TSTP Solution File: SWW231+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n028.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  : 600s
% DateTime : Thu Jul 21 00:01:47 EDT 2022

% Result   : Theorem 10.07s 3.04s
% Output   : CNFRefutation 10.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   78 (  57 unt;   3 nHn;  22 RR)
%            Number of literals    :   99 (  70 equ;  24 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :  105 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_789,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Rings_Oring(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_789) ).

cnf(i_0_601,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2))) = c_Complex_OIm(c_Complex_Orcis(X1,X2)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_601) ).

cnf(i_0_186,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_186) ).

cnf(i_0_788,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_788) ).

cnf(i_0_142,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_142) ).

cnf(i_0_1374,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2))) = c_Complex_ORe(c_Complex_Orcis(X1,X2)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_1374) ).

cnf(i_0_792,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
    | ~ class_Rings_Oring(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_792) ).

cnf(i_0_8,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_8) ).

cnf(i_0_422,plain,
    c_Complex_Ocomplex_OComplex(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X1)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X1))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_422) ).

cnf(i_0_445,plain,
    c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1),c_Complex_OIm(X1)) = X1,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_445) ).

cnf(i_0_193,negated_conjecture,
    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/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_193) ).

cnf(i_0_1351,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_NthRoot_Osqrt(X2)) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_1351) ).

cnf(i_0_1317,plain,
    c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_1317) ).

cnf(i_0_216,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_216) ).

cnf(i_0_148,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_148) ).

cnf(i_0_465,plain,
    c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_465) ).

cnf(i_0_1420,plain,
    c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_1420) ).

cnf(i_0_378,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_378) ).

cnf(i_0_169,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_169) ).

cnf(i_0_251,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_251) ).

cnf(i_0_250,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_250) ).

cnf(i_0_391,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_391) ).

cnf(i_0_791,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
    | ~ class_Rings_Oring(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-r1fyow0m/lgb.p',i_0_791) ).

cnf(c_0_1444,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Rings_Oring(X1) ),
    i_0_789 ).

cnf(c_0_1445,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2))) = c_Complex_OIm(c_Complex_Orcis(X1,X2)),
    i_0_601 ).

cnf(c_0_1446,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    i_0_186 ).

cnf(c_0_1447,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    i_0_788 ).

cnf(c_0_1448,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    i_0_142 ).

cnf(c_0_1449,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2))) = c_Complex_ORe(c_Complex_Orcis(X1,X2)),
    i_0_1374 ).

cnf(c_0_1450,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
    | ~ class_Rings_Oring(X1) ),
    i_0_792 ).

cnf(c_0_1451,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2)))) = c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1444,c_0_1445]),c_0_1446])]) ).

cnf(c_0_1452,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
    inference(spm,[status(thm)],[c_0_1447,c_0_1448]) ).

cnf(c_0_1453,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2)))) = c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1444,c_0_1449]),c_0_1446])]) ).

cnf(c_0_1454,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2))) = c_Complex_OIm(c_Complex_Orcis(X1,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1450,c_0_1451]),c_0_1452]),c_0_1445]),c_0_1446])]) ).

cnf(c_0_1455,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    i_0_8 ).

cnf(c_0_1456,plain,
    c_Complex_Ocomplex_OComplex(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X1)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X1))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
    i_0_422 ).

cnf(c_0_1457,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2))) = c_Complex_ORe(c_Complex_Orcis(X1,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1450,c_0_1453]),c_0_1452]),c_0_1449]),c_0_1446])]) ).

cnf(c_0_1458,plain,
    c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(X1,X2))),
    inference(spm,[status(thm)],[c_0_1452,c_0_1454]) ).

cnf(c_0_1459,plain,
    c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1),c_Complex_OIm(X1)) = X1,
    i_0_445 ).

cnf(c_0_1460,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = X1,
    inference(spm,[status(thm)],[c_0_1447,c_0_1455]) ).

cnf(c_0_1461,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)) = c_Complex_Orcis(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1456,c_0_1457]),c_0_1458]),c_0_1452]),c_0_1459]) ).

cnf(c_0_1462,negated_conjecture,
    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),
    i_0_193 ).

cnf(c_0_1463,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_NthRoot_Osqrt(X2)) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),
    i_0_1351 ).

cnf(c_0_1464,plain,
    c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    i_0_1317 ).

cnf(c_0_1465,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    i_0_216 ).

cnf(c_0_1466,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    i_0_148 ).

cnf(c_0_1467,plain,
    c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),
    i_0_465 ).

cnf(c_0_1468,plain,
    c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),
    i_0_1420 ).

cnf(c_0_1469,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    i_0_378 ).

cnf(c_0_1470,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    i_0_169 ).

cnf(c_0_1471,plain,
    c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)),
    inference(spm,[status(thm)],[c_0_1460,c_0_1461]) ).

cnf(c_0_1472,negated_conjecture,
    c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1462,c_0_1463]),c_0_1464]) ).

