TSTP Solution File: GRP012-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 10:32:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 32
% Syntax : Number of clauses : 147 ( 72 unt; 0 nHn; 80 RR)
% Number of literals : 259 ( 140 equ; 114 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 262 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ) ).
cnf(associativity1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(prove_inverse_of_product_is_product_of_inverses,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) ).
cnf(refute_0_0,plain,
( ~ product(multiply(X_166,inverse(X_165)),X_165,W)
| ~ product(multiply(X_166,inverse(X_165)),X_165,X_166)
| X_166 = W ),
inference(subst,[],[total_function2:[bind(X,$fot(multiply(X_166,inverse(X_165)))),bind(Y,$fot(X_165)),bind(Z,$fot(X_166))]]) ).
cnf(refute_0_1,plain,
product(multiply(X_163,inverse(Y)),Y,multiply(multiply(X_163,inverse(Y)),Y)),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(X_163,inverse(Y))))]]) ).
cnf(refute_0_2,plain,
product(X_51,X_52,multiply(X_51,X_52)),
inference(subst,[],[total_function1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_51,X_52,X_53)
| ~ product(X_51,X_52,multiply(X_51,X_52))
| X_53 = multiply(X_51,X_52) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_51,X_52))),bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_4,plain,
( ~ product(X_51,X_52,X_53)
| X_53 = multiply(X_51,X_52) ),
inference(resolve,[$cnf( product(X_51,X_52,multiply(X_51,X_52)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(X_161,identity,multiply(multiply(X_161,inverse(X_162)),X_162))
| multiply(multiply(X_161,inverse(X_162)),X_162) = multiply(X_161,identity) ),
inference(subst,[],[refute_0_4:[bind(X_51,$fot(X_161)),bind(X_52,$fot(identity)),bind(X_53,$fot(multiply(multiply(X_161,inverse(X_162)),X_162)))]]) ).
cnf(refute_0_6,plain,
product(X_158,inverse(X_159),multiply(X_158,inverse(X_159))),
inference(subst,[],[total_function1:[bind(X,$fot(X_158)),bind(Y,$fot(inverse(X_159)))]]) ).
cnf(refute_0_7,plain,
product(X_136,X_135,multiply(X_136,X_135)),
inference(subst,[],[total_function1:[bind(X,$fot(X_136)),bind(Y,$fot(X_135))]]) ).
cnf(refute_0_8,plain,
product(inverse(X_104),X_104,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_104))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_102,inverse(X_104),X_99)
| ~ product(X_99,X_104,X_101)
| ~ product(inverse(X_104),X_104,identity)
| product(X_102,identity,X_101) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_99)),bind(V,$fot(identity)),bind(W,$fot(X_101)),bind(X,$fot(X_102)),bind(Y,$fot(inverse(X_104))),bind(Z,$fot(X_104))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_102,inverse(X_104),X_99)
| ~ product(X_99,X_104,X_101)
| product(X_102,identity,X_101) ),
inference(resolve,[$cnf( product(inverse(X_104),X_104,identity) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ product(X_134,inverse(X_135),X_136)
| ~ product(X_136,X_135,multiply(X_136,X_135))
| product(X_134,identity,multiply(X_136,X_135)) ),
inference(subst,[],[refute_0_10:[bind(X_101,$fot(multiply(X_136,X_135))),bind(X_102,$fot(X_134)),bind(X_104,$fot(X_135)),bind(X_99,$fot(X_136))]]) ).
cnf(refute_0_12,plain,
( ~ product(X_134,inverse(X_135),X_136)
| product(X_134,identity,multiply(X_136,X_135)) ),
inference(resolve,[$cnf( product(X_136,X_135,multiply(X_136,X_135)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ product(X_158,inverse(X_159),multiply(X_158,inverse(X_159)))
| product(X_158,identity,multiply(multiply(X_158,inverse(X_159)),X_159)) ),
inference(subst,[],[refute_0_12:[bind(X_134,$fot(X_158)),bind(X_135,$fot(X_159)),bind(X_136,$fot(multiply(X_158,inverse(X_159))))]]) ).
cnf(refute_0_14,plain,
product(X_158,identity,multiply(multiply(X_158,inverse(X_159)),X_159)),
inference(resolve,[$cnf( product(X_158,inverse(X_159),multiply(X_158,inverse(X_159))) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
product(X_161,identity,multiply(multiply(X_161,inverse(X_162)),X_162)),
inference(subst,[],[refute_0_14:[bind(X_158,$fot(X_161)),bind(X_159,$fot(X_162))]]) ).
cnf(refute_0_16,plain,
multiply(multiply(X_161,inverse(X_162)),X_162) = multiply(X_161,identity),
inference(resolve,[$cnf( product(X_161,identity,multiply(multiply(X_161,inverse(X_162)),X_162)) )],[refute_0_15,refute_0_5]) ).
