TSTP Solution File: SWW173+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWW173+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : Tue May 21 06:41:39 EDT 2024
% Result : Theorem 29.19s 4.23s
% Output : CNFRefutation 29.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 32
% Syntax : Number of formulae : 132 ( 89 unt; 0 def)
% Number of atoms : 224 ( 156 equ)
% Maximal formula atoms : 30 ( 1 avg)
% Number of connectives : 160 ( 68 ~; 60 |; 10 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 163 ( 6 sgn 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_minus__real__def,axiom,
! [X23,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X23) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_number__of__Min,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Min) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_real__add__minus__iff,axiom,
! [X26,X20] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X26)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X20 = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_minus__minus,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_real__average__minus__first,axiom,
! [X8,X4] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X8),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X8,X4),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__average__minus__first) ).
fof(fact_Bit0__def,axiom,
! [X12] : c_Int_OBit0(X12) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X12] : c_Int_OBit1(X12) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X12),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_real__sum__of__halves,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X6,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,X6,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(fact_divide__self,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> c_Rings_Oinverse__class_Odivide(X5,X4,X4) = c_Groups_Oone__class_Oone(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
fof(fact_add__Pls__right,axiom,
! [X12] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Int_OPls) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_divide__zero__left,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [X21,X31,X26,X5] :
( ( class_Fields_Ofield__inverse__zero(X5)
& class_Int_Onumber(X5) )
=> ( X26 = c_Rings_Oinverse__class_Odivide(X5,X31,c_Int_Onumber__class_Onumber__of(X5,X21))
<=> ( ( c_Int_Onumber__class_Onumber__of(X5,X21) != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),c_Int_Onumber__class_Onumber__of(X5,X21)) = X31 )
& ( c_Int_Onumber__class_Onumber__of(X5,X21) = c_Groups_Ozero__class_Ozero(X5)
=> X26 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_four__x__squared,axiom,
! [X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X6),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X6)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_four__x__squared) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oone__class_Oone(X5) = c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_zadd__assoc,axiom,
! [X29,X27,X28] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,X27),X29) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_power__one,axiom,
! [X7,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X7) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_real__mult__1,axiom,
! [X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X16) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_real__mult__commute,axiom,
! [X13,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X24,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X24) = c_Groups_Oplus__class_Oplus(X5,X24,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(conj_0,conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_number__of__add,axiom,
! [X13,X15,X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X13)) = c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X15),c_Int_Onumber__class_Onumber__of(X5,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_power__divide,axiom,
! [X7,X8,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Odivide(X5,X4,X8)),X7) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
fof(c_0_32,plain,
! [X269,X270] :
( ~ class_Rings_Ocomm__semiring__1(X270)
| c_Groups_Oplus__class_Oplus(X270,c_Groups_Ozero__class_Ozero(X270),X269) = X269 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).
fof(c_0_33,plain,
! [X657,X658] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X658,X657) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X658,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X657)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_34,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(c_0_36,plain,
! [X767] :
( ~ class_Int_Onumber__ring(X767)
| c_Int_Onumber__class_Onumber__of(X767,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(X767,c_Groups_Oone__class_Oone(X767)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])])]) ).
cnf(c_0_37,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_33]) ).
cnf(c_0_38,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_41,plain,
! [X722,X723] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X723,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X722)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X723 = X722 )
& ( X723 != X722
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X723,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X722)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])])]) ).
fof(c_0_42,plain,
! [X2321,X2322] :
( ~ class_Groups_Ogroup__add(X2322)
| c_Groups_Ouminus__class_Ouminus(X2322,c_Groups_Ouminus__class_Ouminus(X2322,X2321)) = X2321 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])])]) ).
cnf(c_0_43,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_40])]) ).
fof(c_0_45,plain,
! [X1548,X1549] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1549,X1548),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1549) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1548,X1549),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[fact_real__average__minus__first]) ).
fof(c_0_46,plain,
! [X389] : c_Int_OBit0(X389) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X389,X389),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_47,plain,
! [X286] : c_Int_OBit1(X286) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X286),X286),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
cnf(c_0_48,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,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_42]) ).
cnf(c_0_50,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_38]) ).
cnf(c_0_51,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(c_0_52,plain,
! [X562] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X562,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,X562,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X562,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
fof(c_0_53,plain,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> c_Rings_Oinverse__class_Odivide(X5,X4,X4) = c_Groups_Oone__class_Oone(X5) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__self]) ).
cnf(c_0_54,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),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_45]) ).
cnf(c_0_55,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,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_47]) ).
