TSTP Solution File: SWW227+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWW227+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 00:38:33 EDT 2023

% Result   : Theorem 45.67s 7.22s
% Output   : CNFRefutation 45.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  153 (  88 unt;   0 def)
%            Number of atoms       :  240 (  96 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  162 (  75   ~;  67   |;   0   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;  10 con; 0-3 aty)
%            Number of variables   :  191 (   0 sgn; 118   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

fof(f4,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e) ).

fof(f7,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
   => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) ).

fof(f10,axiom,
    ! [X3,X2] :
      ( class_Int_Onumber__ring(X2)
     => c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X3)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(f20,axiom,
    ! [X9] : c_Int_OBit1(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9),X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(f25,axiom,
    ! [X11,X12,X13] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X11)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(f29,axiom,
    ! [X17,X18,X19] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X18),X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(f32,axiom,
    ! [X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OPls) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).

fof(f33,axiom,
    ! [X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X9) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(f35,axiom,
    ! [X9] : c_Int_OBit0(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(f42,axiom,
    ! [X26] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X26) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X26),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).

fof(f204,axiom,
    ! [X12,X13] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X13,X12) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).

fof(f205,axiom,
    ! [X12,X13] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).

fof(f210,axiom,
    ! [X37] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X37)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X37),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).

fof(f579,axiom,
    ! [X37] : c_Nat_OSuc(X37) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X37),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f586,axiom,
    ! [X2] :
      ( class_Int_Onumber__ring(X2)
     => c_Groups_Oone__class_Oone(X2) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(f735,axiom,
    ! [X2] :
      ( class_Rings_Olinordered__semidom(X2)
     => c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(f766,axiom,
    ! [X28,X10,X2] :
      ( class_Fields_Ofield__inverse__zero(X2)
     => c_Rings_Oinverse__class_Oinverse(X2,c_Rings_Oinverse__class_Odivide(X2,X10,X28)) = c_Rings_Oinverse__class_Odivide(X2,X28,X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__divide) ).

fof(f774,axiom,
    ! [X12,X13,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X13)
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X12)
         => c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X13,X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(f978,axiom,
    ! [X10,X2] :
      ( class_Fields_Ofield(X2)
     => c_Rings_Oinverse__class_Oinverse(X2,X10) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).

fof(f987,axiom,
    ! [X31,X10,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Groups_Oplus__class_Oplus(X2,X10,X31) = c_Groups_Oplus__class_Oplus(X2,X31,X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(f1100,axiom,
    class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

fof(f1101,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(f1105,axiom,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

fof(f1112,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(f1125,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

fof(f1129,axiom,
    class_Fields_Ofield(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

fof(f1171,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1172,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(negated_conjecture,[],[f1171]) ).

fof(f1175,plain,
    ! [X0,X1] :
      ( class_Int_Onumber__ring(X1)
     => c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)) ),
    inference(rectify,[],[f10]) ).

fof(f1183,plain,
    ! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
    inference(rectify,[],[f20]) ).

fof(f1188,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
    inference(rectify,[],[f25]) ).

fof(f1192,plain,
    ! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
    inference(rectify,[],[f29]) ).

fof(f1195,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
    inference(rectify,[],[f32]) ).

fof(f1196,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
    inference(rectify,[],[f33]) ).

fof(f1198,plain,
    ! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
    inference(rectify,[],[f35]) ).

fof(f1204,plain,
    ! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(rectify,[],[f42]) ).

fof(f1340,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
    inference(rectify,[],[f204]) ).

fof(f1341,plain,
    ! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
    inference(rectify,[],[f205]) ).

fof(f1346,plain,
    ! [X0] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rectify,[],[f210]) ).

fof(f1702,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(rectify,[],[f579]) ).

fof(f1709,plain,
    ! [X0] :
      ( class_Int_Onumber__ring(X0)
     => c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) ),
    inference(rectify,[],[f586]) ).

