TSTP Solution File: SWW177+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW177+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 : n026.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 00:16:21 EDT 2023
% Result : Theorem 11.12s 11.28s
% Output : CNFRefutation 11.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 191
% Syntax : Number of formulae : 412 ( 112 unt; 119 typ; 0 def)
% Number of atoms : 723 ( 175 equ)
% Maximal formula atoms : 62 ( 2 avg)
% Number of connectives : 736 ( 306 ~; 306 |; 45 &)
% ( 18 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 150 ( 109 >; 41 *; 0 +; 0 <<)
% Number of predicates : 74 ( 72 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 10 con; 0-4 aty)
% Number of variables : 473 ( 7 sgn; 257 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_24,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_25,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
c_Int_OPls: $i ).
tff(decl_27,type,
c_Int_OBit1: $i > $i ).
tff(decl_28,type,
c_Int_OBit0: $i > $i ).
tff(decl_29,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_30,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
class_Fields_Ofield: $i > $o ).
tff(decl_33,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_34,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_35,type,
tc_Int_Oint: $i ).
tff(decl_36,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_37,type,
tc_Nat_Onat: $i ).
tff(decl_38,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_39,type,
class_Int_Onumber: $i > $o ).
tff(decl_40,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_41,type,
c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_43,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_44,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_45,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_46,type,
c_Int_Oiszero: ( $i * $i ) > $o ).
tff(decl_47,type,
tc_RealDef_Oreal: $i ).
tff(decl_48,type,
c_Transcendental_Opi: $i ).
tff(decl_49,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_50,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_51,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_52,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_53,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_54,type,
class_Orderings_Oord: $i > $o ).
tff(decl_55,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_56,type,
c_Transcendental_Otan: $i > $i ).
tff(decl_57,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_58,type,
c_Transcendental_Ocos: $i > $i ).
tff(decl_59,type,
c_Transcendental_Osin: $i > $i ).
tff(decl_60,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_61,type,
tc_Code__Numeral_Ocode__numeral: $i ).
tff(decl_62,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_63,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_64,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_65,type,
hBOOL: $i > $o ).
tff(decl_66,type,
c_Transcendental_Oarcsin: $i > $i ).
tff(decl_67,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_68,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_69,type,
class_Groups_Ozero: $i > $o ).
tff(decl_70,type,
class_Groups_Oone: $i > $o ).
tff(decl_71,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_72,type,
c_Int_OMin: $i ).
tff(decl_73,type,
c_Transcendental_Oarccos: $i > $i ).
tff(decl_74,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_77,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_78,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_79,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_80,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_81,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_82,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_83,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_84,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_85,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_86,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_87,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_88,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_89,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_90,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_91,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_92,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_93,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_94,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_95,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_96,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_97,type,
class_Rings_Oring: $i > $o ).
tff(decl_98,type,
class_Rings_Oidom: $i > $o ).
tff(decl_99,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_100,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_101,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_102,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_103,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_104,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_105,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_106,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_107,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_108,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_109,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_110,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_111,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_112,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_113,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
class_Groups_Ominus: $i > $o ).
tff(decl_116,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_117,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_118,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_119,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_120,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_121,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
tc_HOL_Obool: $i ).
tff(decl_123,type,
v_d1: $i ).
tff(decl_124,type,
v_d2: $i ).
tff(decl_125,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_126,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_128,type,
esk3_1: $i > $i ).
tff(decl_129,type,
esk4_1: $i > $i ).
tff(decl_130,type,
esk5_1: $i > $i ).
tff(decl_131,type,
esk6_1: $i > $i ).
tff(decl_132,type,
esk7_1: $i > $i ).
tff(decl_133,type,
esk8_1: $i > $i ).
tff(decl_134,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_136,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_137,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_138,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_139,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk15_3: ( $i * $i * $i ) > $i ).
