%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW180+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:29:27 PM UTC 2026
% Result : Theorem 26.67s 16.31s
% Output : CNFRefutation 26.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 51
% Syntax : Number of formulae : 185 ( 88 unt; 0 def)
% Number of atoms : 408 ( 115 equ)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 380 ( 157 ~; 145 |; 28 &)
% ( 16 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 258 ( 9 sgn 159 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_norm__eq__zero,axiom,
! [X13,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_RealVector_Onorm__class_Onorm(X6,X13) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(fact_real__norm__def,axiom,
! [X20] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X20) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(fact_abs__minus__cancel,axiom,
! [X9,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Ouminus__class_Ouminus(X6,X9)) = c_Groups_Oabs__class_Oabs(X6,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_abs__of__nonneg,axiom,
! [X9,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X9)
=> c_Groups_Oabs__class_Oabs(X6,X9) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(fact_rp,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X14,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Ouminus__class_Ouminus(X6,X14))
<=> c_Orderings_Oord__class_Oless__eq(X6,X14,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_real__le__refl,axiom,
! [X27] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X9,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X9,c_Groups_Ozero__class_Ozero(X6)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_abs__of__nonpos,axiom,
! [X9,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X9,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X9) = c_Groups_Ouminus__class_Ouminus(X6,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(fact_minus__real__def,axiom,
! [X4,X5] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X4) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__less__def,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12)
& X13 != X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_real__abs__def,axiom,
! [X20] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__abs__def) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X13),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_le0,axiom,
! [X44] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_add__0__iff,axiom,
! [X14,X18,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( X18 = c_Groups_Oplus__class_Oplus(X6,X18,X14)
<=> X14 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_real__add__mult__distrib,axiom,
! [X27,X41,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X42,X41)),X27) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X42),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X41),X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X9,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X15,X9,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X9,X15) = c_Groups_Oplus__class_Oplus(X6,X15,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_real__add__minus__iff,axiom,
! [X14,X13] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X13 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X5] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5)) = c_RealDef_Oreal(tc_Nat_Onat,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_add__le__cancel__right,axiom,
! [X18,X19,X14,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X14,X19),c_Groups_Oplus__class_Oplus(X6,X18,X19))
<=> c_Orderings_Oord__class_Oless__eq(X6,X14,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_mult__left_Ozero,axiom,
! [X4,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ozero__class_Ozero(X6)),X4) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_add__less__cancel__right,axiom,
! [X18,X19,X14,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X14,X19),c_Groups_Oplus__class_Oplus(X6,X18,X19))
<=> c_Orderings_Oord__class_Oless(X6,X14,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(fact_less__add__iff2,axiom,
! [X32,X18,X19,X81,X14,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X14),X81),X19),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X18),X81),X32))
<=> c_Orderings_Oord__class_Oless(X6,X19,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X18,X14)),X81),X32)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(fact_less__le__not__le,axiom,
! [X12,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X12)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X12,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__less__imp__le,axiom,
! [X4,X5,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(fact_mult__le__0__iff,axiom,
! [X18,X14,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X14),X18),c_Groups_Ozero__class_Ozero(X6))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X14)
& c_Orderings_Oord__class_Oless__eq(X6,X18,c_Groups_Ozero__class_Ozero(X6)) )
| ( c_Orderings_Oord__class_Oless__eq(X6,X14,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X18) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_abs__not__less__zero,axiom,
! [X9,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X9),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(fact_real__le__trans,axiom,
! [X37,X38,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X38,X37)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_minus__le__self__iff,axiom,
! [X14,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X14),X14)
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X12,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X12)
<=> X13 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_th,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(fact_real__0__less__add__iff,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_mult__right_Ozero,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(c_0_51,plain,
! [X2913,X2914] :
( ( c_RealVector_Onorm__class_Onorm(X2914,X2913) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2913 = c_Groups_Ozero__class_Ozero(X2914)
| ~ class_RealVector_Oreal__normed__vector(X2914) )
& ( X2913 != c_Groups_Ozero__class_Ozero(X2914)
| c_RealVector_Onorm__class_Onorm(X2914,X2913) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X2914) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(c_0_52,plain,
! [X3107] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3107) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3107),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
cnf(c_0_53,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| 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_51]) ).
cnf(c_0_54,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_55,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_52]) ).
