TSTP Solution File: GRP778+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : GRP778+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n021.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 : Sat Jul 16 08:40:37 EDT 2022
% Result : Theorem 17.10s 5.22s
% Output : CNFRefutation 17.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 16
% Syntax : Number of clauses : 196 ( 192 unt; 0 nHn; 122 RR)
% Number of literals : 200 ( 181 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_5,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_5) ).
cnf(i_0_6,plain,
product(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_6) ).
cnf(i_0_7,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_7) ).
cnf(i_0_4,plain,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_4) ).
cnf(i_0_9,plain,
( product(X1,X2) = product(X2,X3)
| ~ d(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_9) ).
cnf(i_0_14,plain,
d(a,b,c1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_14) ).
cnf(i_0_2,plain,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_2) ).
cnf(i_0_13,plain,
d(a,b1,c),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_13) ).
cnf(i_0_1,plain,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_1) ).
cnf(i_0_12,plain,
d(a1,b,c),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_12) ).
cnf(i_0_3,plain,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_3) ).
cnf(i_0_16,plain,
d(a1,b2,c1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_16) ).
cnf(i_0_15,plain,
d(a2,b1,c1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_15) ).
cnf(i_0_17,plain,
d(a1,b1,c2),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_17) ).
cnf(i_0_18,negated_conjecture,
~ m(b1,b,b2),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_18) ).
cnf(i_0_10,plain,
( m(X1,X2,X3)
| product(product(X1,X2),product(X2,X3)) != product(X1,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-db2c0mhv/lgb.p',i_0_10) ).
cnf(c_0_35,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
i_0_5 ).
cnf(c_0_36,plain,
product(X1,X1) = X1,
i_0_6 ).
cnf(c_0_37,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
i_0_7 ).
cnf(c_0_39,plain,
product(quotient(X1,X2),X2) = X1,
i_0_4 ).
cnf(c_0_40,plain,
( product(X1,X2) = product(X2,X3)
| ~ d(X1,X2,X3) ),
i_0_9 ).
cnf(c_0_41,plain,
d(a,b,c1),
i_0_14 ).
cnf(c_0_42,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_43,plain,
product(X1,difference(X1,X2)) = X2,
i_0_2 ).
cnf(c_0_44,plain,
product(product(X1,X2),product(X2,product(X2,quotient(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
d(a,b1,c),
i_0_13 ).
cnf(c_0_46,plain,
product(a,b) = product(b,c1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
difference(X1,product(X1,X2)) = X2,
i_0_1 ).
cnf(c_0_48,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
product(product(X1,X2),product(X2,X1)) = product(X2,product(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_42,c_0_44]),c_0_35]),c_0_42]),c_0_39]),c_0_37]),c_0_36]) ).
cnf(c_0_50,plain,
product(a,b1) = product(b1,c),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_51,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_52,plain,
product(product(a,X1),product(b,X2)) = product(product(b,c1),product(X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_53,plain,
product(product(X1,X2),product(b,c1)) = product(product(X1,a),product(X2,b)),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_54,plain,
d(a1,b,c),
i_0_12 ).
cnf(c_0_55,plain,
product(product(product(difference(X1,X2),X1),X1),product(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_43]) ).
cnf(c_0_56,plain,
product(difference(X1,X2),X1) = difference(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,plain,
product(b1,product(c,a)) = product(b1,product(b1,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_58,plain,
product(product(b,X1),c1) = product(a,product(X1,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_36]),c_0_37]) ).
cnf(c_0_59,plain,
product(b,c) = product(a1,b),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
cnf(c_0_60,plain,
product(b,product(c1,a)) = product(b,product(b,c1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_46]),c_0_51]) ).
cnf(c_0_61,plain,
product(difference(X1,product(product(X2,X1),X1)),product(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).
cnf(c_0_62,plain,
product(c,a) = product(b1,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_57]),c_0_47]) ).
cnf(c_0_63,plain,
product(product(b1,c),a) = product(a,product(b1,a)),
inference(spm,[status(thm)],[c_0_42,c_0_50]) ).
cnf(c_0_64,plain,
product(a,difference(b,product(X1,b))) = product(X1,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_43]),c_0_56]) ).
cnf(c_0_65,plain,
difference(b,product(a1,b)) = c,
inference(spm,[status(thm)],[c_0_47,c_0_59]) ).