fof(c_0_57,plain,
! [X388] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X388,c_Int_OPls) = X388,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_58,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_59,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
fof(c_0_60,plain,
! [X354,X355] :
( ~ class_Rings_Odivision__ring(X355)
| c_Rings_Oinverse__class_Odivide(X355,c_Groups_Ozero__class_Ozero(X355),X354) = c_Groups_Ozero__class_Ozero(X355) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])])]) ).
fof(c_0_61,plain,
! [X21,X31,X26,X5] :
( ( class_Fields_Ofield__inverse__zero(X5)
& class_Int_Onumber(X5) )
=> ( X26 = c_Rings_Oinverse__class_Odivide(X5,X31,c_Int_Onumber__class_Onumber__of(X5,X21))
<=> ( ( c_Int_Onumber__class_Onumber__of(X5,X21) != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),c_Int_Onumber__class_Onumber__of(X5,X21)) = X31 )
& ( c_Int_Onumber__class_Onumber__of(X5,X21) = c_Groups_Ozero__class_Ozero(X5)
=> X26 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_eq__divide__eq__number__of1]) ).
fof(c_0_62,plain,
! [X104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X104),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X104)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[fact_four__x__squared]) ).
cnf(c_0_63,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).
cnf(c_0_64,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_52]) ).
fof(c_0_65,plain,
! [X229,X230] :
( ~ class_Rings_Odivision__ring(X230)
| X229 = c_Groups_Ozero__class_Ozero(X230)
| c_Rings_Oinverse__class_Odivide(X230,X229,X229) = c_Groups_Oone__class_Oone(X230) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_66,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),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) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,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)))),
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_54,c_0_55]),c_0_55]),c_0_56]),c_0_56]),c_0_56]),c_0_56]) ).
cnf(c_0_67,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_58,c_0_37]) ).
cnf(c_0_69,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_37,c_0_59]) ).
cnf(c_0_70,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
fof(c_0_72,plain,
! [X531,X532,X533,X534] :
( ( c_Int_Onumber__class_Onumber__of(X534,X531) = c_Groups_Ozero__class_Ozero(X534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X534),X533),c_Int_Onumber__class_Onumber__of(X534,X531)) = X532
| X533 != c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( c_Int_Onumber__class_Onumber__of(X534,X531) != c_Groups_Ozero__class_Ozero(X534)
| X533 = c_Groups_Ozero__class_Ozero(X534)
| X533 != c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( c_Int_Onumber__class_Onumber__of(X534,X531) = c_Groups_Ozero__class_Ozero(X534)
| c_Int_Onumber__class_Onumber__of(X534,X531) != c_Groups_Ozero__class_Ozero(X534)
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( X533 != c_Groups_Ozero__class_Ozero(X534)
| c_Int_Onumber__class_Onumber__of(X534,X531) != c_Groups_Ozero__class_Ozero(X534)
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( c_Int_Onumber__class_Onumber__of(X534,X531) = c_Groups_Ozero__class_Ozero(X534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X534),X533),c_Int_Onumber__class_Onumber__of(X534,X531)) != X532
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( X533 != c_Groups_Ozero__class_Ozero(X534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X534),X533),c_Int_Onumber__class_Onumber__of(X534,X531)) != X532
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
fof(c_0_73,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[fact_real__zero__not__eq__one]) ).
fof(c_0_74,plain,
! [X495] :
( ~ class_Int_Onumber__ring(X495)
| c_Groups_Oone__class_Oone(X495) = c_Int_Onumber__class_Onumber__of(X495,c_Int_OBit1(c_Int_OPls)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])])]) ).
cnf(c_0_75,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_76,plain,
! [X622,X623,X624] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X624,X623),X622) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X624,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X623,X622)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
cnf(c_0_77,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_63,c_0_55]),c_0_56]),c_0_56]) ).
fof(c_0_78,plain,
! [X392,X393] :
( ~ class_Groups_Omonoid__mult(X393)
| hAPP(hAPP(c_Power_Opower__class_Opower(X393),c_Groups_Oone__class_Oone(X393)),X392) = c_Groups_Oone__class_Oone(X393) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])])]) ).
fof(c_0_79,plain,
! [X1488] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1488) = X1488,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_80,plain,
! [X1477,X1478] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1478),X1477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1477),X1478),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_81,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_64,c_0_55]),c_0_55]),c_0_56]),c_0_56]),c_0_56]),c_0_56]) ).
cnf(c_0_82,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_83,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),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) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,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)))),
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_66,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]) ).
cnf(c_0_84,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_85,plain,
c_Rings_Oinverse__class_Odivide(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_70,c_0_71]) ).
cnf(c_0_86,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_87,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[c_0_73]) ).
cnf(c_0_88,plain,
( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_89,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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_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(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))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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)],[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_75,c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]) ).
