TSTP Solution File: ALG337-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG337-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 : Wed Aug 30 16:07:23 EDT 2023
% Result : Unsatisfiable 4.74s 4.83s
% Output : CNFRefutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 129
% Syntax : Number of formulae : 172 ( 52 unt; 104 typ; 0 def)
% Number of atoms : 94 ( 65 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 123 ( 97 >; 26 *; 0 +; 0 <<)
% Number of predicates : 77 ( 75 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 7 con; 0-3 aty)
% Number of variables : 98 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_RealDef_Oreal: $i ).
tff(decl_23,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_24,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_27,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_28,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_30,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_31,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_33,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_34,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_35,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_36,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_38,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_39,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_40,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_41,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_43,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_44,type,
c_Transcendental_Ocos: $i > $i ).
tff(decl_45,type,
c_Transcendental_Opi: $i ).
tff(decl_46,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_47,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_48,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_49,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_50,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_52,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_53,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_54,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_55,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(decl_56,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(decl_57,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_58,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_59,type,
class_RealVector_Oreal__div__algebra: $i > $o ).
tff(decl_60,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_62,type,
c_Transcendental_Otan: $i > $i ).
tff(decl_63,type,
c_Int_OPls: $i ).
tff(decl_64,type,
c_Int_OBit1: $i > $i ).
tff(decl_65,type,
c_Int_OBit0: $i > $i ).
tff(decl_66,type,
tc_nat: $i ).
tff(decl_67,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_68,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_71,type,
class_Int_Onumber: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_73,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_74,type,
class_Power_Opower: $i > $o ).
tff(decl_75,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_79,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_81,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_83,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_84,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_86,type,
c_Transcendental_Osin: $i > $i ).
tff(decl_87,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_89,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_90,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_91,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_92,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_93,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_94,type,
tc_Int_Oint: $i ).
tff(decl_95,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_96,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_97,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_98,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_99,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_100,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_101,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_102,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_103,type,
c_Int_Oiszero: ( $i * $i ) > $o ).
tff(decl_104,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_106,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_107,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_108,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_109,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_110,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_111,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_112,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_113,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_114,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_115,type,
v_y____: $i ).
tff(decl_116,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_117,type,
v_x____: $i ).
tff(decl_118,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_119,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_120,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_121,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_122,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_123,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_124,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_125,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
cnf(cls_CHAINED_0_01,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_Bit0__def_0,axiom,
c_Int_OBit0(X1) = c_HOL_Oplus__class_Oplus(X1,X1,tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__def_0) ).
cnf(cls_add__Bit1__Bit0_0,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OBit1(X1),c_Int_OBit0(X2),tc_Int_Oint) = c_Int_OBit1(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Bit1__Bit0_0) ).
cnf(cls_CHAINED_0,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_zadd__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint),X3,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Int_Oint),tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zadd__assoc_0) ).
cnf(cls_add__Pls_0,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OPls,X1,tc_Int_Oint) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Pls_0) ).
cnf(cls_real__mult__right__cancel_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_real__zero__not__eq__one_0,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
cnf(cls_divide__eq__eq_0,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_diff__divide__distrib_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
cnf(cls_real__diff__def_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
cnf(cls_minus__diff__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(cls_add__num__frac_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1),X4,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
cnf(cls_real__sum__of__halves_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
cnf(cls_real__add__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).
cnf(cls_real__divide__def_0,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__divide__def_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(c_0_25,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_CHAINED_0_01 ).
cnf(c_0_26,axiom,
c_Int_OBit0(X1) = c_HOL_Oplus__class_Oplus(X1,X1,tc_Int_Oint),
cls_Bit0__def_0 ).
cnf(c_0_27,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OBit1(X1),c_Int_OBit0(X2),tc_Int_Oint) = c_Int_OBit1(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint)),
cls_add__Bit1__Bit0_0 ).
cnf(c_0_28,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_CHAINED_0 ).
cnf(c_0_29,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
cls_conjecture_0 ).
cnf(c_0_30,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_31,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint),X3,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Int_Oint),tc_Int_Oint),
cls_zadd__assoc_0 ).
cnf(c_0_32,plain,
c_HOL_Oplus__class_Oplus(c_Int_OBit1(X1),c_HOL_Oplus__class_Oplus(X2,X2,tc_Int_Oint),tc_Int_Oint) = c_Int_OBit1(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint)),
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_33,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OPls,X1,tc_Int_Oint) = X1,
cls_add__Pls_0 ).
cnf(c_0_34,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_35,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal) ),
cls_real__mult__right__cancel_0 ).
cnf(c_0_36,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I12_J_0 ).
cnf(c_0_37,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_38,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_real__zero__not__eq__one_0 ).
cnf(c_0_39,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_40,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_41,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_42,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_0 ).
cnf(c_0_43,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38])]) ).
cnf(c_0_44,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ofield ).
cnf(c_0_45,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_46,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
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_39,c_0_31]),c_0_32]),c_0_33]),c_0_40]),c_0_31]),c_0_32]),c_0_33]),c_0_41]) ).
cnf(c_0_47,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_diff__divide__distrib_0 ).
cnf(c_0_48,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__diff__def_0 ).
cnf(c_0_49,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__diff__eq_0 ).
cnf(c_0_50,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add ).
cnf(c_0_51,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1),X4,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_add__num__frac_0 ).
cnf(c_0_52,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),c_0_38]) ).
cnf(c_0_53,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
cls_real__sum__of__halves_0 ).
cnf(c_0_54,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__add__mult__distrib_0 ).
cnf(c_0_55,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__divide__def_0 ).
cnf(c_0_56,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44])]) ).
cnf(c_0_57,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_58,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),
inference(sr,[status(thm)],[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_51,c_0_52]),c_0_43]),c_0_52]),c_0_44]),c_0_45])]),c_0_38]) ).
cnf(c_0_59,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0 ).
cnf(c_0_60,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add ).
cnf(c_0_61,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_26]),c_0_26]) ).
cnf(c_0_62,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_55]),c_0_55]) ).
cnf(c_0_63,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_64,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0 ).
cnf(c_0_65,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_58]),c_0_60])]) ).
cnf(c_0_66,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG337-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 03:10:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 4.74/4.83 % Version : CSE_E---1.5
% 4.74/4.83 % Problem : theBenchmark.p
% 4.74/4.83 % Proof found
% 4.74/4.83 % SZS status Theorem for theBenchmark.p
% 4.74/4.83 % SZS output start Proof
% See solution above
% 4.82/4.84 % Total time : 4.192000 s
% 4.82/4.84 % SZS output end Proof
% 4.82/4.84 % Total time : 4.237000 s
%------------------------------------------------------------------------------