%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW180+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:02 PM UTC 2026
% Result : Theorem 27.39s 4.58s
% Output : CNFRefutation 27.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 107 ( 55 unt; 0 def)
% Number of atoms : 200 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 162 ( 69 ~; 62 |; 5 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 149 ( 6 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
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/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__mult__pos,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X4)),X5) = c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X4),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
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/sandbox2/benchmark/theBenchmark.p',fact_rp) ).
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/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
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/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
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/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
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/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
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/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
fof(fact_le__add__iff2,axiom,
! [X32,X18,X19,X81,X14,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(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__eq(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/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
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/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(fact_real__le__linear,axiom,
! [X27,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X16)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_xt1_I6_J,axiom,
! [X16,X5,X4,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X4,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_leI,axiom,
! [X4,X5,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_real__le__antisym,axiom,
! [X27,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X27)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X16)
=> X16 = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(fact_norm__not__less__zero,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
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/sandbox2/benchmark/theBenchmark.p',fact_th) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(c_0_32,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(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_33,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)],[c_0_32]) ).
fof(c_0_34,plain,
! [X400,X401] :
( c_Groups_Oabs__class_Oabs(X401,X400) = X400
| ~ c_Orderings_Oord__class_Oless__eq(X401,c_Groups_Ozero__class_Ozero(X401),X400)
| ~ class_Groups_Oordered__ab__group__add__abs(X401) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])])]) ).
fof(c_0_35,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_nnf,[status(thm)],[c_0_33]) ).
fof(c_0_36,plain,
! [X690,X691,X692] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X692),c_Groups_Oabs__class_Oabs(X692,X690)),X691) = c_Groups_Oabs__class_Oabs(X692,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X692),X690),X691))
| ~ c_Orderings_Oord__class_Oless__eq(X692,c_Groups_Ozero__class_Ozero(X692),X691)
| ~ class_Rings_Olinordered__idom(X692) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])])]) ).
cnf(c_0_37,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,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]) ).
cnf(c_0_39,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]) ).
fof(c_0_40,plain,
! [X564,X565,X566] :
( c_Groups_Oplus__class_Oplus(X566,X565,X564) = c_Groups_Oplus__class_Oplus(X566,X564,X565)
| ~ class_Rings_Ocomm__semiring__1(X566) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
fof(c_0_41,plain,
! [X1597,X1598] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1597)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1598 != X1597 )
& ( X1598 = X1597
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1597)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])])]) ).
fof(c_0_42,plain,
! [X1634] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1634),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1634,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1634,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1634),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])])]) ).
fof(c_0_43,plain,
! [X1103] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1103),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(c_0_44,plain,
! [X333,X334] :
( c_Groups_Oplus__class_Oplus(X334,c_Groups_Ozero__class_Ozero(X334),X333) = X333
| ~ class_Rings_Ocomm__semiring__1(X334) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).
cnf(c_0_45,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_35]) ).
cnf(c_0_46,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),X2) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,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_37,c_0_38]),c_0_39])]) ).
cnf(c_0_48,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_49,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_51,plain,
( X1 != X2
| 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) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_52,plain,
! [X2790,X2791] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2791,X2790) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2791,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2790)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
fof(c_0_53,plain,
! [X314,X315] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X315),c_Groups_Ozero__class_Ozero(X315)),X314) = c_Groups_Ozero__class_Ozero(X315)
| ~ class_RealVector_Oreal__normed__algebra(X315) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])])]) ).
fof(c_0_54,plain,
! [X596,X597,X598,X599] :
( ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X599)
| c_Orderings_Oord__class_Oless__eq(X599,c_Groups_Oplus__class_Oplus(X599,X598,X597),c_Groups_Oplus__class_Oplus(X599,X596,X597))
| ~ c_Orderings_Oord__class_Oless__eq(X599,X598,X596) )
& ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X599)
| c_Orderings_Oord__class_Oless__eq(X599,X598,X596)
| ~ c_Orderings_Oord__class_Oless__eq(X599,c_Groups_Oplus__class_Oplus(X599,X598,X597),c_Groups_Oplus__class_Oplus(X599,X596,X597)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])])]) ).
cnf(c_0_55,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,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_57,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_43]) ).
cnf(c_0_58,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ 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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]) ).
cnf(c_0_60,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_49,c_0_50]) ).