fof(c_0_56,plain,
! [X4275,X4276] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4276)
| c_Groups_Oabs__class_Oabs(X4276,c_Groups_Ouminus__class_Ouminus(X4276,X4275)) = c_Groups_Oabs__class_Oabs(X4276,X4275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).
fof(c_0_57,plain,
! [X3170,X3171] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3171)
| ~ c_Orderings_Oord__class_Oless__eq(X3171,c_Groups_Ozero__class_Ozero(X3171),X3170)
| c_Groups_Oabs__class_Oabs(X3171,X3170) = X3170 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
cnf(c_0_58,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_60,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_61,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(split_conjunct,[status(thm)],[fact_rp]) ).
fof(c_0_63,plain,
! [X4322,X4323] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4323,c_Groups_Ozero__class_Ozero(X4323),c_Groups_Ouminus__class_Ouminus(X4323,X4322))
| c_Orderings_Oord__class_Oless__eq(X4323,X4322,c_Groups_Ozero__class_Ozero(X4323))
| ~ class_Groups_Oordered__ab__group__add(X4323) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4323,X4322,c_Groups_Ozero__class_Ozero(X4323))
| c_Orderings_Oord__class_Oless__eq(X4323,c_Groups_Ozero__class_Ozero(X4323),c_Groups_Ouminus__class_Ouminus(X4323,X4322))
| ~ class_Groups_Oordered__ab__group__add(X4323) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
cnf(c_0_64,plain,
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_65,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_60])]) ).
fof(c_0_66,plain,
! [X3470] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3470,X3470),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(c_0_67,plain,
! [X3095,X3096] :
( ~ class_Rings_Ocomm__semiring__1(X3096)
| c_Groups_Oplus__class_Oplus(X3096,X3095,c_Groups_Ozero__class_Ozero(X3096)) = X3095 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(c_0_68,plain,
! [X4383,X4384] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4384)
| ~ c_Orderings_Oord__class_Oless__eq(X4384,X4383,c_Groups_Ozero__class_Ozero(X4384))
| c_Groups_Oabs__class_Oabs(X4384,X4383) = c_Groups_Ouminus__class_Ouminus(X4384,X4383) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
cnf(c_0_69,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_70,plain,
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,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_72,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_73,plain,
! [X5560,X5561] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5561,X5560) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5561,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5560)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_74,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_75,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_76,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72])]) ).
fof(c_0_78,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_79,plain,
! [X3512,X3513] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3513,X3512)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3513,X3512) )
& ( X3513 != X3512
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3513,X3512) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3513,X3512)
| X3513 = X3512
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3513,X3512) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(c_0_80,plain,
! [X20] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = X20 ) ),
inference(fof_simplification,[status(thm)],[fact_real__abs__def]) ).
fof(c_0_81,plain,
! [X4404] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4404),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4404,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4404,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4404),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])]) ).
fof(c_0_82,plain,
! [X3873] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3873),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(c_0_83,plain,
! [X3090,X3091,X3092] :
( ( X3091 != c_Groups_Oplus__class_Oplus(X3092,X3091,X3090)
| X3090 = c_Groups_Ozero__class_Ozero(X3092)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3092) )
& ( X3090 != c_Groups_Ozero__class_Ozero(X3092)
| X3091 = c_Groups_Oplus__class_Oplus(X3092,X3091,X3090)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3092) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(c_0_84,plain,
! [X3527,X3528,X3529] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3529,X3528)),X3527) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3529),X3527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3528),X3527)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
cnf(c_0_85,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_86,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_87,plain,
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r) = v_r
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_65]),c_0_60])]) ).
fof(c_0_88,plain,
! [X3103,X3104] :
( ~ class_Rings_Ocomm__semiring__1(X3104)
| c_Groups_Oplus__class_Oplus(X3104,c_Groups_Ozero__class_Ozero(X3104),X3103) = X3103 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
cnf(c_0_89,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),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_78]) ).
cnf(c_0_90,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_79]) ).
fof(c_0_91,plain,
! [X4397] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4397,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4397) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4397) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4397,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4397) = X4397 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])]) ).
fof(c_0_92,plain,
! [X3334,X3335,X3336] :
( ~ class_Rings_Ocomm__semiring__1(X3336)
| c_Groups_Oplus__class_Oplus(X3336,X3335,X3334) = c_Groups_Oplus__class_Oplus(X3336,X3334,X3335) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_93,plain,
! [X4367,X4368] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4368,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4367)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4368 = X4367 )
& ( X4368 != X4367
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4368,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4367)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])]) ).
