TSTP Solution File: SWW245+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SWW245+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n019.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 00:01:49 EDT 2022

% Result   : Theorem 5.08s 2.74s
% Output   : CNFRefutation 5.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   58 (  25 unt;  16 nHn;  40 RR)
%            Number of literals    :  127 ( 108 equ;  62 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  10 con; 0-4 aty)
%            Number of variables   :   54 (   9 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_1537,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_1537) ).

cnf(i_0_970,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_970) ).

cnf(i_0_167,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk4_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk2_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_167) ).

cnf(i_0_971,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_971) ).

cnf(i_0_1585,hypothesis,
    class_Rings_Oidom(t_a),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_1585) ).

cnf(i_0_171,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk5_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_171) ).

cnf(i_0_390,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_390) ).

cnf(i_0_385,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_385) ).

cnf(i_0_163,negated_conjecture,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X3)),esk1_3(X2,X1,X3))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X2,X1,X3))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_163) ).

cnf(i_0_166,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk4_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk2_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_166) ).

cnf(i_0_165,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk2_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk3_0,esk4_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_165) ).

cnf(i_0_168,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != esk3_0
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_168) ).

cnf(i_0_169,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk5_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk6_0,esk7_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_169) ).

cnf(i_0_976,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_976) ).

cnf(i_0_170,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk5_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_170) ).

cnf(i_0_172,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != esk6_0
    | ~ class_Rings_Oidom(t_a) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ye3n09d6/lgb.p',i_0_172) ).

cnf(c_0_1602,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    i_0_1537 ).

cnf(c_0_1603,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    i_0_970 ).

cnf(c_0_1604,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk4_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk2_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    i_0_167 ).

cnf(c_0_1605,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    i_0_971 ).

cnf(c_0_1606,hypothesis,
    class_Rings_Oidom(t_a),
    i_0_1585 ).

cnf(c_0_1607,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk5_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    i_0_171 ).

cnf(c_0_1608,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(spm,[status(thm)],[c_0_1602,c_0_1603]) ).

cnf(c_0_1609,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
    i_0_390 ).

cnf(c_0_1610,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk2_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk4_0))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_c____,v_cs____)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1604,c_0_1605]),c_0_1605]),c_0_1603]),c_0_1605]),c_0_1606])]) ).

cnf(c_0_1611,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    i_0_385 ).

cnf(c_0_1612,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(spm,[status(thm)],[c_0_1602,c_0_1605]) ).

cnf(c_0_1613,negated_conjecture,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X3)),esk1_3(X2,X1,X3))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X2,X1,X3))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    i_0_163 ).

cnf(c_0_1614,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk7_0))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_c____,v_cs____) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1607,c_0_1605]),c_0_1605]),c_0_1603]),c_0_1605]),c_0_1606])]) ).

cnf(c_0_1615,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(spm,[status(thm)],[c_0_1608,c_0_1605]) ).

cnf(c_0_1616,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_c____,v_cs____)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1609,c_0_1610]),c_0_1611]),c_0_1612]) ).

cnf(c_0_1617,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_c____,v_cs____)
    | X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk1_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X3,X1,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1613,c_0_1605]),c_0_1603]),c_0_1605]) ).

cnf(c_0_1618,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_c____,v_cs____),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_1614,c_0_1615]),c_0_1616]) ).

cnf(c_0_1619,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk4_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk2_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    i_0_166 ).

cnf(c_0_1620,negated_conjecture,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk1_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X3,X1,X2)) ),
    inference(sr,[status(thm)],[c_0_1617,c_0_1618]) ).

cnf(c_0_1621,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(spm,[status(thm)],[c_0_1605,c_0_1603]) ).

cnf(c_0_1622,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk2_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk3_0,esk4_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    i_0_165 ).

cnf(c_0_1623,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk2_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk4_0))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_c____,v_cs____)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1619,c_0_1605]),c_0_1605]),c_0_1603]),c_0_1605]),c_0_1605]),c_0_1606])]) ).

