TSTP Solution File: ALG373-1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n023.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 : Sun May  5 04:30:01 EDT 2024

% Result   : Unsatisfiable 0.22s 0.50s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   79 (  38 unt;   0 def)
%            Number of atoms       :  136 (  63 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  119 (  62   ~;  57   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   69 (  69   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3501,plain,
    $false,
    inference(resolution,[],[f3411,f2575]) ).

fof(f2575,plain,
    ! [X27,X4] : c_HOL_Oord__class_Oless(v_r,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X27,X4),tc_RealDef_Oreal),
    inference(backward_demodulation,[],[f188,f2546]) ).

fof(f2546,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
    inference(resolution,[],[f2545,f407]) ).

fof(f407,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).

fof(f2545,plain,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
    | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
    inference(trivial_inequality_removal,[],[f2543]) ).

fof(f2543,plain,
    ( v_r != v_r
    | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
    | ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    inference(superposition,[],[f112,f2489]) ).

fof(f2489,plain,
    v_r = c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),
    inference(forward_demodulation,[],[f2447,f1557]) ).

fof(f1557,plain,
    v_r = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),
    inference(resolution,[],[f736,f270]) ).

fof(f270,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rp_0) ).

fof(f736,plain,
    ! [X0] :
      ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
      | c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
    inference(resolution,[],[f729,f232]) ).

fof(f232,axiom,
    ! [X4] :
      ( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
      | c_HOL_Oabs__class_Oabs(X4,tc_RealDef_Oreal) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).

fof(f729,plain,
    ! [X0,X1] :
      ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
      | ~ c_lessequals(X1,X0,tc_RealDef_Oreal) ),
    inference(resolution,[],[f327,f431]) ).

fof(f431,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

fof(f327,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_lessequals(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

fof(f2447,plain,
    c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),
    inference(superposition,[],[f881,f2437]) ).

fof(f2437,plain,
    v_r = v_x(v_r),
    inference(duplicate_literal_removal,[],[f2429]) ).

fof(f2429,plain,
    ( v_r = v_x(v_r)
    | v_r = v_x(v_r) ),
    inference(resolution,[],[f2425,f1265]) ).

fof(f1265,plain,
    ! [X0] :
      ( c_lessequals(X0,v_x(X0),tc_RealDef_Oreal)
      | v_x(X0) = X0 ),
    inference(resolution,[],[f1239,f277]) ).

fof(f277,axiom,
    ! [X21,X9] :
      ( c_lessequals(X21,X9,tc_RealDef_Oreal)
      | c_lessequals(X9,X21,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).

fof(f1239,plain,
    ! [X0] :
      ( ~ c_lessequals(v_x(X0),X0,tc_RealDef_Oreal)
      | v_x(X0) = X0 ),
    inference(resolution,[],[f307,f351]) ).

fof(f351,axiom,
    ! [X33] : ~ c_HOL_Oord__class_Oless(v_x(X33),X33,tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f307,axiom,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
      | ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
      | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).

fof(f2425,plain,
    ( ~ c_lessequals(v_r,v_x(v_r),tc_RealDef_Oreal)
    | v_r = v_x(v_r) ),
    inference(superposition,[],[f2393,f1557]) ).

fof(f2393,plain,
    ! [X0] :
      ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),v_x(X0),tc_RealDef_Oreal)
      | v_x(X0) = X0 ),
    inference(resolution,[],[f266,f1906]) ).

fof(f1906,plain,
    ! [X0] :
      ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
      | v_x(X0) = X0 ),
    inference(resolution,[],[f1903,f400]) ).

fof(f400,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).

fof(f1903,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
      | v_x(X0) = X0 ),
    inference(forward_demodulation,[],[f1885,f881]) ).

fof(f1885,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
      | v_x(X0) = X0 ),
    inference(resolution,[],[f95,f1239]) ).

fof(f95,axiom,
    ! [X10,X0,X11] :
      ( c_lessequals(X10,X11,X0)
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X10,X0),X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).

fof(f266,axiom,
    ! [X1,X4] :
      ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).

fof(f881,plain,
    ! [X0] : c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),
    inference(superposition,[],[f869,f644]) ).

fof(f644,plain,
    ! [X0] : c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolution,[],[f232,f537]) ).

fof(f537,plain,
    ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(superposition,[],[f535,f350]) ).

fof(f350,axiom,
    ! [X33] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X33),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X33),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f535,plain,
    ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolution,[],[f259,f444]) ).

fof(f444,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f259,axiom,
    ! [X0,X1] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).

fof(f869,plain,
    ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolution,[],[f105,f400]) ).

fof(f105,axiom,
    ! [X10,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(X10,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).

fof(f112,axiom,
    ! [X10,X0] :
      ( c_HOL_Ouminus__class_Ouminus(X10,X0) != X10
      | c_HOL_Ozero__class_Ozero(X0) = X10
      | ~ class_OrderedGroup_Oordered__ab__group__add(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

fof(f188,axiom,
    ! [X27,X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X27,X4),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).

fof(f3411,plain,
    ! [X0] : ~ c_HOL_Oord__class_Oless(v_r,X0,tc_RealDef_Oreal),
    inference(backward_demodulation,[],[f1807,f3390]) ).