cnf(c_0_66,plain,
product(c1,a) = product(b,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_60]),c_0_47]) ).
cnf(c_0_67,plain,
product(product(b,c1),a) = product(a,product(b,a)),
inference(spm,[status(thm)],[c_0_42,c_0_46]) ).
cnf(c_0_68,plain,
product(product(b1,a),product(a,c)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_47]) ).
cnf(c_0_69,plain,
product(a,c) = product(a1,c1),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,plain,
quotient(product(X1,X2),X2) = X1,
i_0_3 ).
cnf(c_0_71,plain,
product(product(b,a),product(a,c1)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_66]),c_0_67]),c_0_47]) ).
cnf(c_0_72,plain,
product(difference(X1,product(X2,X1)),X2) = product(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_43]),c_0_56]),c_0_56]),c_0_43]) ).
cnf(c_0_73,plain,
product(product(b1,a1),product(a,c1)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_35]) ).
cnf(c_0_74,plain,
quotient(a,product(a,c1)) = product(b,a),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_70,c_0_42]) ).
cnf(c_0_76,plain,
product(difference(X1,X2),quotient(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_72,c_0_39]) ).
cnf(c_0_77,plain,
product(b,a) = product(b1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_73]),c_0_74]) ).
cnf(c_0_78,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_75,c_0_39]) ).
cnf(c_0_79,plain,
product(product(c,a1),b) = product(b,product(c,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_59]),c_0_37]) ).
cnf(c_0_80,plain,
difference(difference(X1,X2),X2) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_76]) ).
cnf(c_0_81,plain,
difference(b,product(b1,a1)) = a,
inference(spm,[status(thm)],[c_0_47,c_0_77]) ).
cnf(c_0_82,plain,
quotient(product(b1,a1),b) = product(b,quotient(a,b)),
inference(spm,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_83,plain,
product(c,a1) = product(a1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_79]),c_0_78]),c_0_70]),c_0_59]) ).
cnf(c_0_84,plain,
quotient(product(a1,b),c) = b,
inference(spm,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_85,plain,
product(b,quotient(a,b)) = difference(a,product(b1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_86,plain,
product(c,quotient(a,c)) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_62]),c_0_70]) ).
cnf(c_0_87,plain,
product(c,quotient(a1,c)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_84]) ).
cnf(c_0_88,plain,
product(c1,difference(a,product(b1,a1))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_85]),c_0_39]),c_0_46]),c_0_47]) ).
cnf(c_0_89,plain,
quotient(a,c) = difference(c,b1),
inference(spm,[status(thm)],[c_0_47,c_0_86]) ).
cnf(c_0_90,plain,
quotient(a1,c) = difference(c,b),
inference(spm,[status(thm)],[c_0_47,c_0_87]) ).
cnf(c_0_91,plain,
difference(a,product(b1,a1)) = difference(c1,b),
inference(spm,[status(thm)],[c_0_47,c_0_88]) ).
cnf(c_0_92,plain,
quotient(product(b1,a1),a) = b,
inference(spm,[status(thm)],[c_0_70,c_0_77]) ).
cnf(c_0_93,plain,
product(product(a,c),product(c,b1)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_89]),c_0_43]) ).
cnf(c_0_94,plain,
product(product(a1,c),product(c,b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_90]),c_0_43]) ).
cnf(c_0_95,plain,
d(a1,b2,c1),
i_0_16 ).
cnf(c_0_96,plain,
d(a2,b1,c1),
i_0_15 ).
cnf(c_0_97,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_98,plain,
product(difference(c1,b),b) = product(b1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_91]),c_0_92]) ).
cnf(c_0_99,plain,
product(product(a1,c),product(c1,b1)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_69]),c_0_35]) ).
cnf(c_0_100,plain,
difference(product(a1,c),c) = product(c,b),
inference(spm,[status(thm)],[c_0_47,c_0_94]) ).
cnf(c_0_101,plain,
product(b2,c1) = product(a1,b2),
inference(spm,[status(thm)],[c_0_40,c_0_95]) ).
cnf(c_0_102,plain,
d(a1,b1,c2),
i_0_17 ).
cnf(c_0_103,plain,
product(a2,b1) = product(b1,c1),
inference(spm,[status(thm)],[c_0_40,c_0_96]) ).
