TSTP Solution File: GRP777-10 by MaedMax---1.4
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- Process Solution
%------------------------------------------------------------------------------
% File : MaedMax---1.4
% Problem : GRP777-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_maedmax %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 26 07:03:17 EDT 2022
% Result : Unsatisfiable 13.60s 13.87s
% Output : CNFRefutation 13.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of clauses : 122 ( 122 unt; 0 nHn; 53 RR)
% Number of literals : 122 ( 121 equ; 10 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 156 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eq_0,axiom,
A = difference(B,product(B,A)),
file('/tmp/MaedMax_20763') ).
cnf(eq_1,axiom,
A = product(B,difference(B,A)),
file('/tmp/MaedMax_20763') ).
cnf(eq_2,axiom,
A = quotient(product(A,B),B),
file('/tmp/MaedMax_20763') ).
cnf(eq_3,axiom,
A = product(quotient(A,B),B),
file('/tmp/MaedMax_20763') ).
cnf(eq_4,axiom,
product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)),
file('/tmp/MaedMax_20763') ).
cnf(eq_5,axiom,
A = product(A,A),
file('/tmp/MaedMax_20763') ).
cnf(eq_6,axiom,
A = product(product(product(B,A),A),product(A,product(A,B))),
file('/tmp/MaedMax_20763') ).
cnf(eq_7,axiom,
product(product(A,B),product(C,A)) = bigC(A,B,C),
file('/tmp/MaedMax_20763') ).
cnf(eq_8,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/tmp/MaedMax_20763') ).
cnf(eq_9,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
file('/tmp/MaedMax_20763') ).
cnf(eq_10,plain,
product(product(D,B),product(C,D)) = bigC(D,C,B),
inference(cp,[status(thm)],[eq_4,eq_7]) ).
cnf(eq_11,plain,
product(A,product(x102,A)) = bigC(A,A,x102),
inference(cp,[status(thm)],[eq_5,eq_7]) ).
cnf(eq_12,plain,
product(product(A,x101),A) = bigC(A,x101,A),
inference(cp,[status(thm)],[eq_5,eq_7]) ).
cnf(eq_13,plain,
product(product(product(difference(B,A),B),B),product(B,A)) = B,
inference(cp,[status(thm)],[eq_1,eq_6]) ).
cnf(eq_14,plain,
difference(product(a,c),product(a,b)) = product(c,b),
inference(cp,[status(thm)],[eq_8,eq_0]) ).
cnf(eq_15,plain,
difference(product(product(B,A),A),A) = product(A,product(A,B)),
inference(cp,[status(thm)],[eq_6,eq_0]) ).
cnf(eq_16,plain,
difference(product(A,B),bigC(A,B,C)) = product(C,A),
inference(cp,[status(thm)],[eq_7,eq_0]) ).
cnf(eq_17,plain,
difference(quotient(A,B),A) = B,
inference(cp,[status(thm)],[eq_3,eq_0]) ).
cnf(eq_18,plain,
quotient(product(a,b),product(c,b)) = product(a,c),
inference(cp,[status(thm)],[eq_8,eq_2]) ).
cnf(eq_19,plain,
quotient(A,product(A,product(A,B))) = product(product(B,A),A),
inference(cp,[status(thm)],[eq_6,eq_2]) ).
cnf(eq_20,plain,
quotient(bigC(A,B,C),product(C,A)) = product(A,B),
inference(cp,[status(thm)],[eq_7,eq_2]) ).
cnf(eq_21,plain,
product(A,product(x102,x103)) = product(product(B,x102),product(difference(B,A),x103)),
inference(cp,[status(thm)],[eq_1,eq_4]) ).
cnf(eq_22,plain,
product(A,product(x102,x103)) = product(product(A,x102),product(A,x103)),
inference(cp,[status(thm)],[eq_5,eq_4]) ).
cnf(eq_23,plain,
product(product(x100,x101),A) = product(product(x100,A),product(x101,A)),
inference(cp,[status(thm)],[eq_5,eq_4]) ).
