TSTP Solution File: SWW210+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW210+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 : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:16:32 EDT 2023
% Result : Theorem 123.99s 124.09s
% Output : CNFRefutation 124.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 142
% Syntax : Number of formulae : 193 ( 24 unt; 127 typ; 0 def)
% Number of atoms : 141 ( 9 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 124 ( 49 ~; 57 |; 3 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 153 ( 111 >; 42 *; 0 +; 0 <<)
% Number of predicates : 75 ( 73 usr; 2 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 15 con; 0-5 aty)
% Number of variables : 105 ( 16 sgn; 44 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_f____: $i ).
tff(decl_24,type,
c_SEQ_Osubseq: $i > $o ).
tff(decl_25,type,
v_ga____: $i ).
tff(decl_26,type,
tc_RealDef_Oreal: $i ).
tff(decl_27,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_28,type,
v_e____: $i ).
tff(decl_29,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
tc_Nat_Onat: $i ).
tff(decl_31,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
v_s: $i > $i ).
tff(decl_33,type,
c_Complex_ORe: $i > $i ).
tff(decl_34,type,
v_x____: $i ).
tff(decl_35,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_37,type,
c_Int_OPls: $i ).
tff(decl_38,type,
c_Int_OBit1: $i > $i ).
tff(decl_39,type,
c_Int_OBit0: $i > $i ).
tff(decl_40,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_41,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Complex_OIm: $i > $i ).
tff(decl_43,type,
v_y____: $i ).
tff(decl_44,type,
class_Fields_Ofield: $i > $o ).
tff(decl_45,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_46,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_47,type,
class_Int_Onumber: $i > $o ).
tff(decl_48,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_49,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_50,type,
v_r: $i ).
tff(decl_51,type,
tc_Complex_Ocomplex: $i ).
tff(decl_52,type,
class_Groups_Ozero: $i > $o ).
tff(decl_53,type,
tc_Int_Oint: $i ).
tff(decl_54,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_55,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_56,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_57,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_58,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_59,type,
class_Orderings_Oord: $i > $o ).
tff(decl_60,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_61,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_62,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_63,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_64,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_65,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_67,type,
hBOOL: $i > $o ).
tff(decl_68,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_69,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_70,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_71,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_73,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_74,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_75,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_76,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_77,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_78,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_79,type,
class_Groups_Olinordered__ab__group__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_Olinordered__semidom: $i > $o ).
tff(decl_84,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_85,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_86,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_87,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_88,type,
class_Groups_Oone: $i > $o ).
tff(decl_89,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_90,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_92,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_93,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_94,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_95,type,
class_Power_Opower: $i > $o ).
tff(decl_96,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_97,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_98,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_99,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(decl_100,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_101,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_102,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_103,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
c_Complex_Oii: $i ).
tff(decl_105,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_106,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_107,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_108,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_109,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_110,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_111,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_112,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_113,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_114,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_115,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_116,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_117,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_118,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_119,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_120,type,
class_Rings_Oring: $i > $o ).
tff(decl_121,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_122,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_123,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_124,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_125,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_126,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_127,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_128,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_129,type,
class_Rings_Oidom: $i > $o ).
tff(decl_130,type,
tc_HOL_Obool: $i ).
tff(decl_131,type,
v_thesis____: $o ).
tff(decl_132,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk2_0: $i ).
tff(decl_134,type,
esk3_0: $i ).
tff(decl_135,type,
esk4_1: $i > $i ).
tff(decl_136,type,
esk5_1: $i > $i ).
tff(decl_137,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_138,type,
esk7_1: $i > $i ).
tff(decl_139,type,
esk8_1: $i > $i ).
tff(decl_140,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_144,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk16_1: $i > $i ).
tff(decl_148,type,
esk17_1: $i > $i ).
fof(fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096,axiom,
? [X4] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X5))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096) ).
fof(fact_Bit0__def,axiom,
! [X17] : c_Int_OBit0(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X17] : c_Int_OBit1(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X17),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(conj_0,hypothesis,
( ? [X81] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X5))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> ( ? [X82] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X82,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X5)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_add__Pls__right,axiom,
! [X17] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Int_OPls) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096,axiom,
? [X4] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X5)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096) ).