fof(c_0_61,plain,
! [X2571,X2572,X2573,X2574,X2575,X2576] :
( ( ~ class_Rings_Oordered__ring(X2576)
| c_Orderings_Oord__class_Oless__eq(X2576,c_Groups_Oplus__class_Oplus(X2576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2576),X2575),X2574),X2573),c_Groups_Oplus__class_Oplus(X2576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2576),X2572),X2574),X2571))
| ~ c_Orderings_Oord__class_Oless__eq(X2576,X2573,c_Groups_Oplus__class_Oplus(X2576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2576),c_Groups_Ominus__class_Ominus(X2576,X2572,X2575)),X2574),X2571)) )
& ( ~ class_Rings_Oordered__ring(X2576)
| c_Orderings_Oord__class_Oless__eq(X2576,X2573,c_Groups_Oplus__class_Oplus(X2576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2576),c_Groups_Ominus__class_Ominus(X2576,X2572,X2575)),X2574),X2571))
| ~ c_Orderings_Oord__class_Oless__eq(X2576,c_Groups_Oplus__class_Oplus(X2576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2576),X2575),X2574),X2573),c_Groups_Oplus__class_Oplus(X2576,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2576),X2572),X2574),X2571)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])])]) ).
cnf(c_0_62,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_51]) ).
cnf(c_0_63,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_52]) ).
cnf(c_0_64,plain,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(c_0_66,plain,
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,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_55,c_0_56]),c_0_57])]) ).
cnf(c_0_68,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_58,c_0_50]) ).
cnf(c_0_69,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_70,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(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_59,c_0_60]),c_0_60]) ).
cnf(c_0_71,plain,
( ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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))
| c_Orderings_Oord__class_Oless__eq(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)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
cnf(c_0_73,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_62,c_0_63]) ).
cnf(c_0_74,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_64,c_0_65]) ).
cnf(c_0_75,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_66,c_0_67]),c_0_68]),c_0_69])]) ).
fof(c_0_76,plain,
! [X701,X702] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X701,X702)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X702,X701) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_77,plain,
! [X426,X427,X428,X429] :
( c_Orderings_Oord__class_Oless__eq(X429,X426,X427)
| ~ c_Orderings_Oord__class_Oless__eq(X429,X426,X428)
| ~ c_Orderings_Oord__class_Oless__eq(X429,X428,X427)
| ~ class_Orderings_Oorder(X429) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])])]) ).
cnf(c_0_78,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
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_70,c_0_71]),c_0_72]),c_0_73]),c_0_74]),c_0_68]),c_0_75])]) ).
cnf(c_0_79,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_80,plain,
! [X1546,X1547] :
( ( ~ class_Groups_Olinordered__ab__group__add(X1547)
| c_Orderings_Oord__class_Oless__eq(X1547,c_Groups_Ouminus__class_Ouminus(X1547,X1546),X1546)
| ~ c_Orderings_Oord__class_Oless__eq(X1547,c_Groups_Ozero__class_Ozero(X1547),X1546) )
& ( ~ class_Groups_Olinordered__ab__group__add(X1547)
| c_Orderings_Oord__class_Oless__eq(X1547,c_Groups_Ozero__class_Ozero(X1547),X1546)
| ~ c_Orderings_Oord__class_Oless__eq(X1547,c_Groups_Ouminus__class_Ouminus(X1547,X1546),X1546) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])])]) ).
fof(c_0_81,plain,
! [X1645] : 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,X1645)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1645)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(c_0_82,plain,
! [X4,X5,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X4,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(c_0_83,plain,
! [X706,X707] :
( X707 = X706
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X706,X707)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X707,X706) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])])]) ).
cnf(c_0_84,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_85,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_87,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_88,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_81]) ).
cnf(c_0_89,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
fof(c_0_90,plain,
! [X258,X259,X260] :
( c_Orderings_Oord__class_Oless__eq(X260,X258,X259)
| c_Orderings_Oord__class_Oless(X260,X259,X258)
| ~ class_Orderings_Olinorder(X260) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])]) ).
fof(c_0_91,plain,
! [X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
cnf(c_0_92,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_93,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_94,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_95,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_87,c_0_88]),c_0_89])]) ).
cnf(c_0_96,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_97,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_98,plain,
! [X123,X124] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X124,X123),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X124) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])]) ).
cnf(c_0_99,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)) = v_m____ ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,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_98]) ).
cnf(c_0_103,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)) = v_m____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
cnf(c_0_104,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_78,c_0_101]) ).
cnf(c_0_105,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_106,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW180+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 09:41:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.39/4.58 % Version: 3.5.1
% 27.39/4.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 27.39/4.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.39/4.58 % Starting new_bool_3 with 300s (1) cores
% 27.39/4.58 % Starting new_bool_1 with 300s (1) cores
% 27.39/4.58 % Starting sh5l with 300s (1) cores
% 27.39/4.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3980988 completed with status 0
% 27.39/4.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 27.39/4.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 27.39/4.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.39/4.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.39/4.58 % No SInE strategy applied
% 27.39/4.58 % Search class: FGHSM-SSLM32-DFFFFFNN
% 27.39/4.58 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 27.39/4.58 % Starting SubtermCWHack with 136s (1) cores
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 27.39/4.58 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 27.39/4.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3980996 completed with status 0
% 27.39/4.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 27.39/4.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 27.39/4.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.39/4.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.39/4.58 % No SInE strategy applied
% 27.39/4.58 % Search class: FGHSM-SSLM32-DFFFFFNN
% 27.39/4.58 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 27.39/4.58 % Starting SubtermCWHack with 136s (1) cores
% 27.39/4.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.39/4.58 % Preprocessing time : 0.040 s
% 27.39/4.58 % Presaturation interreduction done
% 27.39/4.58
% 27.39/4.58 % Proof found!