cnf(c_0_94,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_95,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natceiling__zero]) ).
cnf(c_0_96,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_97,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_98,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_99,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]) ).
cnf(c_0_100,plain,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,v_r) = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_70]),c_0_86]) ).
cnf(c_0_101,plain,
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,v_r) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_r)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(spm,[status(thm)],[c_0_85,c_0_87]) ).
fof(c_0_102,plain,
! [X4429] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4429)) = c_RealDef_Oreal(tc_Nat_Onat,X4429),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(c_0_103,plain,
! [X3366,X3367,X3368,X3369] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3369,c_Groups_Oplus__class_Oplus(X3369,X3368,X3367),c_Groups_Oplus__class_Oplus(X3369,X3366,X3367))
| c_Orderings_Oord__class_Oless__eq(X3369,X3368,X3366)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3369) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3369,X3368,X3366)
| c_Orderings_Oord__class_Oless__eq(X3369,c_Groups_Oplus__class_Oplus(X3369,X3368,X3367),c_Groups_Oplus__class_Oplus(X3369,X3366,X3367))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3369) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
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_88]) ).
cnf(c_0_105,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),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(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_106,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_107,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_92]) ).
cnf(c_0_108,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_109,plain,
! [X3084,X3085] :
( ~ class_RealVector_Oreal__normed__algebra(X3085)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3085),c_Groups_Ozero__class_Ozero(X3085)),X3084) = c_Groups_Ozero__class_Ozero(X3085) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(c_0_110,plain,
! [X3074,X3075,X3076,X3077] :
( ( ~ c_Orderings_Oord__class_Oless(X3077,c_Groups_Oplus__class_Oplus(X3077,X3076,X3075),c_Groups_Oplus__class_Oplus(X3077,X3074,X3075))
| c_Orderings_Oord__class_Oless(X3077,X3076,X3074)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3077) )
& ( ~ c_Orderings_Oord__class_Oless(X3077,X3076,X3074)
| c_Orderings_Oord__class_Oless(X3077,c_Groups_Oplus__class_Oplus(X3077,X3076,X3075),c_Groups_Oplus__class_Oplus(X3077,X3074,X3075))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3077) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
cnf(c_0_111,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_79]) ).
cnf(c_0_112,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]) ).
cnf(c_0_113,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__zero__not__eq__one]) ).
cnf(c_0_114,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1)),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).
cnf(c_0_115,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_r) = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_116,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_117,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]) ).
cnf(c_0_118,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_119,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[c_0_104,c_0_75]) ).
cnf(c_0_120,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]) ).
cnf(c_0_121,negated_conjecture,
( c_Orderings_Oord__class_Oless(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_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_122,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_107,c_0_75]) ).
fof(c_0_123,plain,
! [X5353,X5354,X5355,X5356,X5357,X5358] :
( ( ~ c_Orderings_Oord__class_Oless(X5358,c_Groups_Oplus__class_Oplus(X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5358),X5357),X5356),X5355),c_Groups_Oplus__class_Oplus(X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5358),X5354),X5356),X5353))
| c_Orderings_Oord__class_Oless(X5358,X5355,c_Groups_Oplus__class_Oplus(X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5358),c_Groups_Ominus__class_Ominus(X5358,X5354,X5357)),X5356),X5353))
| ~ class_Rings_Oordered__ring(X5358) )
& ( ~ c_Orderings_Oord__class_Oless(X5358,X5355,c_Groups_Oplus__class_Oplus(X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5358),c_Groups_Ominus__class_Ominus(X5358,X5354,X5357)),X5356),X5353))
| c_Orderings_Oord__class_Oless(X5358,c_Groups_Oplus__class_Oplus(X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5358),X5357),X5356),X5355),c_Groups_Oplus__class_Oplus(X5358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5358),X5354),X5356),X5353))
| ~ class_Rings_Oordered__ring(X5358) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
cnf(c_0_124,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(er,[status(thm)],[c_0_108]) ).
cnf(c_0_125,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_126,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(c_0_127,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_128,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
fof(c_0_129,plain,
! [X12,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X12)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X12,X13) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
cnf(c_0_130,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_131,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_132,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_112]),c_0_119]),c_0_120])]) ).
