TSTP Solution File: SWW231+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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 : Thu Sep 29 20:57:59 EDT 2022

% Result   : Theorem 8.00s 5.30s
% Output   : Proof 8.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :  104
% Syntax   : Number of formulae    :  233 ( 123 unt;  24 typ;   0 def)
%            Number of atoms       :  423 ( 291 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  320 ( 125   ~; 121   |;   0   &)
%                                         (  62 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of FOOLs       :   19 (  19 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  19   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   5 con; 0-3 aty)
%            Number of variables   :  366 ( 328   !;   0   ?; 366   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_Complex_Orcis_type,type,
    c_Complex_Orcis: ( $i * $i ) > $i ).

tff(v_a_type,type,
    v_a: $i ).

tff(c_Groups_Ouminus__class_Ouminus_type,type,
    c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(c_Groups_Oabs__class_Oabs_type,type,
    c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(v_r_type,type,
    v_r: $i ).

tff(tc_RealDef_Oreal_type,type,
    tc_RealDef_Oreal: $i ).

tff(c_Groups_Oplus__class_Oplus_type,type,
    c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(c_Transcendental_Opi_type,type,
    c_Transcendental_Opi: $i ).

tff(hAPP_type,type,
    hAPP: ( $i * $i ) > $i ).

tff(c_NthRoot_Osqrt_type,type,
    c_NthRoot_Osqrt: $i > $i ).

tff(c_Groups_Otimes__class_Otimes_type,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

tff(c_Complex_Ocis_type,type,
    c_Complex_Ocis: $i > $i ).

tff(c_RealVector_Oof__real_type,type,
    c_RealVector_Oof__real: ( $i * $i ) > $i ).

tff(tc_Complex_Ocomplex_type,type,
    tc_Complex_Ocomplex: $i ).

tff(c_Complex_Ocomplex_OComplex_type,type,
    c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).

tff(c_Complex_ORe_type,type,
    c_Complex_ORe: $i > $i ).

tff(c_Complex_OIm_type,type,
    c_Complex_OIm: $i > $i ).

tff(c_Groups_Ominus__class_Ominus_type,type,
    c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(c_Transcendental_Osin_type,type,
    c_Transcendental_Osin: $i > $i ).

tff(c_Groups_Osgn__class_Osgn_type,type,
    c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).

tff(class_Rings_Olinordered__idom_type,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(class_Rings_Oring_type,type,
    class_Rings_Oring: $i > $o ).

tff(c_Transcendental_Ocos_type,type,
    c_Transcendental_Ocos: $i > $i ).

tff(class_Rings_Ocomm__semiring__1_type,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(1,plain,
    ^ [V_a: $i,V_r: $i] :
      refl(
        ( ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
      <=> ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
  <=> ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
  <=> ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__def) ).

tff(5,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
    | ( c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ^ [V_y: $i,V_x: $i] :
      refl(
        ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
      <=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
  <=> ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
  <=> ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mult__def) ).

tff(15,plain,
    ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ( ~ ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))),
    inference(unit_resolution,[status(thm)],[18,17]) ).

tff(20,plain,
    c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)),
    inference(symmetry,[status(thm)],[19]) ).

tff(21,plain,
    ^ [V_a: $i,V_r: $i] :
      refl(
        ( ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
      <=> ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
  <=> ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
  <=> ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__rcis) ).

tff(25,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
    | ( c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(unit_resolution,[status(thm)],[28,27]) ).

tff(30,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(symmetry,[status(thm)],[29]) ).

tff(31,plain,
    ^ [V_x: $i] :
      refl(
        ( ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
      <=> ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
  <=> ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ( ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
  <=> ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,axiom,
    ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__periodic__pi2) ).

tff(35,plain,
    ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
    inference(skolemize,[status(sab)],[35]) ).

tff(37,plain,
    ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
    inference(modus_ponens,[status(thm)],[36,32]) ).

tff(38,plain,
    ( ~ ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
    | ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)),
    inference(unit_resolution,[status(thm)],[38,37]) ).

tff(40,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
    inference(symmetry,[status(thm)],[39]) ).

tff(41,plain,
    ^ [V_x: $i] :
      refl(
        ( ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
      <=> ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
  <=> ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
  <=> ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,axiom,
    ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).

