0.40/23.58 # Proof object clause steps : 95
% 0.40/23.58 # Proof object formula steps : 76
% 0.40/23.58 # Proof object conjectures : 12
% 0.40/23.58 # Proof object clause conjectures : 9
% 0.40/23.58 # Proof object formula conjectures : 3
% 0.40/23.58 # Proof object initial clauses used : 46
% 0.40/23.58 # Proof object initial formulas used : 45
% 0.40/23.58 # Proof object generating inferences : 46
% 0.40/23.58 # Proof object simplifying inferences : 82
% 0.40/23.58 # Training examples: 0 positive, 0 negative
% 0.40/23.58 # Parsed axioms : 1188
% 0.40/23.58 # Removed by relevancy pruning/SinE : 0
% 0.40/23.58 # Initial clauses : 1702
% 0.40/23.58 # Removed in clause preprocessing : 44
% 0.40/23.58 # Initial clauses in saturation : 1658
% 0.40/23.58 # Processed clauses : 33328
% 0.40/23.58 # ...of these trivial : 935
% 0.40/23.58 # ...subsumed : 21490
% 0.40/23.58 # ...remaining for further processing : 10903
% 0.40/23.58 # Other redundant clauses eliminated : 1145
% 0.40/23.58 # Clauses deleted for lack of memory : 753966
% 0.40/23.58 # Backward-subsumed : 318
% 0.40/23.58 # Backward-rewritten : 1263
% 0.40/23.58 # Generated clauses : 1064088
% 0.40/23.58 # ...of the previous two non-trivial : 989595
% 0.40/23.58 # Contextual simplify-reflections : 6470
% 0.40/23.58 # Paramodulations : 1062566
% 0.40/23.58 # Factorizations : 13
% 0.40/23.58 # Equation resolutions : 1290
% 0.40/23.58 # Current number of processed clauses : 9184
% 0.40/23.58 # Positive orientable unit clauses : 720
% 0.40/23.58 # Positive unorientable unit clauses: 62
% 0.40/23.58 # Negative unit clauses : 380
% 0.40/23.58 # Non-unit-clauses : 8022
% 0.40/23.58 # Current number of unprocessed clauses: 127778
% 0.40/23.58 # ...number of literals in the above : 428145
% 0.40/23.58 # Current number of archived formulas : 0
% 0.40/23.58 # Current number of archived clauses : 1608
% 0.40/23.58 # Clause-clause subsumption calls (NU) : 15503889
% 0.40/23.58 # Rec. Clause-clause subsumption calls : 11095901
% 0.40/23.58 # Non-unit clause-clause subsumptions : 19190
% 0.40/23.58 # Unit Clause-clause subsumption calls : 294170
% 0.40/23.58 # Rewrite failures with RHS unbound : 0
% 0.40/23.58 # BW rewrite match attempts : 14302
% 0.40/23.58 # BW rewrite match successes : 533
% 0.40/23.58 # Condensation attempts : 0
% 0.40/23.58 # Condensation successes : 0
% 0.40/23.58 # Termbank termtop insertions : 24183119
% 0.40/23.58
% 0.40/23.58 # -------------------------------------------------
% 0.40/23.58 # User time : 22.353 s
% 0.40/23.58 # System time : 0.151 s
% 0.40/23.58 # Total time : 22.504 s
% 0.40/23.58 # Maximum resident set size: 155584 pages
% 0.40/46.45 eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 0.40/46.45
% 0.40/46.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.46 eprover: No such file or directory
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% 0.40/46.46 eprover: No such file or directory
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% 0.40/46.47 eprover: No such file or directory
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% 0.40/46.47 eprover: No such file or directory
% 0.40/46.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.47 eprover: No such file or directory
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% 0.40/46.49 eprover: No such file or directory
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% 0.40/46.49 eprover: No such file or directory
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% 0.40/46.49 eprover: No such file or directory
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% 0.40/46.50 eprover: No such file or directory
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% 0.40/46.50 eprover: No such file or directory
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% 0.40/46.50 eprover: No such file or directory
% 0.40/46.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.51 eprover: No such file or directory
%------------------------------------------------------------------------------