cnf(eq_24,plain,
product(A,product(B,A)) = bigC(A,A,B),
eq_11 ).
cnf(eq_25,plain,
bigC(A,B,C) = bigC(A,C,B),
inference(rw,[status(thm)],[eq_10,eq_7]) ).
cnf(eq_26,plain,
product(A,B) = difference(product(B,C),bigC(B,C,A)),
eq_16 ).
cnf(eq_27,plain,
A = difference(quotient(B,A),B),
eq_17 ).
cnf(eq_28,plain,
product(product(A,B),A) = bigC(A,B,A),
eq_12 ).
cnf(eq_29,plain,
product(product(A,B),B) = quotient(B,product(B,product(B,A))),
eq_19 ).
cnf(eq_30,plain,
product(A,product(B,C)) = product(product(A,B),product(A,C)),
eq_22 ).
cnf(eq_31,plain,
product(A,product(B,C)) = product(product(D,B),product(difference(D,A),C)),
eq_21 ).
cnf(eq_32,plain,
product(product(A,B),C) = product(product(A,C),product(B,C)),
eq_23 ).
cnf(eq_33,negated_conjecture,
bigC(c,x0,c) != bigC(a,b,x0),
inference(cp,[status(thm)],[eq_25,eq_9]) ).
cnf(eq_34,negated_conjecture,
bigC(a,b,x0) != bigC(c,x0,c),
eq_33 ).
cnf(eq_35,negated_conjecture,
bigC(a,x0,b) != bigC(c,x0,c),
inference(cp,[status(thm)],[eq_25,eq_34]) ).
cnf(eq_36,negated_conjecture,
product(product(c,x0),c) != bigC(a,x0,b),
inference(rw,[status(thm)],[eq_35,eq_28]) ).
cnf(eq_37,plain,
product(product(A,B),A) = bigC(A,A,B),
inference(cp,[status(thm)],[eq_28,eq_25]) ).
cnf(eq_38,plain,
product(A,product(B,A)) = product(product(A,B),A),
inference(rw,[status(thm)],[eq_37,eq_24]) ).
cnf(eq_39,plain,
product(A,B) = product(B,product(difference(B,A),B)),
inference(cp,[status(thm)],[eq_1,eq_38]) ).
cnf(eq_40,plain,
product(A,product(x102,B)) = product(product(quotient(A,B),x102),B),
inference(cp,[status(thm)],[eq_3,eq_32]) ).
cnf(eq_41,plain,
difference(product(A,C),product(product(A,B),C)) = product(B,C),
inference(cp,[status(thm)],[eq_32,eq_0]) ).
cnf(eq_42,plain,
difference(product(A,C),bigC(A,B,C)) = product(B,A),
inference(cp,[status(thm)],[eq_25,eq_26]) ).
cnf(eq_43,plain,
quotient(product(A,product(B,A)),A) = product(A,B),
inference(cp,[status(thm)],[eq_38,eq_2]) ).
cnf(eq_44,plain,
quotient(product(product(A,B),C),product(B,C)) = product(A,C),
inference(cp,[status(thm)],[eq_32,eq_2]) ).
cnf(eq_45,plain,
quotient(bigC(A,B,C),product(B,A)) = product(A,C),
inference(cp,[status(thm)],[eq_25,eq_20]) ).
cnf(eq_46,plain,
product(A,B) = quotient(product(product(A,C),B),product(C,B)),
eq_44 ).
cnf(eq_47,plain,
product(A,B) = quotient(bigC(A,C,B),product(C,A)),
eq_45 ).
cnf(eq_48,plain,
product(A,product(B,C)) = product(product(quotient(A,C),B),C),
eq_40 ).
cnf(eq_49,plain,
product(A,B) = difference(product(C,B),product(product(C,A),B)),
eq_41 ).
cnf(eq_50,plain,
product(A,B) = difference(product(B,C),bigC(B,A,C)),
eq_42 ).
cnf(eq_51,plain,
difference(B,product(A,B)) = product(difference(B,A),B),
inference(cp,[status(thm)],[eq_39,eq_0]) ).