fof(f3390,plain,
    ! [X33] : v_r = c_HOL_Ouminus__class_Ouminus(v_x(X33),tc_RealDef_Oreal),
    inference(forward_demodulation,[],[f3381,f2594]) ).

fof(f2594,plain,
    v_r = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f521,f2546]) ).

fof(f521,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(resolution,[],[f214,f444]) ).

fof(f214,axiom,
    ! [X0] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).

fof(f3381,plain,
    ! [X33] : c_HOL_Ouminus__class_Ouminus(v_x(X33),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f3351,f3369]) ).

fof(f3369,plain,
    c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f2689,f3350]) ).

fof(f3350,plain,
    ! [X0] : v_xa(X0) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(resolution,[],[f3346,f444]) ).

fof(f3346,plain,
    ! [X0] :
      ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | v_xa(X0) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(trivial_inequality_removal,[],[f3345]) ).

fof(f3345,plain,
    ! [X0] :
      ( v_r != v_r
      | v_xa(X0) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(superposition,[],[f2555,f3034]) ).

fof(f3034,plain,
    ! [X0] : v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),
    inference(resolution,[],[f2979,f444]) ).

fof(f2979,plain,
    ! [X0] :
      ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
      | v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
    inference(resolution,[],[f2586,f1359]) ).

fof(f1359,plain,
    ! [X0] :
      ( ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | v_r = c_RealVector_Onorm__class_Onorm(v_xa(X0),tc_Complex_Ocomplex) ),
    inference(resolution,[],[f318,f349]) ).

fof(f349,axiom,
    ! [X33] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X33),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f318,axiom,
    ! [X21,X9] :
      ( ~ c_lessequals(X21,X9,tc_RealDef_Oreal)
      | ~ c_lessequals(X9,X21,tc_RealDef_Oreal)
      | X9 = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).

fof(f2586,plain,
    ! [X0,X1] :
      ( c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(backward_demodulation,[],[f258,f2546]) ).

fof(f258,axiom,
    ! [X0,X1] :
      ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).

fof(f2555,plain,
    ! [X0,X1] :
      ( c_RealVector_Onorm__class_Onorm(X1,X0) != v_r
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    inference(backward_demodulation,[],[f14,f2546]) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | ~ class_RealVector_Oreal__normed__vector(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).

fof(f2689,plain,
    c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_xa(v_r),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f1612,f2546]) ).

fof(f1612,plain,
    c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_xa(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),
    inference(resolution,[],[f1611,f444]) ).

fof(f1611,plain,
    ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_xa(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex) ),
    inference(trivial_inequality_removal,[],[f1610]) ).

fof(f1610,plain,
    ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_xa(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex)
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(forward_demodulation,[],[f1609,f513]) ).

fof(f513,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolution,[],[f101,f407]) ).

fof(f101,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

fof(f1609,plain,
    ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_xa(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex)
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(superposition,[],[f1604,f942]) ).

fof(f942,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(resolution,[],[f938,f407]) ).

fof(f938,plain,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
    | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(trivial_inequality_removal,[],[f937]) ).

fof(f937,plain,
    ( v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    inference(superposition,[],[f112,f892]) ).

fof(f892,plain,
    v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal),
    inference(superposition,[],[f881,f645]) ).

fof(f645,plain,
    v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal),
    inference(resolution,[],[f232,f351]) ).

fof(f1604,plain,
    ! [X0] :
      ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal)
      | c_Polynomial_Opoly(v_p,v_xa(X0),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
      | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(superposition,[],[f14,f350]) ).

fof(f3351,plain,
    ! [X33] : c_HOL_Ouminus__class_Ouminus(v_x(X33),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(backward_demodulation,[],[f350,f3350]) ).

fof(f1807,plain,
    ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),
    inference(resolution,[],[f1799,f419]) ).

fof(f419,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).

fof(f1799,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
    inference(forward_demodulation,[],[f1758,f881]) ).

fof(f1758,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(v_x(X0),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
    inference(resolution,[],[f77,f351]) ).

fof(f77,axiom,
    ! [X10,X0,X11] :
      ( c_HOL_Oord__class_Oless(X10,X11,X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X10,X0),X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n023.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 20:02:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (18181)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40  % (18184)WARNING: value z3 for option sas not known
% 0.15/0.40  % (18182)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.40  % (18185)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40  % (18184)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.40  % (18183)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.40  % (18186)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.40  % (18187)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.40  % (18188)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.44  TRYING [1]
% 0.22/0.44  TRYING [2]
% 0.22/0.50  % (18187)First to succeed.
% 0.22/0.50  % (18187)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18181"
% 0.22/0.50  % (18187)Refutation found. Thanks to Tanya!
% 0.22/0.50  % SZS status Unsatisfiable for theBenchmark
% 0.22/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.50  % (18187)------------------------------
% 0.22/0.50  % (18187)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.50  % (18187)Termination reason: Refutation
% 0.22/0.50  
% 0.22/0.50  % (18187)Memory used [KB]: 2066
% 0.22/0.50  % (18187)Time elapsed: 0.100 s
% 0.22/0.50  % (18187)Instructions burned: 158 (million)
% 0.22/0.50  % (18181)Success in time 0.133 s
%------------------------------------------------------------------------------