TSTP Solution File: SWW204+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n006.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 00:38:28 EDT 2023

% Result   : Theorem 31.60s 5.21s
% Output   : CNFRefutation 31.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   64 (  28 unt;   0 def)
%            Number of atoms       :  114 (  28 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   89 (  39   ~;  35   |;   5   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :   72 (  10 sgn;  46   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X5))),v_r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).

fof(f8,axiom,
    ! [X6,X7] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6),X7))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).

fof(f35,axiom,
    ! [X19] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(f59,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).

fof(f129,axiom,
    ! [X12,X3] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X12))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3)),c_RComplete_Onatceiling(X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__mono) ).

fof(f130,axiom,
    ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X3)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).

fof(f134,axiom,
    ! [X3] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__neg) ).

fof(f206,axiom,
    ! [X13,X14] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X13))
    <=> ( X13 = X14
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

fof(f242,axiom,
    ! [X3,X4] :
      ( class_RealVector_Oreal__normed__vector(X4)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X3)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

fof(f1177,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f1264,conjecture,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1265,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(negated_conjecture,[],[f1264]) ).

fof(f1267,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
    inference(rectify,[],[f4]) ).

fof(f1269,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(rectify,[],[f8]) ).

fof(f1295,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(rectify,[],[f35]) ).

fof(f1386,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X0))) ),
    inference(rectify,[],[f129]) ).

fof(f1387,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0)))),
    inference(rectify,[],[f130]) ).

fof(f1391,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
     => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0) ),
    inference(rectify,[],[f134]) ).

fof(f1461,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
    <=> ( X0 = X1
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0)) ) ),
    inference(rectify,[],[f206]) ).

fof(f1497,plain,
    ! [X0,X1] :
      ( class_RealVector_Oreal__normed__vector(X1)
     => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(rectify,[],[f242]) ).

fof(f2291,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(flattening,[],[f1265]) ).

fof(f2422,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X0)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(ennf_transformation,[],[f1386]) ).

fof(f2426,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(ennf_transformation,[],[f1391]) ).

fof(f2576,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(ennf_transformation,[],[f1497]) ).

fof(f3355,plain,
    ! [X0] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(nnf_transformation,[],[f1295]) ).

fof(f3436,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
        | ( X0 != X1
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0)) ) )
      & ( X0 = X1
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1461]) ).

fof(f3437,plain,
    ! [X0,X1] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
        | ( X0 != X1
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0)) ) )
      & ( X0 = X1
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ) ),
    inference(flattening,[],[f3436]) ).

fof(f3793,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
    inference(cnf_transformation,[],[f1267]) ).

fof(f3797,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(cnf_transformation,[],[f1269]) ).

fof(f3830,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(cnf_transformation,[],[f3355]) ).

fof(f3862,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[],[f59]) ).

fof(f3966,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1)),c_RComplete_Onatceiling(X0)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(cnf_transformation,[],[f2422]) ).

fof(f3967,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0)))),
    inference(cnf_transformation,[],[f1387]) ).

fof(f3971,plain,
    ! [X0] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(cnf_transformation,[],[f2426]) ).

fof(f4077,plain,
    ! [X0,X1] :
      ( X0 = X1
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(cnf_transformation,[],[f3437]) ).

fof(f4144,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
      | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(cnf_transformation,[],[f2576]) ).

fof(f5374,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1177]) ).

fof(f5461,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(cnf_transformation,[],[f2291]) ).

cnf(c_52,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
    inference(cnf_transformation,[],[f3793]) ).

cnf(c_56,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(cnf_transformation,[],[f3797]) ).

cnf(c_85,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
    inference(cnf_transformation,[],[f3830]) ).

cnf(c_111,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(cnf_transformation,[],[f3862]) ).

cnf(c_212,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0)),c_RComplete_Onatceiling(X1))) ),
    inference(cnf_transformation,[],[f3966]) ).

cnf(c_213,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0)))),
    inference(cnf_transformation,[],[f3967]) ).

cnf(c_217,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | c_RComplete_Onatceiling(X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(cnf_transformation,[],[f3971]) ).

cnf(c_317,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
    | X0 = X1
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1)) ),
    inference(cnf_transformation,[],[f4077]) ).