tff(45,plain,
    ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
    inference(skolemize,[status(sab)],[45]) ).

tff(47,plain,
    ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
    inference(modus_ponens,[status(thm)],[46,42]) ).

tff(48,plain,
    ( ~ ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
    | ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),
    inference(unit_resolution,[status(thm)],[48,47]) ).

tff(50,plain,
    ( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
  <=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

tff(52,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ^ [V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Rings_Olinordered__idom(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
      <=> ( ~ class_Rings_Olinordered__idom(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(54,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) ),
    inference(quant_intro,[status(thm)],[53]) ).

tff(55,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ^ [V_a: $i,T_a: $i] :
      rewrite(
        ( ( class_Rings_Olinordered__idom(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
      <=> ( ~ class_Rings_Olinordered__idom(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( class_Rings_Olinordered__idom(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,axiom,
    ! [V_a: $i,T_a: $i] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).

tff(59,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
    inference(modus_ponens,[status(thm)],[59,55]) ).

tff(61,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
    inference(skolemize,[status(sab)],[60]) ).

tff(62,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
    inference(modus_ponens,[status(thm)],[61,54]) ).

tff(63,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_Rings_Olinordered__idom(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
      | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_Rings_Olinordered__idom(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
      | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(64,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_Rings_Olinordered__idom(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
    | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(65,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_Rings_Olinordered__idom(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
    | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r),
    inference(unit_resolution,[status(thm)],[65,62,52]) ).

tff(67,plain,
    c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)),
    inference(monotonicity,[status(thm)],[66]) ).

tff(68,plain,
    ^ [V_y: $i,V_x: $i] :
      refl(
        ( ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
      <=> ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ) )),
    inference(bind,[status(th)],]) ).

tff(69,plain,
    ( ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
  <=> ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ) ),
    inference(quant_intro,[status(thm)],[68]) ).

tff(70,plain,
    ( ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
  <=> ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(71,axiom,
    ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).

tff(72,plain,
    ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
    inference(modus_ponens,[status(thm)],[71,70]) ).

tff(73,plain,
    ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
    inference(skolemize,[status(sab)],[72]) ).

tff(74,plain,
    ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
    inference(modus_ponens,[status(thm)],[73,69]) ).

tff(75,plain,
    ( ~ ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
    | ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
    inference(unit_resolution,[status(thm)],[75,74]) ).

tff(77,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
    inference(symmetry,[status(thm)],[76]) ).

tff(78,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),
    inference(transitivity,[status(thm)],[77,67,49]) ).

tff(79,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
    inference(monotonicity,[status(thm)],[78]) ).

tff(80,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
    inference(symmetry,[status(thm)],[79]) ).

tff(81,plain,
    ^ [V_k: $i,T_a: $i] :
      refl(
        ( ( ~ class_Rings_Olinordered__idom(T_a)
          | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
      <=> ( ~ class_Rings_Olinordered__idom(T_a)
          | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(82,plain,
    ( ! [V_k: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
  <=> ! [V_k: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
    inference(quant_intro,[status(thm)],[81]) ).

tff(83,plain,
    ( ! [V_k: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
  <=> ! [V_k: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,plain,
    ^ [V_k: $i,T_a: $i] :
      rewrite(
        ( ( class_Rings_Olinordered__idom(T_a)
         => ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
      <=> ( ~ class_Rings_Olinordered__idom(T_a)
          | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(85,plain,
    ( ! [V_k: $i,T_a: $i] :
        ( class_Rings_Olinordered__idom(T_a)
       => ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
  <=> ! [V_k: $i,T_a: $i] :
        ( ~ class_Rings_Olinordered__idom(T_a)
        | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
    inference(quant_intro,[status(thm)],[84]) ).

tff(86,axiom,
    ! [V_k: $i,T_a: $i] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).

tff(87,plain,
    ! [V_k: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
    inference(modus_ponens,[status(thm)],[86,85]) ).

tff(88,plain,
    ! [V_k: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
    inference(modus_ponens,[status(thm)],[87,83]) ).

tff(89,plain,
    ! [V_k: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
    inference(skolemize,[status(sab)],[88]) ).

tff(90,plain,
    ! [V_k: $i,T_a: $i] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
    inference(modus_ponens,[status(thm)],[89,82]) ).