cnf(c_0_104,plain,
product(product(c1,X1),product(b1,a1)) = product(b,product(X1,b)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
product(c1,b1) = product(c,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_99]),c_0_100]) ).
cnf(c_0_106,plain,
product(product(c1,a1),b2) = product(b2,product(c1,b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_101]),c_0_37]) ).
cnf(c_0_107,plain,
product(b1,c2) = product(a1,b1),
inference(spm,[status(thm)],[c_0_40,c_0_102]) ).
cnf(c_0_108,plain,
quotient(product(b1,c1),b1) = a2,
inference(spm,[status(thm)],[c_0_70,c_0_103]) ).
cnf(c_0_109,plain,
product(product(c,b),product(X1,a1)) = product(b,product(X1,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_104]),c_0_105]) ).
cnf(c_0_110,plain,
product(c1,a1) = product(a1,b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_106]),c_0_78]),c_0_70]),c_0_101]) ).
cnf(c_0_111,plain,
product(product(a1,b),product(b,X1)) = product(b,product(c,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_59]) ).
cnf(c_0_112,plain,
product(product(c2,a1),b1) = product(b1,product(c2,b1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_107]),c_0_37]) ).
cnf(c_0_113,plain,
product(b1,quotient(c1,b1)) = a2,
inference(rw,[status(thm)],[c_0_108,c_0_78]) ).
cnf(c_0_114,plain,
product(b,product(c1,b)) = product(b,product(c,b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_35]),c_0_83]),c_0_111]) ).
cnf(c_0_115,plain,
product(c2,a1) = product(a1,b1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_112]),c_0_78]),c_0_70]),c_0_107]) ).
cnf(c_0_116,plain,
product(b,quotient(c,b)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_59]),c_0_70]) ).
cnf(c_0_117,plain,
quotient(product(b1,c),b1) = a,
inference(spm,[status(thm)],[c_0_70,c_0_50]) ).
cnf(c_0_118,plain,
quotient(c1,b1) = difference(b1,a2),
inference(spm,[status(thm)],[c_0_47,c_0_113]) ).
cnf(c_0_119,plain,
product(c1,b) = product(c,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_114]),c_0_47]) ).
cnf(c_0_120,plain,
product(b,product(c,b1)) = product(b,product(c2,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_115]),c_0_35]),c_0_83]),c_0_111]) ).
cnf(c_0_121,plain,
quotient(c,b) = difference(b,a1),
inference(spm,[status(thm)],[c_0_47,c_0_116]) ).
cnf(c_0_122,plain,
product(b1,quotient(c,b1)) = a,
inference(rw,[status(thm)],[c_0_117,c_0_78]) ).
cnf(c_0_123,plain,
product(product(c1,b1),product(b1,a2)) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_118]),c_0_43]) ).
cnf(c_0_124,plain,
product(product(c,b1),product(b2,a1)) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_119]),c_0_35]),c_0_36]),c_0_36]) ).
cnf(c_0_125,plain,
product(c,b1) = product(c2,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_120]),c_0_47]) ).
cnf(c_0_126,plain,
product(product(c,b),product(b,a1)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_121]),c_0_43]) ).
cnf(c_0_127,plain,
quotient(c,b1) = difference(b1,a),
inference(spm,[status(thm)],[c_0_47,c_0_122]) ).
cnf(c_0_128,plain,
product(product(a2,X1),product(b1,X2)) = product(product(b1,c1),product(X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_103]) ).
cnf(c_0_129,plain,
product(product(X1,X2),product(b1,c1)) = product(product(X1,a2),product(X2,b1)),
inference(spm,[status(thm)],[c_0_35,c_0_103]) ).
cnf(c_0_130,plain,
quotient(b1,product(b1,a2)) = product(c1,b1),
inference(spm,[status(thm)],[c_0_70,c_0_123]) ).
cnf(c_0_131,plain,
quotient(product(product(X1,X2),product(X3,X4)),product(X2,X4)) = product(X1,X3),
inference(spm,[status(thm)],[c_0_70,c_0_35]) ).
cnf(c_0_132,plain,
product(product(c2,b),product(b2,a1)) = b,
inference(rw,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_133,plain,
quotient(b,product(b,a1)) = product(c,b),
inference(spm,[status(thm)],[c_0_70,c_0_126]) ).