fof(conj_2,conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(fact_mult__2__right,axiom,
! [X26,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Otimes__class_Otimes(X5,X26,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X5,X26,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_Bit0__def,axiom,
! [X21] : c_Int_OBit0(X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X21] : c_Int_OBit1(X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_real__less__def,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
& X10 != X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_add__Pls__right,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Int_OPls) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_min__less__iff__conj,axiom,
! [X9,X10,X25,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X25,c_Orderings_Oord__class_Omin(X5,X10,X9))
<=> ( c_Orderings_Oord__class_Oless(X5,X25,X10)
& c_Orderings_Oord__class_Oless(X5,X25,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X9)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X9)
<=> X10 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_real__le__trans,axiom,
! [X21,X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X42,X41)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X41,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X42,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_real__mult__1,axiom,
! [X26] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X26) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
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_min__max_Oless__infI1,axiom,
! [X24,X8,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X8)
=> c_Orderings_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X5,X7,X24),X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).
fof(fact_min__max_Ole__infI1,axiom,
! [X24,X8,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X7,X8)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Orderings_Oord__class_Omin(X5,X7,X24),X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,c_Groups_Otimes__class_Otimes(X5,X10,X10),c_Groups_Otimes__class_Otimes(X5,X9,X9)),c_Groups_Ozero__class_Ozero(X5))
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_add__0__right,axiom,
! [X7,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X7,c_Groups_Ozero__class_Ozero(X5)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_mult_Ozero__right,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Otimes__class_Otimes(X5,X7,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_zadd__commute,axiom,
! [X27,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X27) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_less__divide__eq,axiom,
! [X43,X11,X12,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Rings_Oinverse__class_Odivide(X5,X11,X43))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Otimes__class_Otimes(X5,X12,X43),X11) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> ( ( c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Otimes__class_Otimes(X5,X12,X43)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
fof(fact_mult_Ozero__left,axiom,
! [X24,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Otimes__class_Otimes(X5,c_Groups_Ozero__class_Ozero(X5),X24) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_zero__less__two,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
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_zminus__zminus,axiom,
! [X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_mult__Min,axiom,
! [X21] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X21) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Min) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_real__add__mult__distrib,axiom,
! [X27,X50,X51] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X51,X50),X27) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X51,X27),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X50,X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_real__mult__commute,axiom,
! [X27,X26] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X26,X27) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X27,X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
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(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(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [X24,X7,X5] :
( class_Orderings_Olinorder(X5)
=> c_Orderings_Oord__class_Omin(X5,X7,X24) = c_Orderings_Oord__class_Omin(X5,X24,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_xt1_I8_J,axiom,
! [X26,X8,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ( c_Orderings_Oord__class_Oless(X5,X26,X13)
=> c_Orderings_Oord__class_Oless(X5,X26,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X8 != X13
=> ( ~ c_Orderings_Oord__class_Oless(X5,X8,X13)
=> c_Orderings_Oord__class_Oless(X5,X13,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_mult__2,axiom,
! [X26,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Otimes__class_Otimes(X5,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X26) = c_Groups_Oplus__class_Oplus(X5,X26,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).
fof(fact_number__of__is__id,axiom,
! [X21] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(conj_0,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_leD,axiom,
! [X8,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ~ c_Orderings_Oord__class_Oless(X5,X8,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_xt1_I6_J,axiom,
! [X26,X8,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X26,X13)
=> c_Orderings_Oord__class_Oless__eq(X5,X26,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
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_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X23,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X7,X23) = c_Groups_Oplus__class_Oplus(X5,X23,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_real__sum__of__halves,axiom,
! [X8] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X8,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X8,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
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(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(fact_real__add__less__0__iff,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [X12,X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X11),c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_real__diff__def,axiom,
! [X38,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X38) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(fact_add__left__cancel,axiom,
! [X43,X11,X12,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X12,X11) = c_Groups_Oplus__class_Oplus(X5,X12,X43)
<=> X11 = X43 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X24,X7,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X7,X24),X24) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
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(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(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(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
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(fact_add__0__iff,axiom,
! [X12,X11,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X11 = c_Groups_Oplus__class_Oplus(X5,X11,X12)
<=> X12 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__special_I2_J,axiom,
! [X27,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Int_Onumber__class_Onumber__of(X5,X27)) = c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
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_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_min__max_Oinf__le2,axiom,
! [X13,X8,X5] :
( class_Orderings_Olinorder(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Orderings_Oord__class_Omin(X5,X8,X13),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).