tff(91,plain,
    ( ( ~ ! [V_k: $i,T_a: $i] :
            ( ~ class_Rings_Olinordered__idom(T_a)
            | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
      | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
      | ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) )
  <=> ( ~ ! [V_k: $i,T_a: $i] :
            ( ~ class_Rings_Olinordered__idom(T_a)
            | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
      | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
      | ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(92,plain,
    ( ~ ! [V_k: $i,T_a: $i] :
          ( ~ class_Rings_Olinordered__idom(T_a)
          | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
    | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
    | ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(93,plain,
    ( ~ ! [V_k: $i,T_a: $i] :
          ( ~ class_Rings_Olinordered__idom(T_a)
          | ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
    | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
    | ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ),
    inference(modus_ponens,[status(thm)],[92,91]) ).

tff(94,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),
    inference(unit_resolution,[status(thm)],[93,90,52]) ).

tff(95,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),
    inference(symmetry,[status(thm)],[94]) ).

tff(96,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
    inference(monotonicity,[status(thm)],[95]) ).

tff(97,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
    inference(transitivity,[status(thm)],[96,80]) ).

tff(98,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(monotonicity,[status(thm)],[97,40]) ).

tff(99,plain,
    ( class_Rings_Oring(tc_RealDef_Oreal)
  <=> class_Rings_Oring(tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(100,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

tff(101,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[100,99]) ).

tff(102,plain,
    ^ [V_b: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
      <=> ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(103,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Oring(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Oring(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ),
    inference(quant_intro,[status(thm)],[102]) ).

tff(104,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Oring(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Oring(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(105,plain,
    ^ [V_b: $i,V_a: $i,T_a: $i] :
      rewrite(
        ( ( class_Rings_Oring(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
      <=> ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(106,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( class_Rings_Oring(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Oring(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ),
    inference(quant_intro,[status(thm)],[105]) ).

tff(107,axiom,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( class_Rings_Oring(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

tff(108,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Oring(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
    inference(modus_ponens,[status(thm)],[107,106]) ).

tff(109,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Oring(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
    inference(modus_ponens,[status(thm)],[108,104]) ).

tff(110,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Oring(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
    inference(skolemize,[status(sab)],[109]) ).

tff(111,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Oring(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
    inference(modus_ponens,[status(thm)],[110,103]) ).

tff(112,plain,
    ( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Oring(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
      | ~ class_Rings_Oring(tc_RealDef_Oreal)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) ) )
  <=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Oring(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
      | ~ class_Rings_Oring(tc_RealDef_Oreal)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(113,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
    | ~ class_Rings_Oring(tc_RealDef_Oreal)
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(114,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
    | ~ class_Rings_Oring(tc_RealDef_Oreal)
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) ) ),
    inference(modus_ponens,[status(thm)],[113,112]) ).

tff(115,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),
    inference(unit_resolution,[status(thm)],[114,111,101]) ).

tff(116,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
    inference(monotonicity,[status(thm)],[95]) ).

tff(117,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
    inference(monotonicity,[status(thm)],[116]) ).

tff(118,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),
    inference(symmetry,[status(thm)],[117]) ).

tff(119,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)),
    inference(monotonicity,[status(thm)],[118]) ).

tff(120,plain,
    ( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
    | ( c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(121,plain,
    c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)),
    inference(unit_resolution,[status(thm)],[120,27]) ).

tff(122,plain,
    c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)),
    inference(monotonicity,[status(thm)],[10]) ).

tff(123,plain,
    ^ [V_y: $i,V_x: $i] :
      refl(
        ( ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
      <=> ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ) )),
    inference(bind,[status(th)],]) ).

tff(124,plain,
    ( ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
  <=> ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ) ),
    inference(quant_intro,[status(thm)],[123]) ).

tff(125,plain,
    ( ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
  <=> ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(126,axiom,
    ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__mult) ).

tff(127,plain,
    ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
    inference(modus_ponens,[status(thm)],[126,125]) ).

tff(128,plain,
    ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
    inference(skolemize,[status(sab)],[127]) ).

tff(129,plain,
    ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
    inference(modus_ponens,[status(thm)],[128,124]) ).

