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LisaST---0.9.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LisaST---0.9
% Problem  : SWW285+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:11:38 AM UTC 2026

% Result   : Theorem 104.47s 16.57s
% Output   : CNFRefutation 104.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   62 (  32 unt;   0 def)
%            Number of atoms       :  125 (  45 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  121 (  58   ~;  47   |;   4   &)
%                                         (   1 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :   37 (   8 sgn  16   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_pe,axiom,
    'v$up' = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) ).

fof(fact_r,axiom,
    hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$uq'),'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$up'),'v$ur') ).

fof(fact_degree__0,axiom,
    ! [X0] :
      ( 'class$uGroups$uOzero'(X0)
     => 'c$uPolynomial$uOdegree'(X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ) ).

fof(fact_mult__poly__0__left,axiom,
    ! [X0,X1] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u0'(X1)
     => hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'(X1)),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1))),X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X1)) ) ).

fof(fact_dvd__0__right,axiom,
    ! [X0,X1] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u1'(X1)
     => 'c$uRings$uOdvd$u$uclass$uOdvd'(X1,X0,'c$uGroups$uOzero$u$uclass$uOzero'(X1)) ) ).

fof(fact_power__eq__0__iff,axiom,
    ! [X0,X1,X2] :
      ( ( 'class$uRings$uOzero$u$uneq$u$uone'(X2)
        & 'class$uRings$uOno$u$uzero$u$udivisors'(X2)
        & 'class$uRings$uOmult$u$uzero'(X2)
        & 'class$uPower$uOpower'(X2) )
     => ( hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'(X2),X1),X0) = 'c$uGroups$uOzero$u$uclass$uOzero'(X2)
      <=> ( X0 != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
          & X1 = 'c$uGroups$uOzero$u$uclass$uOzero'(X2) ) ) ) ).

fof(fact_dvd__0__left,axiom,
    ! [X0,X1] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u1'(X1)
     => ( 'c$uRings$uOdvd$u$uclass$uOdvd'(X1,'c$uGroups$uOzero$u$uclass$uOzero'(X1),X0)
       => X0 = 'c$uGroups$uOzero$u$uclass$uOzero'(X1) ) ) ).

fof(fact_nat__size,axiom,
    ! [X0] : 'c$uNat$uOsize$u$uclass$uOsize'('tc$uNat$uOnat',X0) = X0 ).

fof(fact_nat_Osize_I3_J,axiom,
    'c$uNat$uOsize$u$uclass$uOsize'('tc$uNat$uOnat','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
    'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uComplex$uOcomplex') ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
    'class$uRings$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex') ).

fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
    'class$uGroups$uOzero'('tc$uComplex$uOcomplex') ).

fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
    'class$uRings$uOidom'('tc$uComplex$uOcomplex') ).

fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
    ! [X0] :
      ( 'class$uRings$uOidom'(X0)
     => 'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'(X0)) ) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
    ! [X0] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u1'(X0)
     => 'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uPolynomial$uOpoly'(X0)) ) ).

fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
    ! [X0] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u1'(X0)
     => 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'(X0)) ) ).

fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
    ! [X0] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u0'(X0)
     => 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'(X0)) ) ).

fof(arity_Polynomial__Opoly__Power_Opower,axiom,
    ! [X0] :
      ( 'class$uRings$uOcomm$u$usemiring$u$u1'(X0)
     => 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'(X0)) ) ).

cnf(c1,plain,
    'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) = 'v$up',
    inference(clausification,[status(esa)],[fact_pe]) ).

cnf(c52,plain,
    hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$up'),'v$ur') = hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$uq'),'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')),
    inference(clausification,[status(esa)],[fact_r]) ).

cnf(c93,plain,
    ( 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') = 'c$uPolynomial$uOdegree'(X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)))
    | ~ 'class$uGroups$uOzero'(X0) ),
    inference(clausification,[status(esa)],[fact_degree__0]) ).

cnf(c101,plain,
    ( 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'(X0)),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))),X1)
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
    inference(clausification,[status(esa)],[fact_mult__poly__0__left]) ).

cnf(c126,plain,
    ( 'c$uRings$uOdvd$u$uclass$uOdvd'(X0,X1,'c$uGroups$uOzero$u$uclass$uOzero'(X0))
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
    inference(clausification,[status(esa)],[fact_dvd__0__right]) ).

cnf(c131,plain,
    ( 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != X2
    | ~ 'class$uRings$uOmult$u$uzero'(X0)
    | ~ 'class$uRings$uOno$u$uzero$u$udivisors'(X0)
    | ~ 'class$uPower$uOpower'(X0)
    | ~ 'class$uRings$uOzero$u$uneq$u$uone'(X0)
    | 'c$uGroups$uOzero$u$uclass$uOzero'(X0) != hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'(X0),X1),X2) ),
    inference(clausification,[status(esa)],[fact_power__eq__0__iff]) ).

cnf(c189,plain,
    ( ~ 'c$uRings$uOdvd$u$uclass$uOdvd'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
    | 'c$uGroups$uOzero$u$uclass$uOzero'(X0) = X1
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
    inference(clausification,[status(esa)],[fact_dvd__0__left]) ).

cnf(c605,plain,
    'c$uNat$uOsize$u$uclass$uOsize'('tc$uNat$uOnat',X0) = X0,
    inference(clausification,[status(esa)],[fact_nat__size]) ).

cnf(c614,plain,
    'c$uNat$uOsize$u$uclass$uOsize'('tc$uNat$uOnat','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
    inference(clausification,[status(esa)],[fact_nat_Osize_I3_J]) ).