fof(fact_less__special_I3_J,axiom,
! [X10,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(X5,X10),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X10,c_Int_OPls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_zmult__1__right,axiom,
! [X26] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X26,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_zless__le,axiom,
! [X15,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X15)
& X25 != X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_min__less__iff__disj,axiom,
! [X25,X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X5,X10,X9),X25)
<=> ( c_Orderings_Oord__class_Oless(X5,X10,X25)
| c_Orderings_Oord__class_Oless(X5,X9,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_order__less__trans,axiom,
! [X26,X13,X8,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X8,X13)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X26)
=> c_Orderings_Oord__class_Oless(X5,X8,X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
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_real__0__less__add__iff,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X9))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_minus__less__iff,axiom,
! [X11,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X11)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X11),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_minus__minus,axiom,
! [X7,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_real__add__le__0__iff,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X12,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(c_0_72,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
fof(c_0_73,plain,
! [X1183,X1184] :
( ~ class_Int_Onumber__ring(X1184)
| c_Groups_Otimes__class_Otimes(X1184,X1183,c_Int_Onumber__class_Onumber__of(X1184,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1184,X1183,X1183) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
fof(c_0_74,plain,
! [X1739] : c_Int_OBit0(X1739) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1739,X1739),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_75,plain,
! [X1888] : c_Int_OBit1(X1888) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1888),X1888),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_76,plain,
! [X795,X796] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X796,X795)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795) )
& ( X796 != X795
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X796,X795)
| X796 = X795
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(c_0_77,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(fof_nnf,[status(thm)],[c_0_72]) ).
cnf(c_0_78,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_81,plain,
! [X1738] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1738,c_Int_OPls) = X1738,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_82,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_83,plain,
! [X178,X179,X180,X181] :
( ( c_Orderings_Oord__class_Oless(X181,X180,X179)
| ~ c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ class_Orderings_Olinorder(X181) )
& ( c_Orderings_Oord__class_Oless(X181,X180,X178)
| ~ c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ class_Orderings_Olinorder(X181) )
& ( ~ c_Orderings_Oord__class_Oless(X181,X180,X179)
| ~ c_Orderings_Oord__class_Oless(X181,X180,X178)
| c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ class_Orderings_Olinorder(X181) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).
fof(c_0_84,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X9)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X9)
<=> X10 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(c_0_85,plain,
! [X759,X760,X761] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X761,X760)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X760,X759)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X761,X759) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
cnf(c_0_86,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_87,plain,
! [X1159] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1159) = X1159,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
cnf(c_0_88,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_80]) ).
cnf(c_0_89,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_90,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_91,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Orderings_Oord__class_Omin(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_93,plain,
! [X170,X171,X172,X173] :
( ~ class_Orderings_Olinorder(X173)
| ~ c_Orderings_Oord__class_Oless(X173,X172,X171)
| c_Orderings_Oord__class_Oless(X173,c_Orderings_Oord__class_Omin(X173,X172,X170),X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).
fof(c_0_94,plain,
! [X467,X468,X469] :
( ( c_Orderings_Oord__class_Oless(X469,X468,X467)
| X468 = X467
| ~ c_Orderings_Oord__class_Oless__eq(X469,X468,X467)
| ~ class_Orderings_Olinorder(X469) )
& ( X468 != X467
| ~ c_Orderings_Oord__class_Oless(X469,X468,X467)
| ~ c_Orderings_Oord__class_Oless__eq(X469,X468,X467)
| ~ class_Orderings_Olinorder(X469) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])]) ).
fof(c_0_95,plain,
! [X536,X537,X538,X539] :
( ~ class_Orderings_Olinorder(X539)
| ~ c_Orderings_Oord__class_Oless__eq(X539,X538,X537)
| c_Orderings_Oord__class_Oless__eq(X539,c_Orderings_Oord__class_Omin(X539,X538,X536),X537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).
cnf(c_0_96,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_85]) ).
cnf(c_0_97,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_76]) ).
