TSTP Solution File: SWW234+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW234+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Fri Sep 1 00:16:40 EDT 2023
% Result : Theorem 3.13s 3.24s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 185
% Syntax : Number of formulae : 264 ( 56 unt; 152 typ; 0 def)
% Number of atoms : 211 ( 53 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 171 ( 72 ~; 66 |; 7 &)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 226 ( 138 >; 88 *; 0 +; 0 <<)
% Number of predicates : 75 ( 73 usr; 1 prp; 0-3 aty)
% Number of functors : 79 ( 79 usr; 14 con; 0-5 aty)
% Number of variables : 162 ( 1 sgn; 99 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_RealDef_Oreal: $i ).
tff(decl_24,type,
v_r____: $i ).
tff(decl_25,type,
tc_Complex_Ocomplex: $i ).
tff(decl_26,type,
v_z____: $i ).
tff(decl_27,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
v_p: $i ).
tff(decl_30,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_31,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_32,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_33,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_34,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_35,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_36,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
class_Groups_Oone: $i > $o ).
tff(decl_38,type,
class_Orderings_Oord: $i > $o ).
tff(decl_39,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_40,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_41,type,
v_cs____: $i ).
tff(decl_42,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_43,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_44,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_45,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_46,type,
class_Groups_Ozero: $i > $o ).
tff(decl_47,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_48,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_49,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_50,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_51,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_52,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_53,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_54,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_55,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_56,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_57,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_58,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_59,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_60,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_62,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_64,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_65,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_66,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_67,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_68,type,
v_c____: $i ).
tff(decl_69,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_71,type,
tc_Nat_Onat: $i ).
tff(decl_72,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_73,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_74,type,
c_Complex_Oii: $i ).
tff(decl_75,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_76,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_77,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_78,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_79,type,
class_Rings_Oidom: $i > $o ).
tff(decl_80,type,
class_Rings_Oring: $i > $o ).
tff(decl_81,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_82,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_83,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_84,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_85,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_86,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_87,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_88,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_89,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_90,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_91,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_92,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_93,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_94,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_95,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_96,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_97,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_98,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_99,type,
class_Groups_Oabs__if: $i > $o ).
tff(decl_100,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_101,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_102,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_103,type,
v_da____: $i ).
tff(decl_104,type,
v_aa____: $i ).
tff(decl_105,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_106,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_107,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_108,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_109,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
hBOOL: $i > $o ).
tff(decl_111,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_112,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_114,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_115,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_116,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_117,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_118,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_119,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_120,type,
class_Groups_Ominus: $i > $o ).
tff(decl_121,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_122,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_123,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_124,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_125,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_126,type,
class_Power_Opower: $i > $o ).
tff(decl_127,type,
tc_Int_Oint: $i ).
tff(decl_128,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_129,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_131,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_132,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_133,type,
class_Rings_Odvd: $i > $o ).
tff(decl_134,type,
c_Nat_OSuc: $i > $i ).
tff(decl_135,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_136,type,
tc_HOL_Obool: $i ).
tff(decl_137,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_139,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_140,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk5_0: $i ).
tff(decl_142,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_144,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk11_1: $i > $i ).
tff(decl_148,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk14_1: $i > $i ).
tff(decl_151,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk20_1: $i > $i ).
tff(decl_157,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_163,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk28_1: $i > $i ).
tff(decl_165,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_171,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_173,type,
esk37_2: ( $i * $i ) > $i ).