cnf(eq_52,plain,
quotient(product(B,A),B) = product(B,quotient(A,B)),
inference(cp,[status(thm)],[eq_3,eq_43]) ).
cnf(eq_53,plain,
product(A,quotient(B,A)) = quotient(product(A,B),A),
eq_52 ).
cnf(eq_54,plain,
product(difference(A,B),A) = difference(A,product(B,A)),
eq_51 ).
cnf(eq_55,plain,
product(product(c,b),product(a,c)) = difference(product(a,c),product(product(a,b),product(a,c))),
inference(cp,[status(thm)],[eq_14,eq_54]) ).
cnf(eq_56,plain,
A = product(difference(A,product(product(B,A),A)),product(A,B)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_13,eq_54]),eq_54]) ).
cnf(eq_57,plain,
difference(product(A,product(C,C)),C) = product(C,product(C,quotient(A,C))),
inference(cp,[status(thm)],[eq_48,eq_15]) ).
cnf(eq_58,plain,
quotient(B,product(B,A)) = product(product(difference(B,A),B),B),
inference(cp,[status(thm)],[eq_1,eq_29]) ).
cnf(eq_59,plain,
quotient(product(A,x102),product(B,x102)) = product(quotient(A,B),x102),
inference(cp,[status(thm)],[eq_3,eq_46]) ).
cnf(eq_60,plain,
difference(A,product(product(B,A),A)) = quotient(A,product(A,B)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_58,eq_54]),eq_54]) ).
cnf(eq_61,plain,
difference(product(A,B),B) = quotient(product(B,product(B,A)),B),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_57,eq_5]),eq_53]),eq_53]) ).
cnf(eq_62,plain,
product(quotient(A,B),C) = quotient(product(A,C),product(B,C)),
eq_59 ).
cnf(eq_63,plain,
difference(A,product(difference(A,product(B,A)),A)) = quotient(A,product(A,difference(A,B))),
inference(cp,[status(thm)],[eq_54,eq_60]) ).
cnf(eq_64,plain,
difference(product(quotient(A,B),x101),product(A,x101)) = product(B,x101),
inference(cp,[status(thm)],[eq_3,eq_49]) ).
cnf(eq_65,plain,
quotient(product(A,quotient(product(A,B),A)),A) = difference(product(quotient(B,A),A),A),
inference(cp,[status(thm)],[eq_53,eq_61]) ).
cnf(eq_66,plain,
product(A,B) = difference(product(quotient(C,A),B),product(C,B)),
eq_64 ).
cnf(eq_67,plain,
difference(A,B) = quotient(difference(product(A,B),B),B),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_65,eq_53]),eq_61]),eq_3]) ).
cnf(eq_68,plain,
difference(A,quotient(A,product(A,B))) = quotient(A,B),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_63,eq_54]),eq_60]),eq_1]) ).
cnf(eq_69,plain,
product(A,quotient(A,B)) = quotient(A,product(A,B)),
inference(cp,[status(thm)],[eq_68,eq_1]) ).
cnf(eq_70,plain,
product(difference(A,B),B) = difference(product(A,B),B),
inference(cp,[status(thm)],[eq_67,eq_3]) ).
cnf(eq_71,plain,
product(quotient(a,c),b) = product(a,c),
inference(cp,[status(thm)],[eq_62,eq_18]) ).
cnf(eq_72,plain,
quotient(A,product(x102,A)) = product(quotient(A,x102),A),
inference(cp,[status(thm)],[eq_5,eq_62]) ).
cnf(eq_73,plain,
quotient(A,product(x102,B)) = product(quotient(quotient(A,B),x102),B),
inference(cp,[status(thm)],[eq_3,eq_62]) ).
cnf(eq_74,plain,
quotient(product(x100,B),A) = product(quotient(x100,quotient(A,B)),B),
inference(cp,[status(thm)],[eq_3,eq_62]) ).
cnf(eq_75,plain,
product(quotient(A,quotient(B,C)),C) = quotient(product(A,C),B),
eq_74 ).