fof(c_0_98,plain,
! [X855,X856,X857] :
( ( X856 = c_Groups_Ozero__class_Ozero(X857)
| ~ c_Orderings_Oord__class_Oless__eq(X857,c_Groups_Oplus__class_Oplus(X857,c_Groups_Otimes__class_Otimes(X857,X856,X856),c_Groups_Otimes__class_Otimes(X857,X855,X855)),c_Groups_Ozero__class_Ozero(X857))
| ~ class_Rings_Olinordered__ring__strict(X857) )
& ( X855 = c_Groups_Ozero__class_Ozero(X857)
| ~ c_Orderings_Oord__class_Oless__eq(X857,c_Groups_Oplus__class_Oplus(X857,c_Groups_Otimes__class_Otimes(X857,X856,X856),c_Groups_Otimes__class_Otimes(X857,X855,X855)),c_Groups_Ozero__class_Ozero(X857))
| ~ class_Rings_Olinordered__ring__strict(X857) )
& ( X856 != c_Groups_Ozero__class_Ozero(X857)
| X855 != c_Groups_Ozero__class_Ozero(X857)
| c_Orderings_Oord__class_Oless__eq(X857,c_Groups_Oplus__class_Oplus(X857,c_Groups_Otimes__class_Otimes(X857,X856,X856),c_Groups_Otimes__class_Otimes(X857,X855,X855)),c_Groups_Ozero__class_Ozero(X857))
| ~ class_Rings_Olinordered__ring__strict(X857) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(c_0_99,plain,
! [X898,X899] :
( ~ class_Groups_Omonoid__add(X899)
| c_Groups_Oplus__class_Oplus(X899,X898,c_Groups_Ozero__class_Ozero(X899)) = X898 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(c_0_100,plain,
! [X1069,X1070] :
( ~ class_RealVector_Oreal__normed__algebra(X1070)
| c_Groups_Otimes__class_Otimes(X1070,X1069,c_Groups_Ozero__class_Ozero(X1070)) = c_Groups_Ozero__class_Ozero(X1070) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
cnf(c_0_101,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_79]),c_0_79]),c_0_79]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]) ).
fof(c_0_102,plain,
! [X1710,X1711] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1711,X1710) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1710,X1711),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
cnf(c_0_103,plain,
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_87]) ).
cnf(c_0_104,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).
cnf(c_0_105,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_106,plain,
! [X43,X11,X12,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Rings_Oinverse__class_Odivide(X5,X11,X43))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Otimes__class_Otimes(X5,X12,X43),X11) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> ( ( c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Otimes__class_Otimes(X5,X12,X43)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(c_0_107,plain,
! [X1063,X1064] :
( ~ class_RealVector_Oreal__normed__algebra(X1064)
| c_Groups_Otimes__class_Otimes(X1064,c_Groups_Ozero__class_Ozero(X1064),X1063) = c_Groups_Ozero__class_Ozero(X1064) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(c_0_108,plain,
! [X1453] :
( ~ class_Rings_Olinordered__semidom(X1453)
| c_Orderings_Oord__class_Oless(X1453,c_Groups_Ozero__class_Ozero(X1453),c_Groups_Oplus__class_Oplus(X1453,c_Groups_Oone__class_Oone(X1453),c_Groups_Oone__class_Oone(X1453))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
cnf(c_0_109,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_110,plain,
( c_Orderings_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X4),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_111,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_94]) ).
cnf(c_0_112,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Oord__class_Omin(X1,X2,X4),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
fof(c_0_113,plain,
! [X764] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X764,X764),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(c_0_114,plain,
! [X692] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X692)) = X692,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(c_0_115,plain,
! [X1904] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1904) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1904),
inference(variable_rename,[status(thm)],[fact_mult__Min]) ).
cnf(c_0_116,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_117,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_118,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
fof(c_0_119,plain,
! [X1038,X1039,X1040] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1040,X1039),X1038) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1040,X1038),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1039,X1038)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(c_0_120,plain,
! [X1025,X1026] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1026,X1025) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1025,X1026),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_121,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_122,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(c_0_123,plain,
( 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_100]) ).
cnf(c_0_124,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(c_0_125,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_d2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).
cnf(c_0_126,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_127,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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_103,c_0_104]),c_0_105])]) ).
fof(c_0_128,plain,
! [X1524,X1525,X1526,X1527] :
( ( ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])])]) ).
cnf(c_0_129,plain,
( 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_107]) ).
cnf(c_0_130,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_131,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
fof(c_0_132,plain,
! [X285,X286,X287] :
( ~ class_Orderings_Olinorder(X287)
| c_Orderings_Oord__class_Omin(X287,X286,X285) = c_Orderings_Oord__class_Omin(X287,X285,X286) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).