cnf(c_0_90,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_91,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_67]),c_0_67]),c_0_67]),c_0_67]) ).
cnf(c_0_92,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_93,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
cnf(c_0_94,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_95,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_96,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_81,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]) ).
cnf(c_0_97,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_82,c_0_71]) ).
cnf(c_0_98,plain,
c_Rings_Oinverse__class_Odivide(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)),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_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_43]),c_0_59]),c_0_69]) ).
cnf(c_0_99,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_100,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]) ).
cnf(c_0_101,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(c_0_102,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_103,plain,
( c_Groups_Oone__class_Oone(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_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_88,c_0_56]) ).
fof(c_0_104,plain,
! [X264,X265,X266] :
( ~ class_Rings_Ocomm__semiring__1(X266)
| c_Groups_Oplus__class_Oplus(X266,X265,X264) = c_Groups_Oplus__class_Oplus(X266,X264,X265) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
fof(c_0_105,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_106,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
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)],[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_89,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_90]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_91]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_91]) ).
cnf(c_0_107,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_108,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_109,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))
| 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_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_110,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_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_101])]),c_0_102]) ).
fof(c_0_111,plain,
! [X280,X281,X282] :
( ~ class_Int_Onumber__ring(X282)
| c_Int_Onumber__class_Onumber__of(X282,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X281,X280)) = c_Groups_Oplus__class_Oplus(X282,c_Int_Onumber__class_Onumber__of(X282,X281),c_Int_Onumber__class_Onumber__of(X282,X280)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])])]) ).
cnf(c_0_112,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_67]),c_0_67]) ).
cnf(c_0_113,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_104]) ).
fof(c_0_114,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[c_0_105]) ).
cnf(c_0_115,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),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_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = 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_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_108]) ).
cnf(c_0_116,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(sr,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_117,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_118,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_112,c_0_40]) ).
cnf(c_0_119,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_113,c_0_35]) ).
cnf(c_0_120,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
fof(c_0_121,plain,
! [X92,X93,X94,X95] :
( ~ class_Fields_Ofield__inverse__zero(X95)
| hAPP(hAPP(c_Power_Opower__class_Opower(X95),c_Rings_Oinverse__class_Odivide(X95,X94,X93)),X92) = c_Rings_Oinverse__class_Odivide(X95,hAPP(hAPP(c_Power_Opower__class_Opower(X95),X94),X92),hAPP(hAPP(c_Power_Opower__class_Opower(X95),X93),X92)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])])]) ).
cnf(c_0_122,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(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))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = 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_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),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(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,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),X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_40])]) ).
cnf(c_0_124,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_40])]),c_0_119]) ).
cnf(c_0_125,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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_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(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))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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)],[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_120,c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56]) ).
cnf(c_0_126,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3)),X4) = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_127,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(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))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_123]),c_0_124]),c_0_118]) ).
cnf(c_0_128,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),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_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
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)],[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_125,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_91]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_90]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_91]) ).
cnf(c_0_129,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) = hAPP(hAPP(c_Power_Opower__class_Opower(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)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_101])]) ).
cnf(c_0_130,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
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_128,c_0_123]),c_0_123]),c_0_124]),c_0_118]),c_0_124]),c_0_118]) ).
cnf(c_0_131,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_129,c_0_130]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW173+1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n032.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat May 18 19:49:07 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.19/4.23 # Version: 3.1.0
% 29.19/4.23 # Preprocessing class: FMLSSMSMSSSNFFN.
% 29.19/4.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.19/4.23 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 29.19/4.23 # Starting new_bool_3 with 600s (2) cores
% 29.19/4.23 # Starting new_bool_1 with 600s (2) cores
% 29.19/4.23 # Starting sh5l with 300s (1) cores
% 29.19/4.23 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 23091 completed with status 0
% 29.19/4.23 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 29.19/4.23 # Preprocessing class: FMLSSMSMSSSNFFN.
% 29.19/4.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.19/4.23 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 29.19/4.23 # No SInE strategy applied
% 29.19/4.23 # Search class: FGHSM-SMLM31-DFFFFFNN
% 29.19/4.23 # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 29.19/4.23 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 520s (1) cores
% 29.19/4.23 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 29.19/4.23 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 82s (1) cores
% 29.19/4.23 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 23101 completed with status 0
% 29.19/4.23 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 29.19/4.23 # Preprocessing class: FMLSSMSMSSSNFFN.