cnf(c_381,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(cnf_transformation,[],[f4144]) ).

cnf(c_1590,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f5374]) ).

cnf(c_1677,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(cnf_transformation,[],[f5461]) ).

cnf(c_2672,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X0)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(prop_impl_just,[status(thm)],[c_381]) ).

cnf(c_2673,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(renaming,[status(thm)],[c_2672]) ).

cnf(c_27094,plain,
    ( X0 != tc_Complex_Ocomplex
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(resolution_lifted,[status(thm)],[c_2673,c_1590]) ).

cnf(c_27095,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
    inference(unflattening,[status(thm)],[c_27094]) ).

cnf(c_108494,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
    inference(superposition,[status(thm)],[c_56,c_1677]) ).

cnf(c_111889,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(v_r),
    inference(superposition,[status(thm)],[c_108494,c_217]) ).

cnf(c_112868,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(superposition,[status(thm)],[c_111889,c_212]) ).

cnf(c_112997,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
    | c_RComplete_Onatceiling(X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(superposition,[status(thm)],[c_112868,c_85]) ).

cnf(c_113034,plain,
    c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(superposition,[status(thm)],[c_52,c_112997]) ).

cnf(c_113556,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(superposition,[status(thm)],[c_113034,c_213]) ).

cnf(c_113557,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
    inference(light_normalisation,[status(thm)],[c_113556,c_111]) ).

cnf(c_122638,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(superposition,[status(thm)],[c_113557,c_317]) ).

cnf(c_122704,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(forward_subsumption_resolution,[status(thm)],[c_122638,c_27095]) ).

cnf(c_122813,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(demodulation,[status(thm)],[c_52,c_122704]) ).

cnf(c_122849,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_122813,c_1677]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n006.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 17:49:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 31.60/5.21  % SZS status Started for theBenchmark.p
% 31.60/5.21  % SZS status Theorem for theBenchmark.p
% 31.60/5.21  
% 31.60/5.21  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 31.60/5.21  
% 31.60/5.21  ------  iProver source info
% 31.60/5.21  
% 31.60/5.21  git: date: 2023-05-31 18:12:56 +0000
% 31.60/5.21  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 31.60/5.21  git: non_committed_changes: false
% 31.60/5.21  git: last_make_outside_of_git: false
% 31.60/5.21  
% 31.60/5.21  ------ Parsing...
% 31.60/5.21  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 31.60/5.21  
% 31.60/5.21  ------ Preprocessing... sup_sim: 125  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: 27  sf_s  rm: 14 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 16 0s  sf_e  pe_s  pe_e 
% 31.60/5.21  
% 31.60/5.21  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 31.60/5.21  
% 31.60/5.21  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 31.60/5.21  ------ Proving...
% 31.60/5.21  ------ Problem Properties 
% 31.60/5.21  
% 31.60/5.21  
% 31.60/5.21  clauses                                 1381
% 31.60/5.21  conjectures                             1
% 31.60/5.21  EPR                                     168
% 31.60/5.21  Horn                                    1179
% 31.60/5.21  unary                                   459
% 31.60/5.21  binary                                  451
% 31.60/5.21  lits                                    2999
% 31.60/5.21  lits eq                                 683
% 31.60/5.21  fd_pure                                 0
% 31.60/5.21  fd_pseudo                               0
% 31.60/5.21  fd_cond                                 98
% 31.60/5.21  fd_pseudo_cond                          64
% 31.60/5.21  AC symbols                              0
% 31.60/5.21  
% 31.60/5.21  ------ Schedule dynamic 5 is on 
% 31.60/5.21  
% 31.60/5.21  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.60/5.21  
% 31.60/5.21  
% 31.60/5.21  ------ 
% 31.60/5.21  Current options:
% 31.60/5.21  ------ 
% 31.60/5.21  
% 31.60/5.21  
% 31.60/5.21  
% 31.60/5.21  
% 31.60/5.21  ------ Proving...
% 31.60/5.21  
% 31.60/5.21  
% 31.60/5.21  % SZS status Theorem for theBenchmark.p
% 31.60/5.21  
% 31.60/5.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.60/5.21  
% 31.60/5.21  
%------------------------------------------------------------------------------