cnf(c_0_134,plain,
product(b1,quotient(c2,b1)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_107]),c_0_70]) ).
cnf(c_0_135,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_136,plain,
product(difference(b1,a),b1) = c,
inference(spm,[status(thm)],[c_0_39,c_0_127]) ).
cnf(c_0_137,plain,
product(product(b1,X1),c1) = product(a2,product(X1,b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_36]),c_0_37]) ).
cnf(c_0_138,plain,
quotient(b1,product(b1,a2)) = product(c,b),
inference(rw,[status(thm)],[c_0_130,c_0_105]) ).
cnf(c_0_139,plain,
product(c,b) = product(c2,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]) ).
cnf(c_0_140,plain,
quotient(c2,b1) = difference(b1,a1),
inference(spm,[status(thm)],[c_0_47,c_0_134]) ).
cnf(c_0_141,plain,
product(product(c,b1),product(b,a2)) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_105]),c_0_35]) ).
cnf(c_0_142,plain,
difference(product(c,b1),b1) = product(b1,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_43]) ).
cnf(c_0_143,plain,
product(product(a,X1),product(b1,X2)) = product(product(b1,c),product(X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_144,plain,
product(product(X1,X2),product(b1,c)) = product(product(X1,a),product(X2,b1)),
inference(spm,[status(thm)],[c_0_35,c_0_50]) ).
cnf(c_0_145,plain,
product(b1,product(c1,a2)) = product(b1,product(b1,c1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_103]),c_0_51]) ).
cnf(c_0_146,plain,
product(product(b1,c1),product(X1,b1)) = product(product(a2,X1),b1),
inference(spm,[status(thm)],[c_0_37,c_0_103]) ).
cnf(c_0_147,plain,
product(product(b1,X1),product(a1,b1)) = product(b1,product(X1,c2)),
inference(spm,[status(thm)],[c_0_51,c_0_107]) ).
cnf(c_0_148,plain,
product(a2,difference(b1,product(X1,b1))) = product(X1,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_43]),c_0_56]) ).
cnf(c_0_149,plain,
difference(b1,product(a1,b1)) = c2,
inference(spm,[status(thm)],[c_0_47,c_0_107]) ).
cnf(c_0_150,plain,
quotient(b1,product(b1,a2)) = product(c2,b2),
inference(rw,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_151,plain,
product(difference(b1,a1),b1) = c2,
inference(spm,[status(thm)],[c_0_39,c_0_140]) ).
cnf(c_0_152,plain,
product(b,a2) = product(b1,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_141]),c_0_142]) ).
cnf(c_0_153,plain,
product(product(b1,X1),c) = product(a,product(X1,b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_36]),c_0_37]) ).
cnf(c_0_154,plain,
product(product(X1,X2),product(X3,difference(X2,X4))) = product(product(X1,X3),X4),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_155,plain,
product(a,difference(c1,b)) = product(b1,a1),
inference(spm,[status(thm)],[c_0_43,c_0_91]) ).
cnf(c_0_156,plain,
product(product(X1,b),product(b,c1)) = product(product(X1,a),b),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_157,plain,
product(product(X1,X2),product(a1,b1)) = product(product(X1,b1),product(X2,c2)),
inference(spm,[status(thm)],[c_0_35,c_0_107]) ).
cnf(c_0_158,plain,
product(c1,a2) = product(b1,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_145]),c_0_47]) ).
cnf(c_0_159,plain,
product(product(a2,a1),b1) = product(b1,product(c1,c2)),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_160,plain,
product(a2,c2) = product(a1,c1),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_161,plain,
product(product(c2,b1),product(b2,a2)) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_150]),c_0_35]) ).
cnf(c_0_162,plain,
difference(product(c2,b1),b1) = product(b1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_151]),c_0_43]) ).
cnf(c_0_163,plain,
product(product(b1,b),product(a,X1)) = product(b,product(a2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_152]),c_0_35]) ).
cnf(c_0_164,plain,
product(a,difference(b1,product(X1,b1))) = product(X1,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_43]),c_0_56]) ).
cnf(c_0_165,plain,
product(product(X1,a1),product(b1,b2)) = product(product(X1,a),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_35]),c_0_110]),c_0_35]) ).