cnf(c_0_1624,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != esk3_0
    | ~ class_Rings_Oidom(t_a) ),
    i_0_168 ).

cnf(c_0_1625,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk5_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk6_0,esk7_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | ~ class_Rings_Oidom(t_a) ),
    i_0_169 ).

cnf(c_0_1626,negated_conjecture,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X3)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk1_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X3,X1,X2)) ),
    inference(rw,[status(thm)],[c_0_1620,c_0_1621]) ).

cnf(c_0_1627,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk2_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk3_0,esk4_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1622,c_0_1606])]) ).

cnf(c_0_1628,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    i_0_976 ).

cnf(c_0_1629,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk2_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk4_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk4_0))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
    inference(sr,[status(thm)],[c_0_1623,c_0_1618]) ).

cnf(c_0_1630,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != esk3_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1624,c_0_1606])]) ).

cnf(c_0_1631,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk5_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ class_Rings_Oidom(t_a) ),
    i_0_170 ).

cnf(c_0_1632,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk5_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk6_0,esk7_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1625,c_0_1606])]) ).

cnf(c_0_1633,plain,
    c_Groups_Ozero__class_Ozero(t_a) != v_c____,
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1626,c_0_1627]),c_0_1605]),c_0_1628]),c_0_1629]),c_0_1630]) ).

cnf(c_0_1634,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk7_0))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_c____,v_cs____)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1631,c_0_1605]),c_0_1605]),c_0_1603]),c_0_1605]),c_0_1605]),c_0_1606])]) ).

cnf(c_0_1635,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk5_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk6_0,esk7_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1),
    inference(sr,[status(thm)],[c_0_1632,c_0_1633]) ).

cnf(c_0_1636,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk7_0))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(sr,[status(thm)],[c_0_1634,c_0_1618]) ).

cnf(c_0_1637,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(t_a) = esk6_0
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk7_0))))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1626,c_0_1635]),c_0_1605]),c_0_1628]) ).

cnf(c_0_1638,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk5_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk7_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk7_0))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),
    inference(sr,[status(thm)],[c_0_1636,c_0_1633]) ).

cnf(c_0_1639,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != esk6_0
    | ~ class_Rings_Oidom(t_a) ),
    i_0_172 ).

cnf(c_0_1640,negated_conjecture,
    c_Groups_Ozero__class_Ozero(t_a) = esk6_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1637,c_0_1638])]) ).

cnf(c_0_1641,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != esk6_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1639,c_0_1606])]) ).

cnf(c_0_1642,plain,
    esk6_0 != v_c____,
    inference(rw,[status(thm)],[c_0_1633,c_0_1640]) ).

cnf(c_0_1643,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1641,c_0_1640]),c_0_1640])]),c_0_1642]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW245+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun  6 06:20:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  # ENIGMATIC: Selected SinE mode:
% 0.19/0.52  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.19/0.52  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.19/0.52  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 5.08/2.74  # ENIGMATIC: Solved by autoschedule-lgb:
% 5.08/2.74  # No SInE strategy applied
% 5.08/2.74  # Trying AutoSched0 for 150 seconds
% 5.08/2.74  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 5.08/2.74  # and selection function SelectComplexExceptUniqMaxHorn.
% 5.08/2.74  #
% 5.08/2.74  # Preprocessing time       : 0.022 s
% 5.08/2.74  # Presaturation interreduction done
% 5.08/2.74  
% 5.08/2.74  # Proof found!
% 5.08/2.74  # SZS status Theorem
% 5.08/2.74  # SZS output start CNFRefutation
% See solution above
% 5.08/2.74  # Training examples: 0 positive, 0 negative
% 5.08/2.74  
% 5.08/2.74  # -------------------------------------------------
% 5.08/2.74  # User time                : 0.035 s
% 5.08/2.74  # System time              : 0.004 s
% 5.08/2.74  # Total time               : 0.038 s
% 5.08/2.74  # Maximum resident set size: 7380 pages
% 5.08/2.74  
%------------------------------------------------------------------------------