fof(f1851,plain,
    ! [X0] :
      ( class_Rings_Olinordered__semidom(X0)
     => c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
    inference(rectify,[],[f735]) ).

fof(f1882,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Ofield__inverse__zero(X2)
     => c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Oinverse(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) ),
    inference(rectify,[],[f766]) ).

fof(f1890,plain,
    ! [X0,X1,X2] :
      ( class_Fields_Olinordered__field(X2)
     => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
       => ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
         => c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X1,X0)) ) ) ),
    inference(rectify,[],[f774]) ).

fof(f2094,plain,
    ! [X0,X1] :
      ( class_Fields_Ofield(X1)
     => c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X0) ),
    inference(rectify,[],[f978]) ).

fof(f2103,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
    inference(rectify,[],[f987]) ).

fof(f2112,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(flattening,[],[f1172]) ).

fof(f2114,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f2115,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
    inference(flattening,[],[f2114]) ).

fof(f2117,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0))
      | ~ class_Int_Onumber__ring(X1) ),
    inference(ennf_transformation,[],[f1175]) ).

fof(f2488,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(X0) ),
    inference(ennf_transformation,[],[f1709]) ).

fof(f2693,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(ennf_transformation,[],[f1851]) ).

fof(f2733,plain,
    ! [X0,X1,X2] :
      ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Oinverse(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
      | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(ennf_transformation,[],[f1882]) ).

fof(f2743,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(ennf_transformation,[],[f1890]) ).

fof(f2744,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(flattening,[],[f2743]) ).

fof(f3044,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Fields_Ofield(X1) ),
    inference(ennf_transformation,[],[f2094]) ).

fof(f3053,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f2103]) ).

fof(f3556,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    inference(cnf_transformation,[],[f1]) ).

fof(f3559,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
    inference(cnf_transformation,[],[f4]) ).

fof(f3562,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
    inference(cnf_transformation,[],[f2115]) ).

fof(f3565,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0))
      | ~ class_Int_Onumber__ring(X1) ),
    inference(cnf_transformation,[],[f2117]) ).

fof(f3577,plain,
    ! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
    inference(cnf_transformation,[],[f1183]) ).

fof(f3584,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
    inference(cnf_transformation,[],[f1188]) ).

fof(f3590,plain,
    ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
    inference(cnf_transformation,[],[f1192]) ).

fof(f3593,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
    inference(cnf_transformation,[],[f1195]) ).

fof(f3594,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
    inference(cnf_transformation,[],[f1196]) ).

fof(f3596,plain,
    ! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
    inference(cnf_transformation,[],[f1198]) ).

fof(f3608,plain,
    ! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(cnf_transformation,[],[f1204]) ).

fof(f3825,plain,
    ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
    inference(cnf_transformation,[],[f1340]) ).

fof(f3826,plain,
    ! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
    inference(cnf_transformation,[],[f1341]) ).

fof(f3835,plain,
    ! [X0] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnf_transformation,[],[f1346]) ).

fof(f4474,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1702]) ).

fof(f4485,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(X0) ),
    inference(cnf_transformation,[],[f2488]) ).

fof(f4690,plain,
    ! [X0] :
      ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
      | ~ class_Rings_Olinordered__semidom(X0) ),
    inference(cnf_transformation,[],[f2693]) ).

fof(f4739,plain,
    ! [X2,X0,X1] :
      ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Oinverse(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
      | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(cnf_transformation,[],[f2733]) ).

fof(f4767,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Fields_Olinordered__field(X2) ),
    inference(cnf_transformation,[],[f2744]) ).

fof(f5087,plain,
    ! [X0,X1] :
      ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X0)
      | ~ class_Fields_Ofield(X1) ),
    inference(cnf_transformation,[],[f3044]) ).

fof(f5096,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f3053]) ).

fof(f5209,plain,
    class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1100]) ).

fof(f5210,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1101]) ).

fof(f5214,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1105]) ).

fof(f5221,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1112]) ).