tff(130,plain,
    ( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
    | ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(131,plain,
    c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))),
    inference(unit_resolution,[status(thm)],[130,129]) ).

tff(132,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))) = c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))),
    inference(symmetry,[status(thm)],[131]) ).

tff(133,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))) = c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(transitivity,[status(thm)],[132,122,121,119,115,98,30]) ).

tff(134,plain,
    ^ [V_a: $i,V_r: $i] :
      refl(
        ( ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
      <=> ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ) )),
    inference(bind,[status(th)],]) ).

tff(135,plain,
    ( ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
  <=> ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ) ),
    inference(quant_intro,[status(thm)],[134]) ).

tff(136,plain,
    ( ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
  <=> ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(137,axiom,
    ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re__rcis) ).

tff(138,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
    inference(modus_ponens,[status(thm)],[137,136]) ).

tff(139,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
    inference(skolemize,[status(sab)],[138]) ).

tff(140,plain,
    ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
    inference(modus_ponens,[status(thm)],[139,135]) ).

tff(141,plain,
    ( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
    | ( c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(142,plain,
    c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(unit_resolution,[status(thm)],[141,140]) ).

tff(143,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(symmetry,[status(thm)],[142]) ).

tff(144,plain,
    ( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
  <=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(145,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

tff(146,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[145,144]) ).

tff(147,plain,
    ^ [V_c: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(148,plain,
    ( ! [V_c: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
  <=> ! [V_c: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
    inference(quant_intro,[status(thm)],[147]) ).

tff(149,plain,
    ( ! [V_c: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
  <=> ! [V_c: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(150,plain,
    ^ [V_c: $i,V_a: $i,T_a: $i] :
      rewrite(
        ( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(151,plain,
    ( ! [V_c: $i,V_a: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
  <=> ! [V_c: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
    inference(quant_intro,[status(thm)],[150]) ).

tff(152,axiom,
    ! [V_c: $i,V_a: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

tff(153,plain,
    ! [V_c: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
    inference(modus_ponens,[status(thm)],[152,151]) ).

tff(154,plain,
    ! [V_c: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
    inference(modus_ponens,[status(thm)],[153,149]) ).

tff(155,plain,
    ! [V_c: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
    inference(skolemize,[status(sab)],[154]) ).

tff(156,plain,
    ! [V_c: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
    inference(modus_ponens,[status(thm)],[155,148]) ).

tff(157,plain,
    ( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
      | ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) )
  <=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
      | ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(158,plain,
    ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
    | ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(159,plain,
    ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
    | ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) ),
    inference(modus_ponens,[status(thm)],[158,157]) ).

tff(160,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a),
    inference(unit_resolution,[status(thm)],[159,156,146]) ).

tff(161,plain,
    c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
    inference(monotonicity,[status(thm)],[160]) ).

tff(162,plain,
    ^ [V_x: $i] :
      refl(
        ( ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
      <=> ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ) )),
    inference(bind,[status(th)],]) ).

tff(163,plain,
    ( ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
  <=> ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ) ),
    inference(quant_intro,[status(thm)],[162]) ).

tff(164,plain,
    ( ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
  <=> ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(165,axiom,
    ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__periodic__pi) ).

tff(166,plain,
    ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
    inference(modus_ponens,[status(thm)],[165,164]) ).

tff(167,plain,
    ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
    inference(skolemize,[status(sab)],[166]) ).

tff(168,plain,
    ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
    inference(modus_ponens,[status(thm)],[167,163]) ).

tff(169,plain,
    ( ~ ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
    | ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(170,plain,
    c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)),
    inference(unit_resolution,[status(thm)],[169,168]) ).

tff(171,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)),
    inference(symmetry,[status(thm)],[170]) ).

tff(172,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
    inference(transitivity,[status(thm)],[171,161]) ).

tff(173,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(monotonicity,[status(thm)],[97,172]) ).

tff(174,plain,
    ( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Oring(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
      | ~ class_Rings_Oring(tc_RealDef_Oreal)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) )
  <=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Oring(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
      | ~ class_Rings_Oring(tc_RealDef_Oreal)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(175,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
    | ~ class_Rings_Oring(tc_RealDef_Oreal)
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(176,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Oring(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
    | ~ class_Rings_Oring(tc_RealDef_Oreal)
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) ),
    inference(modus_ponens,[status(thm)],[175,174]) ).