cnf(refute_0_17,plain,
product(X_64,identity,multiply(X_64,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_64)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_18,plain,
product(X_50,identity,X_50),
inference(subst,[],[right_identity:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_19,plain,
( ~ product(X_50,identity,X_50)
| ~ product(X_50,identity,X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(X_50)),bind(Y,$fot(identity)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_20,plain,
( ~ product(X_50,identity,X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(X_50,identity,X_50) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ product(X_64,identity,multiply(X_64,identity))
| multiply(X_64,identity) = X_64 ),
inference(subst,[],[refute_0_20:[bind(X_50,$fot(X_64)),bind(X_53,$fot(multiply(X_64,identity)))]]) ).
cnf(refute_0_22,plain,
multiply(X_64,identity) = X_64,
inference(resolve,[$cnf( product(X_64,identity,multiply(X_64,identity)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_161,identity) = X_161,
inference(subst,[],[refute_0_22:[bind(X_64,$fot(X_161))]]) ).
cnf(refute_0_24,plain,
( multiply(X_161,identity) != X_161
| multiply(multiply(X_161,inverse(X_162)),X_162) != multiply(X_161,identity)
| multiply(multiply(X_161,inverse(X_162)),X_162) = X_161 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_161,inverse(X_162)),X_162),multiply(X_161,identity)) ),[1],$fot(X_161)]]) ).
cnf(refute_0_25,plain,
( multiply(multiply(X_161,inverse(X_162)),X_162) != multiply(X_161,identity)
| multiply(multiply(X_161,inverse(X_162)),X_162) = X_161 ),
inference(resolve,[$cnf( $equal(multiply(X_161,identity),X_161) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(multiply(X_161,inverse(X_162)),X_162) = X_161,
inference(resolve,[$cnf( $equal(multiply(multiply(X_161,inverse(X_162)),X_162),multiply(X_161,identity)) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(multiply(X_163,inverse(Y)),Y) = X_163,
inference(subst,[],[refute_0_26:[bind(X_161,$fot(X_163)),bind(X_162,$fot(Y))]]) ).
cnf(refute_0_28,plain,
( multiply(multiply(X_163,inverse(Y)),Y) != X_163
| ~ product(multiply(X_163,inverse(Y)),Y,multiply(multiply(X_163,inverse(Y)),Y))
| product(multiply(X_163,inverse(Y)),Y,X_163) ),
introduced(tautology,[equality,[$cnf( product(multiply(X_163,inverse(Y)),Y,multiply(multiply(X_163,inverse(Y)),Y)) ),[2],$fot(X_163)]]) ).
cnf(refute_0_29,plain,
( ~ product(multiply(X_163,inverse(Y)),Y,multiply(multiply(X_163,inverse(Y)),Y))
| product(multiply(X_163,inverse(Y)),Y,X_163) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_163,inverse(Y)),Y),X_163) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
product(multiply(X_163,inverse(Y)),Y,X_163),
inference(resolve,[$cnf( product(multiply(X_163,inverse(Y)),Y,multiply(multiply(X_163,inverse(Y)),Y)) )],[refute_0_1,refute_0_29]) ).
cnf(refute_0_31,plain,
product(multiply(X_166,inverse(X_165)),X_165,X_166),
inference(subst,[],[refute_0_30:[bind(Y,$fot(X_165)),bind(X_163,$fot(X_166))]]) ).
cnf(refute_0_32,plain,
( ~ product(multiply(X_166,inverse(X_165)),X_165,W)
| X_166 = W ),
inference(resolve,[$cnf( product(multiply(X_166,inverse(X_165)),X_165,X_166) )],[refute_0_31,refute_0_0]) ).
cnf(refute_0_33,plain,
( ~ product(multiply(X_166,inverse(identity)),identity,multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))))
| X_166 = multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) ),
inference(subst,[],[refute_0_32:[bind(W,$fot(multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))))),bind(X_165,$fot(identity))]]) ).
cnf(refute_0_34,plain,
( ~ product(X_158,inverse(inverse(X_141)),X_160)
| product(X_158,identity,multiply(X_160,inverse(X_141))) ),
inference(subst,[],[refute_0_12:[bind(X_134,$fot(X_158)),bind(X_135,$fot(inverse(X_141))),bind(X_136,$fot(X_160))]]) ).
cnf(refute_0_35,plain,
( ~ product(inverse(inverse(X_141)),identity,X_141)
| X_141 = multiply(inverse(inverse(X_141)),identity) ),
inference(subst,[],[refute_0_4:[bind(X_51,$fot(inverse(inverse(X_141)))),bind(X_52,$fot(identity)),bind(X_53,$fot(X_141))]]) ).