fof(fact_order__trans,axiom,
! [X26,X15,X8,X7] :
( class_Orderings_Opreorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X8,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X15,X26)
=> c_Orderings_Oord__class_Oless__eq(X7,X8,X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_nat__le__linear,axiom,
! [X37,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X37)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_xt1_I8_J,axiom,
! [X26,X8,X15,X7] :
( class_Orderings_Oorder(X7)
=> ( c_Orderings_Oord__class_Oless__eq(X7,X15,X8)
=> ( c_Orderings_Oord__class_Oless(X7,X26,X15)
=> c_Orderings_Oord__class_Oless(X7,X26,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_less__add__one,axiom,
! [X6,X7] :
( class_Rings_Olinordered__semidom(X7)
=> c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oone__class_Oone(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_order__less__irrefl,axiom,
! [X8,X7] :
( class_Orderings_Opreorder(X7)
=> ~ c_Orderings_Oord__class_Oless(X7,X8,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(c_0_15,plain,
! [X87] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk2_0,X87)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X87))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096])])]) ).
fof(c_0_16,plain,
! [X1039] : c_Int_OBit0(X1039) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1039,X1039),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_17,plain,
! [X1301] : c_Int_OBit1(X1301) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1301),X1301),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_18,hypothesis,
! [X2714,X2716] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2716,esk17_1(X2716))
| v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2714,esk16_1(X2714)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X2716))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2714,esk16_1(X2714)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2716,esk17_1(X2716))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2714)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X2716))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2714)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])])]) ).
cnf(c_0_19,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,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_17]) ).
fof(c_0_22,plain,
! [X1038] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1038,c_Int_OPls) = X1038,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_23,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
cnf(c_0_24,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X1))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X89] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X89)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X89)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096])])]) ).
fof(c_0_26,plain,
! [X231,X232,X233,X234] :
( ~ class_Orderings_Opreorder(X234)
| ~ c_Orderings_Oord__class_Oless__eq(X234,X233,X232)
| ~ c_Orderings_Oord__class_Oless__eq(X234,X232,X231)
| c_Orderings_Oord__class_Oless__eq(X234,X233,X231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(c_0_27,plain,
! [X672,X673] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X673,X672)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X672,X673) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
cnf(c_0_28,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk2_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_29,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X1))
| v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk16_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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)],[c_0_24,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_33,hypothesis,
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk16_1(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(c_0_39,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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__eq(tc_Nat_Onat,esk2_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_40,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk16_1(X2)) ),
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_41,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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))))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_31]) ).
cnf(c_0_42,hypothesis,
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk16_1(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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)],[c_0_33,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_43,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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)],[c_0_34,c_0_20]),c_0_20]),c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_44,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_45,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_46,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk16_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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))))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_31]) ).
cnf(c_0_48,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk16_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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))))) ),
inference(sr,[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_43,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_31]) ).
fof(c_0_49,plain,
! [X366,X367,X368,X369] :
( ~ class_Orderings_Oorder(X369)
| ~ c_Orderings_Oord__class_Oless__eq(X369,X368,X367)
| ~ c_Orderings_Oord__class_Oless(X369,X366,X368)
| c_Orderings_Oord__class_Oless(X369,X366,X367) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
cnf(c_0_50,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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__eq(tc_Nat_Onat,esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_51,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk17_1(X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk17_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,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))))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_48]) ).
fof(c_0_53,plain,
! [X1146,X1147] :
( ~ class_Rings_Olinordered__semidom(X1147)
| c_Orderings_Oord__class_Oless(X1147,X1146,c_Groups_Oplus__class_Oplus(X1147,X1146,c_Groups_Oone__class_Oone(X1147))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(c_0_54,plain,
! [X8,X7] :
( class_Orderings_Opreorder(X7)
=> ~ c_Orderings_Oord__class_Oless(X7,X8,X8) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
cnf(c_0_55,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_49]) ).
cnf(c_0_56,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_57,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
cnf(c_0_58,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
fof(c_0_60,plain,
! [X343,X344] :
( ~ class_Orderings_Opreorder(X344)
| ~ c_Orderings_Oord__class_Oless(X344,X343,X343) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
cnf(c_0_61,hypothesis,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,esk3_0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_62,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,hypothesis,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,esk3_0),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW210+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sun Aug 27 17:56:00 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.17/0.50 start to proof: theBenchmark
% 123.99/124.09 % Version : CSE_E---1.5
% 123.99/124.09 % Problem : theBenchmark.p
% 123.99/124.09 % Proof found
% 123.99/124.09 % SZS status Theorem for theBenchmark.p
% 123.99/124.09 % SZS output start Proof
% See solution above
% 124.12/124.10 % Total time : 123.555000 s
% 124.12/124.10 % SZS output end Proof
% 124.12/124.10 % Total time : 123.590000 s
%------------------------------------------------------------------------------