fof(f5234,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1125]) ).

fof(f5238,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1129]) ).

fof(f5280,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(cnf_transformation,[],[f2112]) ).

fof(f5281,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    inference(definition_unfolding,[],[f3556,f3596,f3577,f4474]) ).

fof(f5286,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
    inference(definition_unfolding,[],[f3562,f4474,f3596,f3577,f3596,f3577,f3596,f3577,f4474]) ).

fof(f5289,plain,
    ! [X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X0))
      | ~ class_Int_Onumber__ring(X1) ),
    inference(definition_unfolding,[],[f3565,f3577]) ).

fof(f5371,plain,
    ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
    inference(definition_unfolding,[],[f3835,f4474]) ).

fof(f5542,plain,
    ! [X0] :
      ( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,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(X0) ),
    inference(definition_unfolding,[],[f4485,f3577]) ).

fof(f5559,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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(definition_unfolding,[],[f5280,f4474,f3596,f3577]) ).

cnf(c_49,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    inference(cnf_transformation,[],[f5281]) ).

cnf(c_52,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
    inference(cnf_transformation,[],[f3559]) ).

cnf(c_55,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ),
    inference(cnf_transformation,[],[f5286]) ).

cnf(c_58,plain,
    ( ~ class_Int_Onumber__ring(X0)
    | c_Int_Onumber__class_Onumber__of(X0,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),X1)) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) ),
    inference(cnf_transformation,[],[f5289]) ).

cnf(c_76,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)),
    inference(cnf_transformation,[],[f3584]) ).

cnf(c_82,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(cnf_transformation,[],[f3590]) ).

cnf(c_85,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
    inference(cnf_transformation,[],[f3593]) ).

cnf(c_86,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
    inference(cnf_transformation,[],[f3594]) ).

cnf(c_99,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(cnf_transformation,[],[f3608]) ).

cnf(c_310,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),
    inference(cnf_transformation,[],[f3825]) ).

cnf(c_311,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))),
    inference(cnf_transformation,[],[f3826]) ).

cnf(c_320,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
    inference(cnf_transformation,[],[f5371]) ).

cnf(c_945,plain,
    ( ~ class_Int_Onumber__ring(X0)
    | c_Int_Onumber__class_Onumber__of(X0,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_Oone__class_Oone(X0) ),
    inference(cnf_transformation,[],[f5542]) ).

cnf(c_1146,plain,
    ( ~ class_Rings_Olinordered__semidom(X0)
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
    inference(cnf_transformation,[],[f4690]) ).

cnf(c_1195,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X0)
    | c_Rings_Oinverse__class_Oinverse(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,X2,X1) ),
    inference(cnf_transformation,[],[f4739]) ).

cnf(c_1223,plain,
    ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
    | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
    | ~ class_Fields_Olinordered__field(X0)
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f4767]) ).

cnf(c_1530,plain,
    ( ~ class_Fields_Ofield(X0)
    | c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),X1) = c_Rings_Oinverse__class_Oinverse(X0,X1) ),
    inference(cnf_transformation,[],[f5087]) ).

cnf(c_1539,plain,
    ( ~ class_Rings_Ocomm__semiring__1(X0)
    | c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) ),
    inference(cnf_transformation,[],[f5096]) ).

cnf(c_1652,plain,
    class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5209]) ).

cnf(c_1653,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5210]) ).

cnf(c_1657,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5214]) ).

cnf(c_1664,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5221]) ).

cnf(c_1677,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5234]) ).

cnf(c_1681,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5238]) ).

cnf(c_1723,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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(cnf_transformation,[],[f5559]) ).

cnf(c_2766,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ),
    inference(prop_impl_just,[status(thm)],[c_49,c_55]) ).

cnf(c_2770,plain,
    ( ~ class_Int_Onumber__ring(X0)
    | c_Int_Onumber__class_Onumber__of(X0,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),X1)) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_58]) ).