tff(177,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))),
    inference(unit_resolution,[status(thm)],[176,111,101]) ).

tff(178,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)),
    inference(monotonicity,[status(thm)],[118]) ).

tff(179,plain,
    ( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
    | ( c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(180,plain,
    c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)),
    inference(unit_resolution,[status(thm)],[179,140]) ).

tff(181,plain,
    c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)),
    inference(monotonicity,[status(thm)],[10]) ).

tff(182,plain,
    ^ [V_y: $i,V_x: $i] :
      refl(
        ( ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
      <=> ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ) )),
    inference(bind,[status(th)],]) ).

tff(183,plain,
    ( ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
  <=> ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ) ),
    inference(quant_intro,[status(thm)],[182]) ).

tff(184,plain,
    ( ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
  <=> ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(185,axiom,
    ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__mult) ).

tff(186,plain,
    ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
    inference(modus_ponens,[status(thm)],[185,184]) ).

tff(187,plain,
    ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
    inference(skolemize,[status(sab)],[186]) ).

tff(188,plain,
    ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
    inference(modus_ponens,[status(thm)],[187,183]) ).

tff(189,plain,
    ( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
    | ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(190,plain,
    c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),
    inference(unit_resolution,[status(thm)],[189,188]) ).

tff(191,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))) = c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))),
    inference(symmetry,[status(thm)],[190]) ).

tff(192,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))) = c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
    inference(transitivity,[status(thm)],[191,181,180,178,177,173,143]) ).

tff(193,plain,
    c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))) = c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),
    inference(monotonicity,[status(thm)],[192,133]) ).

tff(194,plain,
    c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))),
    inference(symmetry,[status(thm)],[193]) ).

tff(195,plain,
    ^ [V_z: $i] :
      refl(
        ( ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
      <=> ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) )),
    inference(bind,[status(th)],]) ).

tff(196,plain,
    ( ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
  <=> ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) ),
    inference(quant_intro,[status(thm)],[195]) ).

tff(197,plain,
    ( ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
  <=> ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) ),
    inference(rewrite,[status(thm)],]) ).

tff(198,axiom,
    ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__surj) ).

tff(199,plain,
    ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
    inference(modus_ponens,[status(thm)],[198,197]) ).

tff(200,plain,
    ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
    inference(skolemize,[status(sab)],[199]) ).

tff(201,plain,
    ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
    inference(modus_ponens,[status(thm)],[200,196]) ).

tff(202,plain,
    ( ~ ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
    | ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(203,plain,
    c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
    inference(unit_resolution,[status(thm)],[202,201]) ).

tff(204,plain,
    c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),
    inference(symmetry,[status(thm)],[203]) ).

tff(205,plain,
    c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
    inference(transitivity,[status(thm)],[204,194,20,10]) ).

tff(206,plain,
    ( ( c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) )
  <=> ( c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(207,axiom,
    c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(208,plain,
    c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
    inference(modus_ponens,[status(thm)],[207,206]) ).

tff(209,plain,
    $false,
    inference(unit_resolution,[status(thm)],[208,205]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.14  % Problem  : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.15  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.36  % Computer : n018.cluster.edu
% 0.12/0.36  % Model    : x86_64 x86_64
% 0.12/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36  % Memory   : 8042.1875MB
% 0.12/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36  % CPULimit : 300
% 0.12/0.36  % WCLimit  : 300
% 0.12/0.36  % DateTime : Sun Sep  4 13:09:31 EDT 2022
% 0.12/0.36  % CPUTime  : 
% 0.12/0.37  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.37  Usage: tptp [options] [-file:]file
% 0.12/0.37    -h, -?       prints this message.
% 0.12/0.37    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.37    -m, -model   generate model.
% 0.12/0.37    -p, -proof   generate proof.
% 0.12/0.37    -c, -core    generate unsat core of named formulas.
% 0.12/0.37    -st, -statistics display statistics.
% 0.12/0.37    -t:timeout   set timeout (in second).
% 0.12/0.37    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.37    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.37    -<param>:<value> configuration parameter and value.
% 0.12/0.37    -o:<output-file> file to place output in.
% 8.00/5.30  % SZS status Theorem
% 8.00/5.30  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------