TSTP Solution File: SWW258+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 03:24:39 EDT 2024

% Result   : Theorem 82.70s 11.74s
% Output   : CNFRefutation 82.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   62 (  29 unt;   0 def)
%            Number of atoms       :  123 (  20 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  114 (  53   ~;  43   |;   1   &)
%                                         (   3 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   70 (   1 sgn  51   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).

fof(f3,axiom,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).

fof(f11,axiom,
    ! [X12,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X12))
      <=> c_Groups_Ozero__class_Ozero(X5) != X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

fof(f146,axiom,
    ! [X3,X4,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(f160,axiom,
    ! [X4,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
       => c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).

fof(f208,axiom,
    ! [X15,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

fof(f256,axiom,
    ! [X7,X9] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

fof(f1133,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(f1137,axiom,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

fof(f1181,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f1272,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(f1273,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(negated_conjecture,[],[f1272]) ).

fof(f1279,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      <=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
    inference(rectify,[],[f11]) ).

fof(f1412,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Olinordered__semidom(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),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
    inference(rectify,[],[f146]) ).

fof(f1426,plain,
    ! [X0,X1] :
      ( class_Fields_Olinordered__field(X1)
     => ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
       => c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) ),
    inference(rectify,[],[f160]) ).

fof(f1472,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
    inference(rectify,[],[f208]) ).

fof(f1519,plain,
    ! [X0,X1] :
      ( 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),X0)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ) ),
    inference(rectify,[],[f256]) ).

fof(f2295,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(flattening,[],[f1273]) ).

fof(f2310,plain,
    ! [X0,X1] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      <=> c_Groups_Ozero__class_Ozero(X1) != X0 )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1279]) ).

fof(f2519,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(ennf_transformation,[],[f1412]) ).

fof(f2520,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(flattening,[],[f2519]) ).

fof(f2546,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(ennf_transformation,[],[f1426]) ).

fof(f2547,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(flattening,[],[f2546]) ).

fof(f2668,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
      | ~ 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) ),
    inference(ennf_transformation,[],[f1519]) ).

fof(f2669,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
      | ~ 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) ),
    inference(flattening,[],[f2668]) ).

fof(f3441,plain,
    ! [X0,X1] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
          | c_Groups_Ozero__class_Ozero(X1) = X0 )
        & ( c_Groups_Ozero__class_Ozero(X1) != X0
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ) )
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(nnf_transformation,[],[f2310]) ).

fof(f3830,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(cnf_transformation,[],[f2]) ).

fof(f3831,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f3]) ).

fof(f3840,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
      | c_Groups_Ozero__class_Ozero(X1) = X0
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f3441]) ).

fof(f4022,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
      | ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
      | ~ class_Rings_Olinordered__semidom(X2) ),
    inference(cnf_transformation,[],[f2520]) ).

fof(f4039,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
      | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
      | ~ class_Fields_Olinordered__field(X1) ),
    inference(cnf_transformation,[],[f2547]) ).

fof(f4101,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
    inference(cnf_transformation,[],[f1472]) ).

fof(f4171,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
      | ~ 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) ),
    inference(cnf_transformation,[],[f2669]) ).

fof(f5359,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1133]) ).

fof(f5363,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f1137]) ).

fof(f5407,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1181]) ).

fof(f5498,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(cnf_transformation,[],[f2295]) ).

cnf(c_50,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(cnf_transformation,[],[f3830]) ).

cnf(c_51,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_w____,
    inference(cnf_transformation,[],[f3831]) ).

cnf(c_59,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X0)
    | c_Groups_Ozero__class_Ozero(X0) = X1
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X1)) ),
    inference(cnf_transformation,[],[f3840]) ).

cnf(c_241,plain,
    ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
    | ~ class_Rings_Olinordered__semidom(X0)
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) ),
    inference(cnf_transformation,[],[f4022]) ).

cnf(c_257,plain,
    ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
    | ~ class_Fields_Olinordered__field(X0)
    | c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Oinverse(X0,X1)) ),
    inference(cnf_transformation,[],[f4039]) ).

cnf(c_313,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0),
    inference(cnf_transformation,[],[f4101]) ).