cnf(c_0_133,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_92])]) ).
cnf(c_0_134,plain,
( c_Orderings_Oord__class_Omin(X1,X2,X3) = X4
| c_Orderings_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_135,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
fof(c_0_136,plain,
! [X442,X443,X444,X445] :
( ~ class_Orderings_Oorder(X445)
| ~ c_Orderings_Oord__class_Oless__eq(X445,X444,X443)
| ~ c_Orderings_Oord__class_Oless(X445,X442,X444)
| c_Orderings_Oord__class_Oless(X445,X442,X443) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(c_0_137,plain,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X8 != X13
=> ( ~ c_Orderings_Oord__class_Oless(X5,X8,X13)
=> c_Orderings_Oord__class_Oless(X5,X13,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(c_0_138,plain,
! [X1185,X1186] :
( ~ class_Int_Onumber__ring(X1186)
| c_Groups_Otimes__class_Otimes(X1186,c_Int_Onumber__class_Onumber__of(X1186,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1185) = c_Groups_Oplus__class_Oplus(X1186,X1185,X1185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).
cnf(c_0_139,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_140,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
fof(c_0_141,plain,
! [X193] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X193) = X193,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_142,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
inference(split_conjunct,[status(thm)],[conj_0]) ).
fof(c_0_143,plain,
! [X8,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ~ c_Orderings_Oord__class_Oless(X5,X8,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(c_0_144,plain,
! [X338,X339,X340,X341] :
( ~ class_Orderings_Oorder(X341)
| ~ c_Orderings_Oord__class_Oless__eq(X341,X340,X339)
| ~ c_Orderings_Oord__class_Oless__eq(X341,X338,X340)
| c_Orderings_Oord__class_Oless__eq(X341,X338,X339) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
cnf(c_0_145,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_d2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_146,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_118])]) ).
cnf(c_0_147,plain,
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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_148,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_149,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_121,c_0_122]) ).
cnf(c_0_150,plain,
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_123,c_0_124]) ).
cnf(c_0_151,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
fof(c_0_152,plain,
! [X1954,X1955,X1956] :
( ~ class_Rings_Ocomm__semiring__1(X1956)
| c_Groups_Oplus__class_Oplus(X1956,X1955,X1954) = c_Groups_Oplus__class_Oplus(X1956,X1954,X1955) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_153,plain,
! [X1696] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1696,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1696,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1696,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
cnf(c_0_154,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_127]),c_0_127]) ).
cnf(c_0_155,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_156,plain,
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_129,c_0_124]) ).
cnf(c_0_157,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_158,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_159,plain,
( c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_160,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_92])]) ).
cnf(c_0_161,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_136]) ).
cnf(c_0_162,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(c_0_163,plain,
! [X229,X230,X231] :
( ~ class_Rings_Olinordered__idom(X231)
| X230 = X229
| c_Orderings_Oord__class_Oless(X231,X230,X229)
| c_Orderings_Oord__class_Oless(X231,X229,X230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])]) ).
cnf(c_0_164,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_165,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_140]) ).
cnf(c_0_166,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_167,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).
cnf(c_0_168,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_d1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_116,c_0_142]) ).
fof(c_0_169,plain,
! [X473,X474,X475] :
( ~ class_Orderings_Olinorder(X475)
| ~ c_Orderings_Oord__class_Oless__eq(X475,X474,X473)
| ~ c_Orderings_Oord__class_Oless(X475,X473,X474) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])]) ).
cnf(c_0_170,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_171,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
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_145,c_0_146]),c_0_147]),c_0_148]),c_0_149]),c_0_150]),c_0_151])]) ).
fof(c_0_172,plain,
! [X1604,X1605] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1605,X1604),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1604,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1605)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1604,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1605))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1605,X1604),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff])]) ).