cnf(eq_76,plain,
product(quotient(quotient(A,B),C),B) = quotient(A,product(C,B)),
eq_73 ).
cnf(eq_77,plain,
product(quotient(A,B),A) = quotient(A,product(B,A)),
eq_72 ).
cnf(eq_78,plain,
product(product(a,c),c) = product(a,product(b,c)),
inference(cp,[status(thm)],[eq_71,eq_48]) ).
cnf(eq_79,plain,
bigC(c,b,a) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_55,eq_7]),eq_30]),eq_78]),eq_49]),eq_5]) ).
cnf(eq_80,plain,
difference(product(c,a),c) = product(b,c),
inference(cp,[status(thm)],[eq_79,eq_50]) ).
cnf(eq_81,plain,
quotient(c,product(a,c)) = product(c,b),
inference(cp,[status(thm)],[eq_79,eq_20]) ).
cnf(eq_82,plain,
quotient(c,product(b,c)) = product(c,a),
inference(cp,[status(thm)],[eq_79,eq_47]) ).
cnf(eq_83,plain,
product(c,a) = quotient(c,product(b,c)),
eq_82 ).
cnf(eq_84,plain,
quotient(quotient(c,product(b,c)),c) = product(c,quotient(a,c)),
inference(cp,[status(thm)],[eq_83,eq_53]) ).
cnf(eq_85,plain,
product(c,quotient(a,c)) = quotient(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_84,eq_77]),eq_2]) ).
cnf(eq_86,plain,
product(quotient(c,b),c) = product(c,a),
inference(rw,[status(thm)],[eq_83,eq_77]) ).
cnf(eq_87,plain,
product(product(product(quotient(a,c),c),c),product(c,quotient(c,b))) = c,
inference(cp,[status(thm)],[eq_85,eq_6]) ).
cnf(eq_88,plain,
product(product(a,c),product(c,quotient(c,b))) = c,
inference(rw,[status(thm)],[eq_87,eq_3]) ).
cnf(eq_89,plain,
quotient(product(c,a),c) = quotient(c,b),
inference(cp,[status(thm)],[eq_86,eq_2]) ).
cnf(eq_90,plain,
product(quotient(c,a),c) = product(c,b),
inference(rw,[status(thm)],[eq_81,eq_77]) ).
cnf(eq_91,plain,
quotient(product(quotient(c,a),c),c) = product(c,quotient(b,c)),
inference(cp,[status(thm)],[eq_90,eq_53]) ).
cnf(eq_92,plain,
product(c,quotient(b,c)) = quotient(c,a),
inference(rw,[status(thm)],[eq_91,eq_2]) ).
cnf(eq_93,plain,
quotient(c,product(c,quotient(c,a))) = product(product(quotient(b,c),c),c),
inference(cp,[status(thm)],[eq_92,eq_29]) ).
cnf(eq_94,plain,
quotient(quotient(c,a),quotient(b,c)) = c,
inference(cp,[status(thm)],[eq_92,eq_2]) ).
cnf(eq_95,plain,
product(b,c) = quotient(c,product(c,quotient(c,a))),
inference(rw,[status(thm)],[eq_93,eq_3]) ).
cnf(eq_96,plain,
product(c,a) = quotient(c,product(quotient(b,c),a)),
inference(cp,[status(thm)],[eq_94,eq_76]) ).
cnf(eq_97,plain,
difference(quotient(c,product(quotient(b,c),a)),c) = product(b,c),
inference(cp,[status(thm)],[eq_96,eq_80]) ).
cnf(eq_98,plain,
product(quotient(b,c),a) = product(b,c),
inference(rw,[status(thm)],[eq_97,eq_27]) ).
cnf(eq_99,plain,
difference(quotient(b,c),product(b,c)) = a,
inference(cp,[status(thm)],[eq_98,eq_0]) ).
cnf(eq_100,plain,
difference(product(b,c),product(b,a)) = product(c,a),
inference(cp,[status(thm)],[eq_98,eq_66]) ).