cnf(c_381,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ),
    inference(cnf_transformation,[],[f4171]) ).

cnf(c_1513,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5359]) ).

cnf(c_1517,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f5363]) ).

cnf(c_1561,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5407]) ).

cnf(c_1652,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(cnf_transformation,[],[f5498]) ).

cnf(c_15144,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(demodulation,[status(thm)],[c_1652,c_313]) ).

cnf(c_19515,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),c_Rings_Oinverse__class_Oinverse(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_257,c_1517]) ).

cnf(c_19516,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),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)) ),
    inference(unflattening,[status(thm)],[c_19515]) ).

cnf(c_22528,plain,
    ( X0 != tc_Complex_Ocomplex
    | c_Groups_Ozero__class_Ozero(X0) = X1
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_59,c_1561]) ).

cnf(c_22529,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
    inference(unflattening,[status(thm)],[c_22528]) ).

cnf(c_58404,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),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)) ),
    inference(prop_impl_just,[status(thm)],[c_19516]) ).

cnf(c_59784,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
    inference(prop_impl_just,[status(thm)],[c_22529]) ).

cnf(c_103865,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(superposition,[status(thm)],[c_58404,c_15144]) ).

cnf(c_113336,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(instantiation,[status(thm)],[c_59784]) ).

cnf(c_206296,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
    inference(superposition,[status(thm)],[c_381,c_103865]) ).

cnf(c_206310,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_206296,c_50]) ).

cnf(c_206677,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm)],[c_241,c_206310]) ).

cnf(c_206681,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(forward_subsumption_resolution,[status(thm)],[c_206677,c_1513]) ).

cnf(c_206687,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_206681,c_113336,c_51]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 22:09:58 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 82.70/11.74  % SZS status Started for theBenchmark.p
% 82.70/11.74  % SZS status Theorem for theBenchmark.p
% 82.70/11.74  
% 82.70/11.74  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 82.70/11.74  
% 82.70/11.74  ------  iProver source info
% 82.70/11.74  
% 82.70/11.74  git: date: 2024-05-02 19:28:25 +0000
% 82.70/11.74  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 82.70/11.74  git: non_committed_changes: false
% 82.70/11.74  
% 82.70/11.74  ------ Parsing...
% 82.70/11.74  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 82.70/11.74  
% 82.70/11.74  ------ Preprocessing... sup_sim: 83  sf_s  rm: 7 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 34  sf_s  rm: 16 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 16 0s  sf_e  pe_s  pe_e 
% 82.70/11.74  
% 82.70/11.74  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 82.70/11.74  
% 82.70/11.74  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 82.70/11.74  ------ Proving...
% 82.70/11.74  ------ Problem Properties 
% 82.70/11.74  
% 82.70/11.74  
% 82.70/11.74  clauses                                 1298
% 82.70/11.74  conjectures                             0
% 82.70/11.74  EPR                                     232
% 82.70/11.74  Horn                                    1159
% 82.70/11.74  unary                                   407
% 82.70/11.74  binary                                  424
% 82.70/11.74  lits                                    2875
% 82.70/11.74  lits eq                                 697
% 82.70/11.74  fd_pure                                 0
% 82.70/11.74  fd_pseudo                               0
% 82.70/11.74  fd_cond                                 84
% 82.70/11.74  fd_pseudo_cond                          93
% 82.70/11.74  AC symbols                              0
% 82.70/11.74  
% 82.70/11.74  ------ Schedule dynamic 5 is on 
% 82.70/11.74  
% 82.70/11.74  ------ no conjectures: strip conj schedule 
% 82.70/11.74  
% 82.70/11.74  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 82.70/11.74  
% 82.70/11.74  
% 82.70/11.74  ------ 
% 82.70/11.74  Current options:
% 82.70/11.74  ------ 
% 82.70/11.74  
% 82.70/11.74  
% 82.70/11.74  
% 82.70/11.74  
% 82.70/11.74  ------ Proving...
% 82.70/11.74  
% 82.70/11.74  
% 82.70/11.74  % SZS status Theorem for theBenchmark.p
% 82.70/11.74  
% 82.70/11.74  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 82.70/11.74  
% 82.70/11.74  
%------------------------------------------------------------------------------