fof(c_0_173,plain,
! [X792,X793,X794] :
( ( ~ c_Orderings_Oord__class_Oless(X794,c_Groups_Ouminus__class_Ouminus(X794,X793),c_Groups_Ouminus__class_Ouminus(X794,X792))
| c_Orderings_Oord__class_Oless(X794,X792,X793)
| ~ class_Groups_Oordered__ab__group__add(X794) )
& ( ~ c_Orderings_Oord__class_Oless(X794,X792,X793)
| c_Orderings_Oord__class_Oless(X794,c_Groups_Ouminus__class_Ouminus(X794,X793),c_Groups_Ouminus__class_Ouminus(X794,X792))
| ~ class_Groups_Oordered__ab__group__add(X794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(c_0_174,plain,
! [X2174,X2175] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2175,X2174) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2175,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2174)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
fof(c_0_175,plain,
! [X1041,X1042,X1043,X1044] :
( ( c_Groups_Oplus__class_Oplus(X1044,X1043,X1042) != c_Groups_Oplus__class_Oplus(X1044,X1043,X1041)
| X1042 = X1041
| ~ class_Groups_Ocancel__semigroup__add(X1044) )
& ( X1042 != X1041
| c_Groups_Oplus__class_Oplus(X1044,X1043,X1042) = c_Groups_Oplus__class_Oplus(X1044,X1043,X1041)
| ~ class_Groups_Ocancel__semigroup__add(X1044) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(c_0_176,plain,
! [X2282,X2283,X2284] :
( ~ class_Groups_Ogroup__add(X2284)
| c_Groups_Oplus__class_Oplus(X2284,c_Groups_Ominus__class_Ominus(X2284,X2283,X2282),X2282) = X2283 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
cnf(c_0_177,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_152]) ).
cnf(c_0_178,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_179,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1,
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_180,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_181,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_92])]) ).
cnf(c_0_182,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_97]),c_0_162])]) ).
cnf(c_0_183,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_184,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_185,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_79]),c_0_80]),c_0_80]) ).
cnf(c_0_186,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Int_OMin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_104]),c_0_166]),c_0_167])]) ).
cnf(c_0_187,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
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_168,c_0_146]),c_0_147]),c_0_148]),c_0_149]),c_0_150]),c_0_151])]) ).
cnf(c_0_188,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_189,hypothesis,
( 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_d2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_162])]) ).
cnf(c_0_190,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_191,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_192,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_174]) ).
cnf(c_0_193,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_194,plain,
( X3 = X4
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_195,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
cnf(c_0_196,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_176]) ).
cnf(c_0_197,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_198,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_177,c_0_178]) ).
fof(c_0_199,plain,
! [X1998,X1999,X2000] :
( ( X1999 != c_Groups_Oplus__class_Oplus(X2000,X1999,X1998)
| X1998 = c_Groups_Ozero__class_Ozero(X2000)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2000) )
& ( X1998 != c_Groups_Ozero__class_Ozero(X2000)
| X1999 = c_Groups_Oplus__class_Oplus(X2000,X1999,X1998)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2000) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
cnf(c_0_200,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_79]),c_0_79]),c_0_80]),c_0_80]),c_0_80]),c_0_80]) ).
cnf(c_0_201,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_117])]),c_0_182]) ).
cnf(c_0_202,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_203,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).
cnf(c_0_204,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Int_OMin))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_127,c_0_186]) ).
fof(c_0_205,plain,
! [X1179,X1180] :
( ~ class_Int_Onumber__ring(X1180)
| c_Groups_Oplus__class_Oplus(X1180,c_Groups_Oone__class_Oone(X1180),c_Int_Onumber__class_Onumber__of(X1180,X1179)) = c_Int_Onumber__class_Onumber__of(X1180,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
fof(c_0_206,plain,
! [X1903] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1903),X1903) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
cnf(c_0_207,hypothesis,
( 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_d1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_187]),c_0_162])]) ).
cnf(c_0_208,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_160]),c_0_142])]),c_0_182]) ).
cnf(c_0_209,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,X1)
| ~ c_Orderings_Oord__class_Oless(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_188,c_0_189]),c_0_92])]) ).
cnf(c_0_210,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_192]),c_0_193])]) ).
cnf(c_0_211,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2) ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_212,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)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198]) ).
cnf(c_0_213,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_199]) ).
cnf(c_0_214,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).
cnf(c_0_215,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_216,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_217,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_218,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_203]),c_0_105])]),c_0_186]),c_0_204]) ).
cnf(c_0_219,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_220,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_221,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_222,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,X1)
| ~ c_Orderings_Oord__class_Oless(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_188,c_0_207]),c_0_92])]) ).