cnf(c_0_1473,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(spm,[status(thm)],[c_0_1465,c_0_1466]) ).

cnf(c_0_1474,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    i_0_251 ).

cnf(c_0_1475,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    i_0_250 ).

cnf(c_0_1476,plain,
    c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1459,c_0_1467]),c_0_1468]),c_0_1456]) ).

cnf(c_0_1477,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
    inference(spm,[status(thm)],[c_0_1469,c_0_1470]) ).

cnf(c_0_1478,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    i_0_391 ).

cnf(c_0_1479,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)))) = c_Complex_ORe(c_Complex_Orcis(X1,X2)),
    inference(rw,[status(thm)],[c_0_1457,c_0_1471]) ).

cnf(c_0_1480,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
    | ~ class_Rings_Oring(X1) ),
    i_0_791 ).

cnf(c_0_1481,negated_conjecture,
    c_Complex_Orcis(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(rw,[status(thm)],[c_0_1472,c_0_1473]) ).

cnf(c_0_1482,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
    | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
    inference(spm,[status(thm)],[c_0_1474,c_0_1475]) ).

cnf(c_0_1483,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2)))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(X1,X2))),
    inference(rw,[status(thm)],[c_0_1451,c_0_1458]) ).

cnf(c_0_1484,plain,
    c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),
    inference(spm,[status(thm)],[c_0_1476,c_0_1477]) ).

cnf(c_0_1485,plain,
    c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),
    inference(rw,[status(thm)],[c_0_1468,c_0_1476]) ).

cnf(c_0_1486,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))),X2) = c_Complex_ORe(c_Complex_Orcis(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1478,c_0_1449]),c_0_1470])]) ).

cnf(c_0_1487,plain,
    c_Complex_ORe(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Orcis(X1,X2))),
    inference(spm,[status(thm)],[c_0_1452,c_0_1479]) ).

cnf(c_0_1488,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1480,c_0_1452]),c_0_1446])]) ).

cnf(c_0_1489,negated_conjecture,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = v_r
    | c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(v_r,v_a) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1481,c_0_1482]),c_0_1452]) ).

cnf(c_0_1490,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(c_Complex_Orcis(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X2)))) = c_Complex_OIm(c_Complex_Orcis(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1483,c_0_1484]),c_0_1485]),c_0_1452]),c_0_1445]) ).

cnf(c_0_1491,plain,
    c_Complex_ORe(c_Complex_Orcis(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X2))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(c_Complex_Orcis(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1486,c_0_1484]),c_0_1487]),c_0_1488]),c_0_1486]),c_0_1471]),c_0_1487]) ).

cnf(c_0_1492,negated_conjecture,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = v_r
    | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(v_r,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) != c_Complex_Orcis(v_r,v_a) ),
    inference(rw,[status(thm)],[c_0_1489,c_0_1471]) ).

cnf(c_0_1493,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X2))) = c_Complex_Orcis(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1456,c_0_1490]),c_0_1491]),c_0_1452]),c_0_1459]) ).

cnf(c_0_1494,negated_conjecture,
    c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),v_a)),
    inference(rw,[status(thm)],[c_0_1481,c_0_1471]) ).

cnf(c_0_1495,negated_conjecture,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = v_r,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1492,c_0_1493])]) ).

cnf(c_0_1496,negated_conjecture,
    c_Complex_Orcis(v_r,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(v_r,v_a)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1494,c_0_1495]),c_0_1495]) ).

cnf(c_0_1497,plain,
    c_Complex_Orcis(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X2)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)),
    inference(spm,[status(thm)],[c_0_1460,c_0_1493]) ).

cnf(c_0_1498,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1496,c_0_1497])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun  4 12:01:57 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.46  # ENIGMATIC: Selected SinE mode:
% 0.20/0.52  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.20/0.52  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.20/0.52  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 10.07/3.04  # ENIGMATIC: Solved by autoschedule-lgb:
% 10.07/3.04  # No SInE strategy applied
% 10.07/3.04  # Trying AutoSched0 for 150 seconds
% 10.07/3.04  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 10.07/3.04  # and selection function SelectComplexExceptUniqMaxHorn.
% 10.07/3.04  #
% 10.07/3.04  # Preprocessing time       : 0.026 s
% 10.07/3.04  # Presaturation interreduction done
% 10.07/3.04  
% 10.07/3.04  # Proof found!
% 10.07/3.04  # SZS status Theorem
% 10.07/3.04  # SZS output start CNFRefutation
% See solution above
% 10.07/3.04  # Training examples: 0 positive, 0 negative
% 10.07/3.04  
% 10.07/3.04  # -------------------------------------------------
% 10.07/3.04  # User time                : 0.174 s
% 10.07/3.04  # System time              : 0.009 s
% 10.07/3.04  # Total time               : 0.184 s
% 10.07/3.04  # Maximum resident set size: 7368 pages
% 10.07/3.04  
%------------------------------------------------------------------------------