cnf(refute_0_36,plain,
product(inverse(inverse(X_139)),inverse(X_139),identity),
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_139)))]]) ).
cnf(refute_0_37,plain,
product(identity,X_133,X_133),
inference(subst,[],[left_identity:[bind(X,$fot(X_133))]]) ).
cnf(refute_0_38,plain,
( ~ product(X_134,inverse(X_133),identity)
| ~ product(identity,X_133,X_133)
| product(X_134,identity,X_133) ),
inference(subst,[],[refute_0_10:[bind(X_101,$fot(X_133)),bind(X_102,$fot(X_134)),bind(X_104,$fot(X_133)),bind(X_99,$fot(identity))]]) ).
cnf(refute_0_39,plain,
( ~ product(X_134,inverse(X_133),identity)
| product(X_134,identity,X_133) ),
inference(resolve,[$cnf( product(identity,X_133,X_133) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ product(inverse(inverse(X_139)),inverse(X_139),identity)
| product(inverse(inverse(X_139)),identity,X_139) ),
inference(subst,[],[refute_0_39:[bind(X_133,$fot(X_139)),bind(X_134,$fot(inverse(inverse(X_139))))]]) ).
cnf(refute_0_41,plain,
product(inverse(inverse(X_139)),identity,X_139),
inference(resolve,[$cnf( product(inverse(inverse(X_139)),inverse(X_139),identity) )],[refute_0_36,refute_0_40]) ).
cnf(refute_0_42,plain,
product(inverse(inverse(X_141)),identity,X_141),
inference(subst,[],[refute_0_41:[bind(X_139,$fot(X_141))]]) ).
cnf(refute_0_43,plain,
X_141 = multiply(inverse(inverse(X_141)),identity),
inference(resolve,[$cnf( product(inverse(inverse(X_141)),identity,X_141) )],[refute_0_42,refute_0_35]) ).
cnf(refute_0_44,plain,
multiply(inverse(inverse(X_141)),identity) = inverse(inverse(X_141)),
inference(subst,[],[refute_0_22:[bind(X_64,$fot(inverse(inverse(X_141))))]]) ).
cnf(refute_0_45,plain,
( X_141 != multiply(inverse(inverse(X_141)),identity)
| multiply(inverse(inverse(X_141)),identity) != inverse(inverse(X_141))
| X_141 = inverse(inverse(X_141)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_141,inverse(inverse(X_141))) ),[0],$fot(multiply(inverse(inverse(X_141)),identity))]]) ).
cnf(refute_0_46,plain,
( X_141 != multiply(inverse(inverse(X_141)),identity)
| X_141 = inverse(inverse(X_141)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_141)),identity),inverse(inverse(X_141))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
X_141 = inverse(inverse(X_141)),
inference(resolve,[$cnf( $equal(X_141,multiply(inverse(inverse(X_141)),identity)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_49,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_50,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( X_141 != inverse(inverse(X_141))
| inverse(inverse(X_141)) = X_141 ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(X_141)),bind(Y0,$fot(inverse(inverse(X_141))))]]) ).
cnf(refute_0_52,plain,
inverse(inverse(X_141)) = X_141,
inference(resolve,[$cnf( $equal(X_141,inverse(inverse(X_141))) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( inverse(inverse(X_141)) != X_141
| ~ product(X_158,X_141,X_160)
| product(X_158,inverse(inverse(X_141)),X_160) ),
introduced(tautology,[equality,[$cnf( ~ product(X_158,inverse(inverse(X_141)),X_160) ),[1],$fot(X_141)]]) ).
cnf(refute_0_54,plain,
( ~ product(X_158,X_141,X_160)
| product(X_158,inverse(inverse(X_141)),X_160) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_141)),X_141) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ product(X_158,X_141,X_160)
| product(X_158,identity,multiply(X_160,inverse(X_141))) ),
inference(resolve,[$cnf( product(X_158,inverse(inverse(X_141)),X_160) )],[refute_0_54,refute_0_34]) ).
cnf(refute_0_56,plain,
( ~ product(X_290,multiply(inverse(X_290),X_291),X_291)
| product(X_290,identity,multiply(X_291,inverse(multiply(inverse(X_290),X_291)))) ),
inference(subst,[],[refute_0_55:[bind(X_141,$fot(multiply(inverse(X_290),X_291))),bind(X_158,$fot(X_290)),bind(X_160,$fot(X_291))]]) ).
cnf(refute_0_57,plain,
product(inverse(X_287),X_289,multiply(inverse(X_287),X_289)),
inference(subst,[],[total_function1:[bind(X,$fot(inverse(X_287))),bind(Y,$fot(X_289))]]) ).