cnf(c_0_166,plain,
product(product(a1,a),b) = product(b,product(c,c1)),
inference(spm,[status(thm)],[c_0_156,c_0_111]) ).
cnf(c_0_167,plain,
product(b,product(c,c1)) = product(b1,product(c1,c2)),
inference(rw,[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)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_146]),c_0_159]),c_0_105]),c_0_160]),c_0_35]),c_0_83]),c_0_111]) ).
cnf(c_0_168,plain,
product(b2,a2) = product(b1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_161]),c_0_162]) ).
cnf(c_0_169,plain,
product(product(b1,a1),product(X1,b1)) = product(b1,product(X1,c2)),
inference(spm,[status(thm)],[c_0_35,c_0_147]) ).
cnf(c_0_170,plain,
product(product(b1,b),product(X1,c)) = product(b,product(X1,c1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_148]) ).
cnf(c_0_171,plain,
product(b1,product(c1,c2)) = product(a1,product(b1,b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_36]),c_0_166]),c_0_167]) ).
cnf(c_0_172,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_173,plain,
product(product(b2,X1),product(b1,c1)) = product(b1,product(X1,c2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_168]),c_0_169]) ).
cnf(c_0_174,plain,
product(a,product(b,b1)) = product(a1,product(b1,b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_36]),c_0_153]),c_0_167]),c_0_171]) ).
cnf(c_0_175,plain,
product(difference(X1,product(b1,X1)),c) = product(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_72]),c_0_47]) ).
cnf(c_0_176,plain,
product(X1,product(X2,quotient(X1,X2))) = product(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_39]) ).
cnf(c_0_177,plain,
difference(product(X1,quotient(X2,X1)),product(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_172,c_0_78]) ).
cnf(c_0_178,plain,
difference(a,product(X1,c1)) = difference(b,product(X1,b)),
inference(spm,[status(thm)],[c_0_47,c_0_64]) ).
cnf(c_0_179,plain,
product(product(b2,b1),c1) = product(a1,product(b1,b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_173]),c_0_171]) ).
cnf(c_0_180,plain,
difference(a,product(a1,product(b1,b2))) = product(b,b1),
inference(spm,[status(thm)],[c_0_47,c_0_174]) ).
cnf(c_0_181,plain,
product(a,product(X1,quotient(b1,X1))) = product(X1,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_177]) ).
cnf(c_0_182,plain,
difference(b,product(product(b2,b1),b)) = product(b,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_180]) ).
cnf(c_0_183,plain,
product(X1,quotient(b1,X1)) = difference(a,product(X1,c)),
inference(spm,[status(thm)],[c_0_47,c_0_181]) ).
cnf(c_0_184,plain,
difference(a,product(X1,c)) = difference(b1,product(X1,b1)),
inference(spm,[status(thm)],[c_0_47,c_0_164]) ).
cnf(c_0_185,plain,
product(product(b2,b1),b) = product(b,product(b,b1)),
inference(spm,[status(thm)],[c_0_43,c_0_182]) ).
cnf(c_0_186,plain,
product(X1,quotient(b1,X1)) = difference(b1,product(X1,b1)),
inference(rw,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_187,plain,
product(b,difference(b1,product(b,b1))) = product(b2,b1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_185]),c_0_78]),c_0_78]),c_0_186]) ).
cnf(c_0_188,plain,
product(difference(X1,product(b,X1)),c1) = product(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_72]),c_0_47]) ).
cnf(c_0_189,plain,
product(b,product(product(b1,b),product(b2,b1))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_187]),c_0_72]),c_0_42]),c_0_51]) ).
cnf(c_0_190,plain,
difference(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_36]) ).
cnf(c_0_191,plain,
product(a,product(X1,quotient(b,X1))) = product(X1,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_176]),c_0_177]) ).
cnf(c_0_192,plain,
product(product(b1,b),product(b2,b1)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_189]),c_0_190]) ).
cnf(c_0_193,plain,
product(X1,quotient(b,X1)) = difference(b,product(X1,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_191]),c_0_178]) ).
cnf(c_0_194,plain,
quotient(b,product(b,b1)) = product(b1,b2),
inference(spm,[status(thm)],[c_0_131,c_0_192]) ).