cnf(c_2794,plain,
    ( ~ class_Int_Onumber__ring(X0)
    | c_Int_Onumber__class_Onumber__of(X0,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_Oone__class_Oone(X0) ),
    inference(prop_impl_just,[status(thm)],[c_945]) ).

cnf(c_2924,plain,
    ( ~ class_Fields_Ofield(X0)
    | c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),X1) = c_Rings_Oinverse__class_Oinverse(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_1530]) ).

cnf(c_2948,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X0)
    | c_Rings_Oinverse__class_Oinverse(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,X2,X1) ),
    inference(prop_impl_just,[status(thm)],[c_1195]) ).

cnf(c_3454,plain,
    ( ~ class_Rings_Olinordered__semidom(X0)
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
    inference(prop_impl_just,[status(thm)],[c_1146]) ).

cnf(c_3548,plain,
    ( ~ class_Rings_Ocomm__semiring__1(X0)
    | c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) ),
    inference(prop_impl_just,[status(thm)],[c_1539]) ).

cnf(c_14445,plain,
    ( ~ class_Int_Onumber__ring(X0)
    | c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X0) ),
    inference(demodulation,[status(thm)],[c_2794,c_76,c_82,c_85,c_86]) ).

cnf(c_14476,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
    inference(demodulation,[status(thm)],[c_52,c_99]) ).

cnf(c_14734,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
    inference(light_normalisation,[status(thm)],[c_311,c_310]) ).

cnf(c_14735,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
    inference(light_normalisation,[status(thm)],[c_14734,c_310]) ).

cnf(c_14736,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
    inference(demodulation,[status(thm)],[c_14735,c_99]) ).

cnf(c_14737,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
    inference(demodulation,[status(thm)],[c_14476,c_14736]) ).

cnf(c_17558,plain,
    ( ~ class_Int_Onumber__ring(X0)
    | c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) ),
    inference(demodulation,[status(thm)],[c_2770,c_76,c_82,c_86]) ).

cnf(c_18776,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),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(demodulation,[status(thm)],[c_1723,c_76,c_82,c_85,c_86,c_99,c_320,c_14736]) ).

cnf(c_18835,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
    inference(demodulation,[status(thm)],[c_2766,c_76,c_82,c_85,c_86,c_99,c_320,c_14736]) ).

cnf(c_21237,plain,
    ( X0 != tc_RealDef_Oreal
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
    inference(resolution_lifted,[status(thm)],[c_3454,c_1653]) ).

cnf(c_21238,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(unflattening,[status(thm)],[c_21237]) ).

cnf(c_22065,plain,
    ( X0 != tc_RealDef_Oreal
    | c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) ),
    inference(resolution_lifted,[status(thm)],[c_3548,c_1664]) ).

cnf(c_22066,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),
    inference(unflattening,[status(thm)],[c_22065]) ).

cnf(c_22458,plain,
    ( X0 != tc_RealDef_Oreal
    | c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),X1) = c_Rings_Oinverse__class_Oinverse(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_2924,c_1681]) ).

cnf(c_22459,plain,
    c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0),
    inference(unflattening,[status(thm)],[c_22458]) ).

cnf(c_24449,plain,
    ( X0 != tc_RealDef_Oreal
    | c_Rings_Oinverse__class_Oinverse(X0,c_Rings_Oinverse__class_Odivide(X0,X1,X2)) = c_Rings_Oinverse__class_Odivide(X0,X2,X1) ),
    inference(resolution_lifted,[status(thm)],[c_2948,c_1652]) ).

cnf(c_24450,plain,
    c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0),
    inference(unflattening,[status(thm)],[c_24449]) ).

cnf(c_29586,plain,
    ( X0 != tc_RealDef_Oreal
    | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
    | ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,X2,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_1223,c_1657]) ).

cnf(c_29587,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0)) ),
    inference(unflattening,[status(thm)],[c_29586]) ).