cnf(eq_101,plain,
product(product(b,c),product(c,a)) = product(b,a),
inference(cp,[status(thm)],[eq_100,eq_1]) ).
cnf(eq_102,negated_conjecture,
bigC(difference(quotient(b,c),product(b,c)),x0,b) != product(product(c,x0),c),
inference(cp,[status(thm)],[eq_99,eq_36]) ).
cnf(eq_103,negated_conjecture,
product(c,product(x0,c)) != bigC(difference(quotient(b,c),product(b,c)),x0,b),
inference(rw,[status(thm)],[eq_102,eq_38]) ).
cnf(eq_104,plain,
product(difference(c,product(product(quotient(b,c),c),c)),quotient(c,a)) = c,
inference(cp,[status(thm)],[eq_92,eq_56]) ).
cnf(eq_105,plain,
product(difference(c,product(b,c)),quotient(c,a)) = c,
inference(rw,[status(thm)],[eq_104,eq_3]) ).
cnf(eq_106,plain,
quotient(c,quotient(c,a)) = difference(c,product(b,c)),
inference(cp,[status(thm)],[eq_105,eq_2]) ).
cnf(eq_107,plain,
difference(c,product(b,c)) = quotient(c,quotient(c,a)),
eq_106 ).
cnf(eq_108,negated_conjecture,
product(c,product(x0,c)) != bigC(difference(quotient(b,c),quotient(c,product(c,quotient(c,a)))),x0,b),
inference(rw,[status(thm)],[eq_103,eq_95]) ).
cnf(eq_109,plain,
product(c,quotient(c,quotient(c,a))) = product(b,c),
inference(cp,[status(thm)],[eq_107,eq_1]) ).
cnf(eq_110,plain,
product(product(c,quotient(c,quotient(c,a))),product(c,a)) = product(b,a),
inference(cp,[status(thm)],[eq_109,eq_101]) ).
cnf(eq_111,plain,
product(b,a) = quotient(product(c,product(c,a)),c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_110,eq_30]),eq_75]),eq_53]) ).
cnf(eq_112,plain,
bigC(a,c,b) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_88,eq_89]),eq_53]),eq_111]),eq_7]) ).
cnf(eq_113,plain,
difference(product(a,c),c) = product(b,a),
inference(cp,[status(thm)],[eq_112,eq_26]) ).
cnf(eq_114,plain,
quotient(c,product(c,a)) = product(a,b),
inference(cp,[status(thm)],[eq_112,eq_47]) ).
cnf(eq_115,plain,
product(difference(a,c),c) = product(b,a),
inference(rw,[status(thm)],[eq_113,eq_70]) ).
cnf(eq_116,plain,
product(b,c) = quotient(c,product(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_95,eq_69]),eq_114]) ).
cnf(eq_117,negated_conjecture,
product(c,product(x0,c)) != bigC(difference(quotient(b,c),quotient(c,product(a,b))),x0,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_108,eq_69]),eq_114]) ).
cnf(eq_118,plain,
product(product(a,x101),product(b,a)) = product(c,product(x101,c)),
inference(cp,[status(thm)],[eq_115,eq_31]) ).
cnf(eq_119,plain,
product(c,product(A,c)) = bigC(a,A,b),
inference(rw,[status(thm)],[eq_118,eq_7]) ).
cnf(eq_120,negated_conjecture,
product(c,product(x0,c)) != product(c,product(x0,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[eq_117,eq_116]),eq_99]),eq_119]) ).
cnf(bot,negated_conjecture,
$false,
inference(cn,[status(thm)],[eq_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP777-10 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12 % Command : run_maedmax %d %s
% 0.12/0.34 % Computer : n004.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 : 300
% 0.12/0.34 % DateTime : Tue Jul 26 04:16:51 EDT 2022
% 0.18/0.34 % CPUTime :
% 13.60/13.87 % SZS status Unsatisfiable
% 13.60/13.87 % SZS output start CNFRefutation for /tmp/MaedMax_20763
% See solution above
% 13.60/13.87
%------------------------------------------------------------------------------