cnf(c_0_223,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(spm,[status(thm)],[c_0_208,c_0_202]) ).
cnf(c_0_224,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_225,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X1) = X2,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212])]) ).
cnf(c_0_226,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_215])]),c_0_127]),c_0_127]) ).
cnf(c_0_227,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d2,v_d2),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_218]),c_0_157]),c_0_158])]) ).
fof(c_0_228,plain,
! [X551,X552,X553] :
( ~ class_Orderings_Olinorder(X553)
| c_Orderings_Oord__class_Oless__eq(X553,c_Orderings_Oord__class_Omin(X553,X552,X551),X551) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).
fof(c_0_229,plain,
! [X91,X92] :
( ( ~ c_Orderings_Oord__class_Oless(X92,c_Int_Onumber__class_Onumber__of(X92,X91),c_Groups_Ozero__class_Ozero(X92))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X91,c_Int_OPls)
| ~ class_Int_Onumber__ring(X92)
| ~ class_Rings_Olinordered__idom(X92) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X91,c_Int_OPls)
| c_Orderings_Oord__class_Oless(X92,c_Int_Onumber__class_Onumber__of(X92,X91),c_Groups_Ozero__class_Ozero(X92))
| ~ class_Int_Onumber__ring(X92)
| ~ class_Rings_Olinordered__idom(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).
cnf(c_0_230,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_219,c_0_80]) ).
cnf(c_0_231,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1),X1) = c_Int_OPls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_220,c_0_140]),c_0_221]) ).
fof(c_0_232,plain,
! [X1843] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1843,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1843,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(c_0_233,plain,
! [X718,X719] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X719,X718)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X719,X718) )
& ( X719 != X718
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X719,X718) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X719,X718)
| X719 = X718
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X719,X718) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
cnf(c_0_234,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_222,c_0_210]) ).
cnf(c_0_235,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_223]),c_0_218]),c_0_157]),c_0_158])]) ).
cnf(c_0_236,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_237,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d2,v_d2),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
fof(c_0_238,plain,
! [X174,X175,X176,X177] :
( ( ~ c_Orderings_Oord__class_Oless(X177,c_Orderings_Oord__class_Omin(X177,X176,X175),X174)
| c_Orderings_Oord__class_Oless(X177,X176,X174)
| c_Orderings_Oord__class_Oless(X177,X175,X174)
| ~ class_Orderings_Olinorder(X177) )
& ( ~ c_Orderings_Oord__class_Oless(X177,X176,X174)
| c_Orderings_Oord__class_Oless(X177,c_Orderings_Oord__class_Omin(X177,X176,X175),X174)
| ~ class_Orderings_Olinorder(X177) )
& ( ~ c_Orderings_Oord__class_Oless(X177,X175,X174)
| c_Orderings_Oord__class_Oless(X177,c_Orderings_Oord__class_Omin(X177,X176,X175),X174)
| ~ class_Orderings_Olinorder(X177) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).
cnf(c_0_239,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_76]) ).
cnf(c_0_240,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_241,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_242,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_89]),c_0_89]) ).
cnf(c_0_243,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1)) = c_Int_OPls,
inference(rw,[status(thm)],[c_0_231,c_0_126]) ).
cnf(c_0_244,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_245,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_246,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_234,c_0_225]) ).
cnf(c_0_247,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(spm,[status(thm)],[c_0_226,c_0_235]) ).
cnf(c_0_248,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_237]),c_0_135])]) ).
fof(c_0_249,plain,
! [X93] :
( ~ class_Int_Onumber__ring(X93)
| c_Groups_Ozero__class_Ozero(X93) = c_Int_Onumber__class_Onumber__of(X93,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
cnf(c_0_250,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_251,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_92])]) ).
cnf(c_0_252,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),c_Int_OPls)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Int_Onumber__ring(X2) ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_253,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_244]) ).
cnf(c_0_254,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OPls,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_126]) ).
cnf(c_0_255,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(er,[status(thm)],[c_0_245]) ).
cnf(c_0_256,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_247]),c_0_135])]) ).
cnf(c_0_257,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| v_d2 = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(spm,[status(thm)],[c_0_248,c_0_202]) ).
cnf(c_0_258,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_259,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_92])]),c_0_90]) ).