cnf(c1522,plain,
    'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uComplex$uOcomplex'),
    inference(clausification,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).

cnf(c1523,plain,
    'class$uRings$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex'),
    inference(clausification,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).

cnf(c1541,plain,
    'class$uGroups$uOzero'('tc$uComplex$uOcomplex'),
    inference(clausification,[status(esa)],[arity_Complex__Ocomplex__Groups_Ozero]) ).

cnf(c1543,plain,
    'class$uRings$uOidom'('tc$uComplex$uOcomplex'),
    inference(clausification,[status(esa)],[arity_Complex__Ocomplex__Rings_Oidom]) ).

cnf(c1568,plain,
    ( 'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'(X0))
    | ~ 'class$uRings$uOidom'(X0) ),
    inference(clausification,[status(esa)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors]) ).

cnf(c1572,plain,
    ( 'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uPolynomial$uOpoly'(X0))
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
    inference(clausification,[status(esa)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1]) ).

cnf(c1577,plain,
    ( 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'(X0))
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
    inference(clausification,[status(esa)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one]) ).

cnf(c1585,plain,
    ( 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'(X0))
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u0'(X0) ),
    inference(clausification,[status(esa)],[arity_Polynomial__Opoly__Rings_Omult__zero]) ).

cnf(c1591,plain,
    ( 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'(X0))
    | ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
    inference(clausification,[status(esa)],[arity_Polynomial__Opoly__Power_Opower]) ).

cnf(d0,plain,
    'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') = 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))),
    inference(resolution,[status(thm)],[c1541,c93]) ).

cnf(d1,plain,
    'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') = 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up'),
    inference(demodulation,[status(thm)],[d0,c1]) ).

cnf(d2,plain,
    'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))),X0),
    inference(resolution,[status(thm)],[c1523,c101]) ).

cnf(d3,plain,
    'v$up' = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))),X0),
    inference(demodulation,[status(thm)],[d2,c1]) ).

cnf(d4,plain,
    'v$up' = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$up'),X0),
    inference(demodulation,[status(thm)],[d3,c1]) ).

cnf(d5,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) != hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$up'),'v$ur') ),
    inference(superposition,[status(thm)],[c52,c131]) ).

cnf(d6,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
    | 'v$up' != hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$up'),'v$ur') ),
    inference(demodulation,[status(thm)],[d5,c1]) ).

cnf(d7,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uPolynomial$uOdegree'('tc$uComplex$uOcomplex','v$up')
    | 'v$up' != 'v$up' ),
    inference(demodulation,[status(thm)],[d6,d4]) ).

cnf(d8,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
    | 'v$up' != 'v$up' ),
    inference(demodulation,[status(thm)],[d7,d1]) ).

cnf(d9,plain,
    'class$uRings$uOno$u$uzero$u$udivisors'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),
    inference(resolution,[status(thm)],[c1568,c1543]) ).

cnf(d10,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
    | 'v$up' != 'v$up' ),
    inference(resolution,[status(thm)],[d9,d8]) ).

cnf(d11,plain,
    'class$uRings$uOzero$u$uneq$u$uone'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),
    inference(resolution,[status(thm)],[c1577,c1522]) ).

cnf(d12,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | ~ 'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'v$up' != 'v$up'
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ),
    inference(resolution,[status(thm)],[d11,d10]) ).

cnf(d13,plain,
    'class$uRings$uOmult$u$uzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),
    inference(resolution,[status(thm)],[c1585,c1523]) ).

cnf(d14,plain,
    ( ~ 'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'v$up' != 'v$up'
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ),
    inference(resolution,[status(thm)],[d13,d12]) ).

cnf(d15,plain,
    'class$uPower$uOpower'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),
    inference(resolution,[status(thm)],[c1591,c1522]) ).

cnf(d16,plain,
    ( 'v$up' != 'v$up'
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ),
    inference(resolution,[status(thm)],[d15,d14]) ).

cnf(d17,plain,
    'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
    inference(demodulation,[status(thm)],[c614,c605]) ).

cnf(d18,plain,
    'v$up' != 'v$up',
    inference(resolution,[status(thm)],[d17,d16]) ).

cnf(d19,plain,
    'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),
    inference(resolution,[status(thm)],[c1572,c1522]) ).

cnf(d20,plain,
    'c$uRings$uOdvd$u$uclass$uOdvd'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'),X0,'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))),
    inference(resolution,[status(thm)],[d19,c126]) ).

cnf(d21,plain,
    'c$uRings$uOdvd$u$uclass$uOdvd'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'),X0,'v$up'),
    inference(demodulation,[status(thm)],[d20,c1]) ).

cnf(d22,plain,
    ( ~ 'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) = 'v$up' ),
    inference(resolution,[status(thm)],[d21,c189]) ).

cnf(d23,plain,
    ( ~ 'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex'))
    | 'v$up' = 'v$up' ),
    inference(demodulation,[status(thm)],[d22,c1]) ).

cnf(d24,plain,
    'v$up' = 'v$up',
    inference(resolution,[status(thm)],[d19,d23]) ).

cnf(d25,plain,
    $false,
    inference(resolution,[status(thm)],[d24,d18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW285+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03  % Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n007.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Sat Sep 26 15:33:23 UTC 2026
% 0.08/0.36  % CPUTime  : 
% 0.08/0.36  Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 104.47/16.57  % SZS status Theorem for theBenchmark.p
% 104.47/16.57  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------