cnf(c_31418,plain,
    ( X0 != tc_RealDef_Oreal
    | c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) ),
    inference(resolution_lifted,[status(thm)],[c_17558,c_1677]) ).

cnf(c_31419,plain,
    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,X0)) = 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),X0)),
    inference(unflattening,[status(thm)],[c_31418]) ).

cnf(c_31442,plain,
    ( X0 != tc_RealDef_Oreal
    | c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X0) ),
    inference(resolution_lifted,[status(thm)],[c_14445,c_1677]) ).

cnf(c_31443,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(unflattening,[status(thm)],[c_31442]) ).

cnf(c_36376,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
    inference(prop_impl_just,[status(thm)],[c_18835]) ).

cnf(c_48900,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),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(demodulation,[status(thm)],[c_18776,c_22066,c_22459,c_31419,c_31443]) ).

cnf(c_49015,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),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(demodulation,[status(thm)],[c_36376,c_22066,c_24450,c_31419,c_31443]) ).

cnf(c_49016,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))),
    inference(forward_subsumption_resolution,[status(thm)],[c_49015,c_48900]) ).

cnf(c_194358,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
    inference(instantiation,[status(thm)],[c_29587]) ).

cnf(c_194359,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_194358,c_49016,c_21238,c_14737]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW227+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 : Sun Aug 27 18:20:04 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 45.67/7.22  % SZS status Started for theBenchmark.p
% 45.67/7.22  % SZS status Theorem for theBenchmark.p
% 45.67/7.22  
% 45.67/7.22  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 45.67/7.22  
% 45.67/7.22  ------  iProver source info
% 45.67/7.22  
% 45.67/7.22  git: date: 2023-05-31 18:12:56 +0000
% 45.67/7.22  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 45.67/7.22  git: non_committed_changes: false
% 45.67/7.22  git: last_make_outside_of_git: false
% 45.67/7.22  
% 45.67/7.22  ------ Parsing...
% 45.67/7.22  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 45.67/7.22  
% 45.67/7.22  ------ Preprocessing... sup_sim: 208  sf_s  rm: 21 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe:64:0s pe_e  sup_sim: 473  sf_s  rm: 60 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 60 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 60 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 60 0s  sf_e  pe_s  pe_e 
% 45.67/7.22  
% 45.67/7.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 45.67/7.22  
% 45.67/7.22  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 45.67/7.22  ------ Proving...
% 45.67/7.22  ------ Problem Properties 
% 45.67/7.22  
% 45.67/7.22  
% 45.67/7.22  clauses                                 1221
% 45.67/7.22  conjectures                             0
% 45.67/7.22  EPR                                     34
% 45.67/7.22  Horn                                    1020
% 45.67/7.22  unary                                   395
% 45.67/7.22  binary                                  454
% 45.67/7.22  lits                                    2523
% 45.67/7.22  lits eq                                 700
% 45.67/7.22  fd_pure                                 0
% 45.67/7.22  fd_pseudo                               0
% 45.67/7.22  fd_cond                                 105
% 45.67/7.22  fd_pseudo_cond                          54
% 45.67/7.22  AC symbols                              0
% 45.67/7.22  
% 45.67/7.22  ------ Schedule dynamic 5 is on 
% 45.67/7.22  
% 45.67/7.22  ------ no conjectures: strip conj schedule 
% 45.67/7.22  
% 45.67/7.22  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 45.67/7.22  
% 45.67/7.22  
% 45.67/7.22  ------ 
% 45.67/7.22  Current options:
% 45.67/7.22  ------ 
% 45.67/7.22  
% 45.67/7.22  
% 45.67/7.22  
% 45.67/7.22  
% 45.67/7.22  ------ Proving...
% 45.67/7.22  
% 45.67/7.22  
% 45.67/7.22  % SZS status Theorem for theBenchmark.p
% 45.67/7.22  
% 45.67/7.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 45.67/7.22  
% 45.67/7.22  
%------------------------------------------------------------------------------