cnf(c_0_195,plain,
product(product(X1,b),product(b,b1)) = product(product(X1,b2),b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_187]),c_0_37]) ).
cnf(c_0_196,plain,
product(product(b,b1),product(b1,b2)) = product(b1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_42]),c_0_47]) ).
cnf(c_0_197,plain,
product(b,product(b1,b)) = product(b1,product(b2,b1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_195]),c_0_42]) ).
cnf(c_0_198,plain,
product(product(b1,b),b) = product(b1,product(b2,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_196]),c_0_35]),c_0_192]),c_0_51]) ).
cnf(c_0_199,plain,
product(b1,product(b2,product(b1,b))) = product(b1,product(b,product(b2,b1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_197]),c_0_198]),c_0_51]),c_0_51]),c_0_51]) ).
cnf(c_0_200,plain,
product(b2,product(b1,b)) = product(b,product(b2,b1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_199]),c_0_47]) ).
cnf(c_0_201,plain,
product(product(X1,X2),product(product(X3,X4),product(X5,X6))) = product(product(X1,product(X3,X5)),product(X2,product(X4,X6))),
inference(spm,[status(thm)],[c_0_35,c_0_35]) ).
cnf(c_0_202,plain,
quotient(X1,product(X1,product(X1,X2))) = product(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_70,c_0_38]) ).
cnf(c_0_203,plain,
product(product(X1,b1),product(b2,b)) = product(product(X1,b),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_200]),c_0_201]),c_0_35]),c_0_192]),c_0_35]) ).
cnf(c_0_204,plain,
difference(X1,product(product(X2,X1),X1)) = quotient(X1,product(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_43]),c_0_56]),c_0_56]) ).
cnf(c_0_205,plain,
product(product(b2,b),b) = product(b,product(b2,b1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_203]),c_0_200]) ).
cnf(c_0_206,plain,
difference(product(b1,b),b) = product(b2,b1),
inference(spm,[status(thm)],[c_0_47,c_0_192]) ).
cnf(c_0_207,plain,
quotient(b,product(b,b2)) = product(b2,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_47]) ).
cnf(c_0_208,plain,
quotient(b,product(b1,b)) = difference(product(b2,b1),b),
inference(spm,[status(thm)],[c_0_80,c_0_206]) ).
cnf(c_0_209,plain,
difference(product(b2,b1),b) = product(b,b2),
inference(spm,[status(thm)],[c_0_172,c_0_207]) ).
cnf(c_0_210,negated_conjecture,
~ m(b1,b,b2),
i_0_18 ).
cnf(c_0_211,plain,
( m(X1,X2,X3)
| product(product(X1,X2),product(X2,X3)) != product(X1,X3) ),
i_0_10 ).
cnf(c_0_212,plain,
quotient(b,product(b1,b)) = product(b,b2),
inference(rw,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_213,negated_conjecture,
product(product(b1,b),product(b,b2)) != product(b1,b2),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_214,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_212]),c_0_204]),c_0_194]),c_0_213]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP778+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 04:07:44 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.20/0.46 # ENIGMATIC: Selected complete mode:
% 17.10/5.22 # ENIGMATIC: Solved by autoschedule-lgb:
% 17.10/5.22 # No SInE strategy applied
% 17.10/5.22 # Trying AutoSched0 for 150 seconds
% 17.10/5.22 # AutoSched0-Mode selected heuristic G_E___107_C00_02_nc_F1_PI_AE_Q4_CS_SP_PS_S070I
% 17.10/5.22 # and selection function SelectVGNonCR.
% 17.10/5.22 #
% 17.10/5.22 # Preprocessing time : 0.012 s
% 17.10/5.22 # Presaturation interreduction done
% 17.10/5.22
% 17.10/5.22 # Proof found!
% 17.10/5.22 # SZS status Theorem
% 17.10/5.22 # SZS output start CNFRefutation
% See solution above
% 17.10/5.22 # Training examples: 0 positive, 0 negative
% 17.10/5.22
% 17.10/5.22 # -------------------------------------------------
% 17.10/5.22 # User time : 1.206 s
% 17.10/5.22 # System time : 0.065 s
% 17.10/5.22 # Total time : 1.271 s
% 17.10/5.22 # Maximum resident set size: 7128 pages
% 17.10/5.22
%------------------------------------------------------------------------------