fof(fact_linorder__not__less,axiom,
! [X21,X11,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
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(fact_less__le__not__le,axiom,
! [X21,X11,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_xt1_I8_J,axiom,
! [X7,X5,X13,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X13,X5)
=> ( c_Orderings_Oord__class_Oless(X4,X7,X13)
=> c_Orderings_Oord__class_Oless(X4,X7,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_real__mult__1,axiom,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(fact_nat__mult__1,axiom,
! [X46] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X46) = X46,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_norm__one,axiom,
! [X4] :
( class_RealVector_Oreal__normed__algebra__1(X4)
=> c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oone__class_Oone(X4)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_real__norm__def,axiom,
! [X15] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X15) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
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__mult__pos,axiom,
! [X13,X5,X4] :
( class_Rings_Olinordered__idom(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oabs__class_Oabs(X4,X13)),X5) = c_Groups_Oabs__class_Oabs(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(fact_natfloor__add__one,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_nat__add__commute,axiom,
! [X46,X40] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X46) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_h,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X18,X14,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,X14,X18) = c_Groups_Oplus__class_Oplus(X4,X18,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_le__add1,axiom,
! [X40,X46] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,X40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
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(fact_real__le__linear,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X6)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_add__0__left,axiom,
! [X14,X4] :
( class_Groups_Omonoid__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X14) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_diff__add__cancel,axiom,
! [X16,X14,X4] :
( class_Groups_Ogroup__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Ominus__class_Ominus(X4,X14,X16),X16) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_real__le__trans,axiom,
! [X8,X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_add__le__cancel__right,axiom,
! [X20,X19,X17,X4] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X17,X19),c_Groups_Oplus__class_Oplus(X4,X20,X19))
<=> c_Orderings_Oord__class_Oless__eq(X4,X17,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(fact_abs__of__nonpos,axiom,
! [X14,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X14,c_Groups_Ozero__class_Ozero(X4))
=> c_Groups_Oabs__class_Oabs(X4,X14) = c_Groups_Ouminus__class_Ouminus(X4,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
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(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_real__diff__def,axiom,
! [X24,X15] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X24) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(c_0_33,plain,
! [X21,X11,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(c_0_34,plain,
! [X440,X441,X442] :
( ( c_Orderings_Oord__class_Oless(X442,X441,X440)
| c_Orderings_Oord__class_Oless__eq(X442,X440,X441)
| ~ class_Orderings_Olinorder(X442) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X442,X440,X441)
| ~ c_Orderings_Oord__class_Oless(X442,X441,X440)
| ~ class_Orderings_Olinorder(X442) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
fof(c_0_35,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_36,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_38,plain,
! [X21,X11,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_39,plain,
! [X503,X504,X505,X506] :
( ~ class_Orderings_Oorder(X506)
| ~ c_Orderings_Oord__class_Oless__eq(X506,X505,X504)
| ~ c_Orderings_Oord__class_Oless(X506,X503,X505)
| c_Orderings_Oord__class_Oless(X506,X503,X504) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
cnf(c_0_40,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_42,plain,
! [X94,X95] :
( hAPP(X95,esk1_2(X94,X95)) != hAPP(X94,esk1_2(X94,X95))
| X95 = X94 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(c_0_43,plain,
! [X971] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X971) = X971,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_44,plain,
! [X452,X453,X454] :
( ( c_Orderings_Oord__class_Oless__eq(X454,X453,X452)
| ~ c_Orderings_Oord__class_Oless(X454,X453,X452)
| ~ class_Orderings_Opreorder(X454) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X454,X452,X453)
| ~ c_Orderings_Oord__class_Oless(X454,X453,X452)
| ~ class_Orderings_Opreorder(X454) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X454,X453,X452)
| c_Orderings_Oord__class_Oless__eq(X454,X452,X453)
| c_Orderings_Oord__class_Oless(X454,X453,X452)
| ~ class_Orderings_Opreorder(X454) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_45,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_48,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_50,plain,
! [X1765] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1765) = X1765,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(c_0_51,plain,
! [X97] :
( ~ class_RealVector_Oreal__normed__algebra__1(X97)
| c_RealVector_Onorm__class_Onorm(X97,c_Groups_Oone__class_Oone(X97)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(c_0_52,plain,
! [X123] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X123) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X123),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
cnf(c_0_53,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_44]) ).
cnf(c_0_54,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_55,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_56,plain,
! [X1319,X1320,X1321] :
( ~ class_Rings_Olinordered__idom(X1321)
| ~ c_Orderings_Oord__class_Oless__eq(X1321,c_Groups_Ozero__class_Ozero(X1321),X1320)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1321),c_Groups_Oabs__class_Oabs(X1321,X1319)),X1320) = c_Groups_Oabs__class_Oabs(X1321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1321),X1319),X1320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
cnf(c_0_57,plain,
( X1 = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| hAPP(X1,esk1_2(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) != esk1_2(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).