fof(c_0_133,plain,
! [X3010,X3011,X3012] :
( ~ class_Orderings_Opreorder(X3012)
| ~ c_Orderings_Oord__class_Oless(X3012,X3011,X3010)
| c_Orderings_Oord__class_Oless__eq(X3012,X3011,X3010) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
cnf(c_0_134,negated_conjecture,
( c_Orderings_Oord__class_Oless(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_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122]),c_0_122]) ).
cnf(c_0_135,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_136,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
cnf(c_0_137,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_124,c_0_85]) ).
cnf(c_0_138,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_139,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_119]),c_0_120])]) ).
fof(c_0_140,plain,
! [X3034,X3035,X3036] :
( ( c_Orderings_Oord__class_Oless__eq(X3036,X3035,X3034)
| ~ c_Orderings_Oord__class_Oless(X3036,X3035,X3034)
| ~ class_Orderings_Opreorder(X3036) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3036,X3034,X3035)
| ~ c_Orderings_Oord__class_Oless(X3036,X3035,X3034)
| ~ class_Orderings_Opreorder(X3036) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3036,X3035,X3034)
| c_Orderings_Oord__class_Oless__eq(X3036,X3034,X3035)
| c_Orderings_Oord__class_Oless(X3036,X3035,X3034)
| ~ class_Orderings_Opreorder(X3036) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])]) ).
cnf(c_0_141,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(spm,[status(thm)],[c_0_111,c_0_62]) ).
cnf(c_0_142,negated_conjecture,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r,
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_89,c_0_130]),c_0_86]),c_0_131]),c_0_86]),c_0_132])]) ).
fof(c_0_143,plain,
! [X3535,X3536,X3537] :
( ( c_Orderings_Oord__class_Oless__eq(X3537,X3536,c_Groups_Ozero__class_Ozero(X3537))
| c_Orderings_Oord__class_Oless__eq(X3537,c_Groups_Ozero__class_Ozero(X3537),X3536)
| ~ c_Orderings_Oord__class_Oless__eq(X3537,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535),c_Groups_Ozero__class_Ozero(X3537))
| ~ class_Rings_Olinordered__ring__strict(X3537) )
& ( c_Orderings_Oord__class_Oless__eq(X3537,c_Groups_Ozero__class_Ozero(X3537),X3535)
| c_Orderings_Oord__class_Oless__eq(X3537,c_Groups_Ozero__class_Ozero(X3537),X3536)
| ~ c_Orderings_Oord__class_Oless__eq(X3537,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535),c_Groups_Ozero__class_Ozero(X3537))
| ~ class_Rings_Olinordered__ring__strict(X3537) )
& ( c_Orderings_Oord__class_Oless__eq(X3537,X3536,c_Groups_Ozero__class_Ozero(X3537))
| c_Orderings_Oord__class_Oless__eq(X3537,X3535,c_Groups_Ozero__class_Ozero(X3537))
| ~ c_Orderings_Oord__class_Oless__eq(X3537,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535),c_Groups_Ozero__class_Ozero(X3537))
| ~ class_Rings_Olinordered__ring__strict(X3537) )
& ( c_Orderings_Oord__class_Oless__eq(X3537,c_Groups_Ozero__class_Ozero(X3537),X3535)
| c_Orderings_Oord__class_Oless__eq(X3537,X3535,c_Groups_Ozero__class_Ozero(X3537))
| ~ c_Orderings_Oord__class_Oless__eq(X3537,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535),c_Groups_Ozero__class_Ozero(X3537))
| ~ class_Rings_Olinordered__ring__strict(X3537) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3537,c_Groups_Ozero__class_Ozero(X3537),X3536)
| ~ c_Orderings_Oord__class_Oless__eq(X3537,X3535,c_Groups_Ozero__class_Ozero(X3537))
| c_Orderings_Oord__class_Oless__eq(X3537,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535),c_Groups_Ozero__class_Ozero(X3537))
| ~ class_Rings_Olinordered__ring__strict(X3537) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3537,X3536,c_Groups_Ozero__class_Ozero(X3537))
| ~ c_Orderings_Oord__class_Oless__eq(X3537,c_Groups_Ozero__class_Ozero(X3537),X3535)
| c_Orderings_Oord__class_Oless__eq(X3537,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535),c_Groups_Ozero__class_Ozero(X3537))
| ~ class_Rings_Olinordered__ring__strict(X3537) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
cnf(c_0_144,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_145,negated_conjecture,
c_Orderings_Oord__class_Oless(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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_137]),c_0_138]),c_0_119]),c_0_139])]) ).