% 27.39/4.58 % SZS status Theorem
% 27.39/4.58 % SZS output start CNFRefutation
% See solution above
% 27.39/4.58 % Parsed axioms : 1275
% 27.39/4.58 % Removed by relevancy pruning/SinE : 0
% 27.39/4.58 % Initial clauses : 1692
% 27.39/4.58 % Removed in clause preprocessing : 69
% 27.39/4.58 % Initial clauses in saturation : 1623
% 27.39/4.58 % Processed clauses : 12920
% 27.39/4.58 % ...of these trivial : 559
% 27.39/4.58 % ...subsumed : 7074
% 27.39/4.58 % ...remaining for further processing : 5287
% 27.39/4.58 % Other redundant clauses eliminated : 504
% 27.39/4.58 % Clauses deleted for lack of memory : 0
% 27.39/4.58 % Backward-subsumed : 420
% 27.39/4.58 % Backward-rewritten : 360
% 27.39/4.58 % Generated clauses : 102128
% 27.39/4.58 % ...of the previous two non-redundant : 87518
% 27.39/4.58 % ...aggressively subsumed : 0
% 27.39/4.58 % Contextual simplify-reflections : 5
% 27.39/4.58 % Paramodulations : 101593
% 27.39/4.58 % Factorizations : 10
% 27.39/4.58 % NegExts : 0
% 27.39/4.58 % Equation resolutions : 538
% 27.39/4.58 % Disequality decompositions : 0
% 27.39/4.58 % Total rewrite steps : 86310
% 27.39/4.58 % ...of those cached : 81036
% 27.39/4.58 % Propositional unsat checks : 1
% 27.39/4.58 % Propositional check models : 0
% 27.39/4.58 % Propositional check unsatisfiable : 0
% 27.39/4.58 % Propositional clauses : 0
% 27.39/4.58 % Propositional clauses after purity: 0
% 27.39/4.58 % Propositional unsat core size : 0
% 27.39/4.58 % Propositional preprocessing time : 0.000
% 27.39/4.58 % Propositional encoding time : 0.155
% 27.39/4.58 % Propositional solver time : 0.140
% 27.39/4.58 % Success case prop preproc time : 0.000
% 27.39/4.58 % Success case prop encoding time : 0.000
% 27.39/4.58 % Success case prop solver time : 0.000
% 27.39/4.58 % Current number of processed clauses : 3039
% 27.39/4.58 % Positive orientable unit clauses : 943
% 27.39/4.58 % Positive unorientable unit clauses: 14
% 27.39/4.58 % Negative unit clauses : 505
% 27.39/4.58 % Non-unit-clauses : 1577
% 27.39/4.58 % Current number of unprocessed clauses: 77092
% 27.39/4.58 % ...number of literals in the above : 192752
% 27.39/4.58 % Current number of archived formulas : 0
% 27.39/4.58 % Current number of archived clauses : 2106
% 27.39/4.58 % Clause-clause subsumption calls (NU) : 424736
% 27.39/4.58 % Rec. Clause-clause subsumption calls : 319452
% 27.39/4.58 % Non-unit clause-clause subsumptions : 3048
% 27.39/4.58 % Unit Clause-clause subsumption calls : 79861
% 27.39/4.58 % Rewrite failures with RHS unbound : 0
% 27.39/4.58 % BW rewrite match attempts : 33117
% 27.39/4.58 % BW rewrite match successes : 666
% 27.39/4.58 % Condensation attempts : 0
% 27.39/4.58 % Condensation successes : 0
% 27.39/4.58 % Termbank termtop insertions : 2779812
% 27.39/4.58 % Search garbage collected termcells : 19953
% 27.39/4.58
% 27.39/4.58 % -------------------------------------------------
% 27.39/4.58 % User time : 3.852 s
% 27.39/4.58 % System time : 0.159 s
% 27.39/4.58 % Total time : 4.011 s
% 27.39/4.58 % Maximum resident set size: 9644 pages
% 27.39/4.58
% 27.39/4.58 % -------------------------------------------------
% 27.39/4.58 % User time : 18.673 s
% 27.39/4.58 % System time : 0.654 s
% 27.39/4.58 % Total time : 19.327 s
% 27.39/4.58 % Maximum resident set size: 5888 pages
% 27.39/4.58 % E exiting
%------------------------------------------------------------------------------