cnf(c_0_61,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_62,plain,
! [X1873] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1873)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1873,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1873),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])]) ).
fof(c_0_63,plain,
! [X1577,X1578] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1578,X1577) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1577,X1578),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_64,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_65,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[fact_h]) ).
cnf(c_0_66,plain,
( 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))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_69,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
fof(c_0_70,plain,
! [X670,X671,X672] :
( ~ class_Rings_Ocomm__semiring__1(X672)
| c_Groups_Oplus__class_Oplus(X672,X671,X670) = c_Groups_Oplus__class_Oplus(X672,X670,X671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_71,plain,
! [X1878] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1878))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1878) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1878)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1878)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
cnf(c_0_72,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_74,plain,
! [X1694,X1695] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1695,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1695,X1694)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
cnf(c_0_75,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_76,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
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_66,c_0_67]),c_0_58]),c_0_68]),c_0_67]),c_0_58]),c_0_69])]) ).
cnf(c_0_77,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_70]) ).
cnf(c_0_78,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_79,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_81,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,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_77,c_0_78]) ).
cnf(c_0_84,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
fof(c_0_85,plain,
! [X101,X102] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X102,X101)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X101,X102) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_86,plain,
! [X132,X133] :
( ~ class_Groups_Omonoid__add(X133)
| c_Groups_Oplus__class_Oplus(X133,c_Groups_Ozero__class_Ozero(X133),X132) = X132 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(c_0_87,plain,
! [X437,X438,X439] :
( ~ class_Groups_Ogroup__add(X439)
| c_Groups_Oplus__class_Oplus(X439,c_Groups_Ominus__class_Ominus(X439,X438,X437),X437) = X438 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(c_0_88,plain,
! [X103,X104,X105] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X105,X104)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X104,X103)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X105,X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(c_0_89,plain,
! [X227,X228,X229,X230] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X230,c_Groups_Oplus__class_Oplus(X230,X229,X228),c_Groups_Oplus__class_Oplus(X230,X227,X228))
| c_Orderings_Oord__class_Oless__eq(X230,X229,X227)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X230) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X230,X229,X227)
| c_Orderings_Oord__class_Oless__eq(X230,c_Groups_Oplus__class_Oplus(X230,X229,X228),c_Groups_Oplus__class_Oplus(X230,X227,X228))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
cnf(c_0_90,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_91,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_92,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
fof(c_0_94,plain,
! [X1229,X1230] :
( ~ class_Groups_Oordered__ab__group__add__abs(X1230)
| ~ c_Orderings_Oord__class_Oless__eq(X1230,X1229,c_Groups_Ozero__class_Ozero(X1230))
| c_Groups_Oabs__class_Oabs(X1230,X1229) = c_Groups_Ouminus__class_Ouminus(X1230,X1229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
cnf(c_0_95,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_96,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_97,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_88]) ).
cnf(c_0_98,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_89]) ).
cnf(c_0_99,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,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_92,c_0_93]) ).
cnf(c_0_101,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_102,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_94]) ).
cnf(c_0_103,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_104,plain,
! [X956,X957] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X957,X956) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X957,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X956)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
cnf(c_0_105,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_106,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ 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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))) ),
inference(spm,[status(thm)],[c_0_97,c_0_65]) ).
cnf(c_0_107,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,X1),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_108,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_99]),c_0_103])]) ).
cnf(c_0_109,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_104]) ).
cnf(c_0_110,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_105,c_0_83]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_109]),c_0_110]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW234+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 21:59:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 3.13/3.24 % Version : CSE_E---1.5
% 3.13/3.24 % Problem : theBenchmark.p
% 3.13/3.24 % Proof found
% 3.13/3.24 % SZS status Theorem for theBenchmark.p
% 3.13/3.24 % SZS output start Proof
% See solution above
% 3.13/3.26 % Total time : 2.618000 s
% 3.13/3.26 % SZS output end Proof
% 3.13/3.26 % Total time : 2.659000 s
%------------------------------------------------------------------------------