cnf(c_0_146,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_147,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_148,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(sr,[status(thm)],[c_0_141,c_0_142]) ).
fof(c_0_149,plain,
! [X9,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X9),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
cnf(c_0_150,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_151,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146])]) ).
cnf(c_0_152,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
cnf(c_0_153,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_146])]) ).
fof(c_0_154,plain,
! [X3473,X3474,X3475] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3475,X3474)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3474,X3473)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3475,X3473) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(c_0_155,plain,
! [X4316,X4317] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4317,c_Groups_Ouminus__class_Ouminus(X4317,X4316),X4316)
| c_Orderings_Oord__class_Oless__eq(X4317,c_Groups_Ozero__class_Ozero(X4317),X4316)
| ~ class_Groups_Olinordered__ab__group__add(X4317) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4317,c_Groups_Ozero__class_Ozero(X4317),X4316)
| c_Orderings_Oord__class_Oless__eq(X4317,c_Groups_Ouminus__class_Ouminus(X4317,X4316),X4316)
| ~ class_Groups_Olinordered__ab__group__add(X4317) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(c_0_156,plain,
! [X4415] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4415)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4415)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(c_0_157,plain,
! [X2891,X2892] :
( ~ class_Groups_Oordered__ab__group__add__abs(X2892)
| ~ c_Orderings_Oord__class_Oless(X2892,c_Groups_Oabs__class_Oabs(X2892,X2891),c_Groups_Ozero__class_Ozero(X2892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])]) ).
cnf(c_0_158,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152])]),c_0_153]) ).
fof(c_0_159,plain,
! [X12,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X12)
<=> X13 = X12 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
cnf(c_0_160,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_161,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)),v_m____),
inference(split_conjunct,[status(thm)],[fact_th]) ).
cnf(c_0_162,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
cnf(c_0_163,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_164,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_165,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_166,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_m____) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_m____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_158]),c_0_60])]) ).
fof(c_0_167,plain,
! [X4395,X4396] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4396,X4395))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4396),X4395) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4396),X4395)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4396,X4395)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
fof(c_0_168,plain,
! [X3007,X3008,X3009] :
( ( c_Orderings_Oord__class_Oless(X3009,X3008,X3007)
| X3008 = X3007
| ~ c_Orderings_Oord__class_Oless__eq(X3009,X3008,X3007)
| ~ class_Orderings_Olinorder(X3009) )
& ( X3008 != X3007
| ~ c_Orderings_Oord__class_Oless(X3009,X3008,X3007)
| ~ c_Orderings_Oord__class_Oless__eq(X3009,X3008,X3007)
| ~ class_Orderings_Olinorder(X3009) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])])]) ).
cnf(c_0_169,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____))) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_170,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,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164])]) ).
cnf(c_0_171,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_m____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_60])]) ).
cnf(c_0_172,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
fof(c_0_173,plain,
! [X3078,X3079] :
( ~ class_RealVector_Oreal__normed__algebra(X3079)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3079),X3078),c_Groups_Ozero__class_Ozero(X3079)) = c_Groups_Ozero__class_Ozero(X3079) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
cnf(c_0_174,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_175,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_176,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_177,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_86]) ).
cnf(c_0_178,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_179,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_147,c_0_145]),c_0_146])]) ).
cnf(c_0_180,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_m____,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_176])]),c_0_177]) ).
cnf(c_0_181,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_178,c_0_126]) ).
cnf(c_0_182,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),
inference(rw,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_183,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),v_m____) = v_m____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_180]),c_0_180]) ).
cnf(c_0_184,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183]),c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW180+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n020.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 06:23:20 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 26.67/16.31 % Version : CSE_E---1.7
% 26.67/16.31 % Problem : theBenchmark.p
% 26.67/16.31 % SZS status Theorem for theBenchmark.p
% 26.67/16.31 % SZS output start CNFRefutation
% See solution above
% 26.78/16.42 % Total time : 11.650s
%------------------------------------------------------------------------------