cnf(c_0_260,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_126]),c_0_254]),c_0_255]) ).
cnf(c_0_261,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| v_d2 = v_d1 ),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_262,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_258,c_0_105]) ).
fof(c_0_263,plain,
! [X269,X270,X271,X272] :
( ~ class_Orderings_Opreorder(X272)
| ~ c_Orderings_Oord__class_Oless(X272,X271,X270)
| ~ c_Orderings_Oord__class_Oless(X272,X270,X269)
| c_Orderings_Oord__class_Oless(X272,X271,X269) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
cnf(c_0_264,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_259]),c_0_92])]) ).
cnf(c_0_265,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| v_d2 = v_d1 ),
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_260,c_0_261]),c_0_184]),c_0_262]),c_0_117]),c_0_105])]) ).
cnf(c_0_266,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_267,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_268,plain,
! [X1602,X1603] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1603,X1602))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1603),X1602) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1603),X1602)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1603,X1602)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
cnf(c_0_269,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_264]),c_0_142])]) ).
cnf(c_0_270,hypothesis,
v_d2 = v_d1,
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_260,c_0_265]),c_0_184]),c_0_262]),c_0_142]),c_0_105])]) ).
fof(c_0_271,plain,
! [X789,X790,X791] :
( ( ~ c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X790),X789)
| c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X789),X790)
| ~ class_Groups_Oordered__ab__group__add(X791) )
& ( ~ c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X789),X790)
| c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X790),X789)
| ~ class_Groups_Oordered__ab__group__add(X791) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
cnf(c_0_272,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_d1)
| ~ c_Orderings_Oord__class_Oless(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_266,c_0_142]),c_0_267])]) ).
cnf(c_0_273,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_268]) ).
fof(c_0_274,plain,
! [X755,X756] :
( ~ class_Groups_Ogroup__add(X756)
| c_Groups_Ouminus__class_Ouminus(X756,c_Groups_Ouminus__class_Ouminus(X756,X755)) = X755 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
cnf(c_0_275,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_269,c_0_270]),c_0_270])]),c_0_90]) ).
fof(c_0_276,plain,
! [X1598,X1599] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1599,X1598),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1599)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1599))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1599,X1598),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff])]) ).
fof(c_0_277,plain,
! [X571,X572] :
( ( ~ c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ouminus__class_Ouminus(X572,X571))
| c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ozero__class_Ozero(X572))
| ~ class_Rings_Olinordered__idom(X572) )
& ( ~ c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ozero__class_Ozero(X572))
| c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ouminus__class_Ouminus(X572,X571))
| ~ class_Rings_Olinordered__idom(X572) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
cnf(c_0_278,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_279,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_149]) ).
cnf(c_0_280,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_281,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(spm,[status(thm)],[c_0_275,c_0_202]) ).
cnf(c_0_282,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_283,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_284,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_d1),X1)
| ~ c_Orderings_Oord__class_Oless(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_278,c_0_279]),c_0_193])]) ).
cnf(c_0_285,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_280,c_0_197]) ).
cnf(c_0_286,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_281]),c_0_218]),c_0_157]),c_0_158])]) ).
cnf(c_0_287,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_282]),c_0_92])]) ).
cnf(c_0_288,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_d1),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(spm,[status(thm)],[c_0_283,c_0_284]),c_0_184]),c_0_285]),c_0_142])]) ).
cnf(c_0_289,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1) ),
inference(spm,[status(thm)],[c_0_226,c_0_286]) ).
cnf(c_0_290,hypothesis,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_149]) ).
cnf(c_0_291,hypothesis,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_289]),c_0_135])]) ).
cnf(c_0_292,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_290,c_0_291]),c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW177+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n026.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 18:33:19 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 11.12/11.28 % Version : CSE_E---1.5
% 11.12/11.28 % Problem : theBenchmark.p
% 11.12/11.28 % Proof found
% 11.12/11.28 % SZS status Theorem for theBenchmark.p
% 11.12/11.28 % SZS output start Proof
% See solution above
% 11.12/11.30 % Total time : 10.675000 s
% 11.12/11.30 % SZS output end Proof
% 11.12/11.30 % Total time : 10.699000 s
%------------------------------------------------------------------------------