% 29.19/4.23 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.19/4.23 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 29.19/4.23 # No SInE strategy applied
% 29.19/4.23 # Search class: FGHSM-SMLM31-DFFFFFNN
% 29.19/4.23 # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 29.19/4.23 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 520s (1) cores
% 29.19/4.23 # Preprocessing time : 0.022 s
% 29.19/4.23 # Presaturation interreduction done
% 29.19/4.23 # SatCheck found unsatisfiable ground set
% 29.19/4.23
% 29.19/4.23 # Proof found!
% 29.19/4.23 # SZS status Theorem
% 29.19/4.23 # SZS output start CNFRefutation
% See solution above
% 29.19/4.23 # Parsed axioms : 1175
% 29.19/4.23 # Removed by relevancy pruning/SinE : 0
% 29.19/4.23 # Initial clauses : 1760
% 29.19/4.23 # Removed in clause preprocessing : 83
% 29.19/4.23 # Initial clauses in saturation : 1677
% 29.19/4.23 # Processed clauses : 20645
% 29.19/4.23 # ...of these trivial : 299
% 29.19/4.23 # ...subsumed : 15346
% 29.19/4.23 # ...remaining for further processing : 5000
% 29.19/4.23 # Other redundant clauses eliminated : 1391
% 29.19/4.23 # Clauses deleted for lack of memory : 0
% 29.19/4.23 # Backward-subsumed : 185
% 29.19/4.23 # Backward-rewritten : 164
% 29.19/4.23 # Generated clauses : 170496
% 29.19/4.23 # ...of the previous two non-redundant : 154006
% 29.19/4.23 # ...aggressively subsumed : 0
% 29.19/4.23 # Contextual simplify-reflections : 19
% 29.19/4.23 # Paramodulations : 169090
% 29.19/4.23 # Factorizations : 12
% 29.19/4.23 # NegExts : 0
% 29.19/4.23 # Equation resolutions : 1423
% 29.19/4.23 # Disequality decompositions : 0
% 29.19/4.23 # Total rewrite steps : 179954
% 29.19/4.23 # ...of those cached : 167565
% 29.19/4.23 # Propositional unsat checks : 1
% 29.19/4.23 # Propositional check models : 0
% 29.19/4.23 # Propositional check unsatisfiable : 1
% 29.19/4.23 # Propositional clauses : 139032
% 29.19/4.23 # Propositional clauses after purity: 32636
% 29.19/4.23 # Propositional unsat core size : 2
% 29.19/4.23 # Propositional preprocessing time : 0.000
% 29.19/4.23 # Propositional encoding time : 0.272
% 29.19/4.23 # Propositional solver time : 0.032
% 29.19/4.23 # Success case prop preproc time : 0.000
% 29.19/4.23 # Success case prop encoding time : 0.272
% 29.19/4.23 # Success case prop solver time : 0.032
% 29.19/4.23 # Current number of processed clauses : 3238
% 29.19/4.23 # Positive orientable unit clauses : 637
% 29.19/4.23 # Positive unorientable unit clauses: 42
% 29.19/4.23 # Negative unit clauses : 550
% 29.19/4.23 # Non-unit-clauses : 2009
% 29.19/4.23 # Current number of unprocessed clauses: 135794
% 29.19/4.23 # ...number of literals in the above : 337964
% 29.19/4.23 # Current number of archived formulas : 0
% 29.19/4.23 # Current number of archived clauses : 1614
% 29.19/4.23 # Clause-clause subsumption calls (NU) : 452549
% 29.19/4.23 # Rec. Clause-clause subsumption calls : 196181
% 29.19/4.23 # Non-unit clause-clause subsumptions : 4348
% 29.19/4.23 # Unit Clause-clause subsumption calls : 27958
% 29.19/4.23 # Rewrite failures with RHS unbound : 0
% 29.19/4.23 # BW rewrite match attempts : 10834
% 29.19/4.23 # BW rewrite match successes : 846
% 29.19/4.23 # Condensation attempts : 0
% 29.19/4.23 # Condensation successes : 0
% 29.19/4.23 # Termbank termtop insertions : 5778978
% 29.19/4.23 # Search garbage collected termcells : 19855
% 29.19/4.23
% 29.19/4.23 # -------------------------------------------------
% 29.19/4.23 # User time : 3.483 s
% 29.19/4.23 # System time : 0.163 s
% 29.19/4.23 # Total time : 3.646 s
% 29.19/4.23 # Maximum resident set size: 8112 pages
% 29.19/4.23
% 29.19/4.23 # -------------------------------------------------
% 29.19/4.23 # User time : 10.475 s
% 29.19/4.23 # System time : 0.398 s
% 29.19/4.23 # Total time : 10.874 s
% 29.19/4.23 # Maximum resident set size: 3000 pages
% 29.19/4.23 % E---3.1 exiting
% 29.19/4.23 % E exiting
%------------------------------------------------------------------------------