cnf(refute_0_58,plain,
product(multiply(X_168,X_167),inverse(X_167),multiply(multiply(X_168,X_167),inverse(X_167))),
inference(subst,[],[total_function1:[bind(X,$fot(multiply(X_168,X_167))),bind(Y,$fot(inverse(X_167)))]]) ).
cnf(refute_0_59,plain,
multiply(multiply(X_163,inverse(inverse(X_141))),inverse(X_141)) = X_163,
inference(subst,[],[refute_0_26:[bind(X_161,$fot(X_163)),bind(X_162,$fot(inverse(X_141)))]]) ).
cnf(refute_0_60,plain,
( multiply(multiply(X_163,inverse(inverse(X_141))),inverse(X_141)) != X_163
| inverse(inverse(X_141)) != X_141
| multiply(multiply(X_163,X_141),inverse(X_141)) = X_163 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_163,inverse(inverse(X_141))),inverse(X_141)),X_163) ),[0,0,1],$fot(X_141)]]) ).
cnf(refute_0_61,plain,
( multiply(multiply(X_163,inverse(inverse(X_141))),inverse(X_141)) != X_163
| multiply(multiply(X_163,X_141),inverse(X_141)) = X_163 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_141)),X_141) )],[refute_0_52,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(multiply(X_163,X_141),inverse(X_141)) = X_163,
inference(resolve,[$cnf( $equal(multiply(multiply(X_163,inverse(inverse(X_141))),inverse(X_141)),X_163) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(multiply(X_168,X_167),inverse(X_167)) = X_168,
inference(subst,[],[refute_0_62:[bind(X_141,$fot(X_167)),bind(X_163,$fot(X_168))]]) ).
cnf(refute_0_64,plain,
( multiply(multiply(X_168,X_167),inverse(X_167)) != X_168
| ~ product(multiply(X_168,X_167),inverse(X_167),multiply(multiply(X_168,X_167),inverse(X_167)))
| product(multiply(X_168,X_167),inverse(X_167),X_168) ),
introduced(tautology,[equality,[$cnf( product(multiply(X_168,X_167),inverse(X_167),multiply(multiply(X_168,X_167),inverse(X_167))) ),[2],$fot(X_168)]]) ).
cnf(refute_0_65,plain,
( ~ product(multiply(X_168,X_167),inverse(X_167),multiply(multiply(X_168,X_167),inverse(X_167)))
| product(multiply(X_168,X_167),inverse(X_167),X_168) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_168,X_167),inverse(X_167)),X_168) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
product(multiply(X_168,X_167),inverse(X_167),X_168),
inference(resolve,[$cnf( product(multiply(X_168,X_167),inverse(X_167),multiply(multiply(X_168,X_167),inverse(X_167))) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
product(multiply(identity,X_167),inverse(X_167),identity),
inference(subst,[],[refute_0_66:[bind(X_168,$fot(identity))]]) ).
cnf(refute_0_68,plain,
product(identity,X_101,X_101),
inference(subst,[],[left_identity:[bind(X,$fot(X_101))]]) ).
cnf(refute_0_69,plain,
( ~ product(X_102,X_103,identity)
| ~ product(X_103,X_101,X_100)
| ~ product(identity,X_101,X_101)
| product(X_102,X_100,X_101) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_100)),bind(W,$fot(X_101)),bind(X,$fot(X_102)),bind(Y,$fot(X_103)),bind(Z,$fot(X_101))]]) ).
cnf(refute_0_70,plain,
( ~ product(X_102,X_103,identity)
| ~ product(X_103,X_101,X_100)
| product(X_102,X_100,X_101) ),
inference(resolve,[$cnf( product(identity,X_101,X_101) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ product(multiply(identity,X_167),inverse(X_167),identity)
| ~ product(inverse(X_167),X_284,X_283)
| product(multiply(identity,X_167),X_283,X_284) ),
inference(subst,[],[refute_0_70:[bind(X_100,$fot(X_283)),bind(X_101,$fot(X_284)),bind(X_102,$fot(multiply(identity,X_167))),bind(X_103,$fot(inverse(X_167)))]]) ).
cnf(refute_0_72,plain,
( ~ product(inverse(X_167),X_284,X_283)
| product(multiply(identity,X_167),X_283,X_284) ),
inference(resolve,[$cnf( product(multiply(identity,X_167),inverse(X_167),identity) )],[refute_0_67,refute_0_71]) ).
cnf(refute_0_73,plain,
product(identity,X_61,multiply(identity,X_61)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(X_61))]]) ).
cnf(refute_0_74,plain,
product(identity,X_50,X_50),
inference(subst,[],[left_identity:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_75,plain,
( ~ product(identity,X_50,X_50)
| ~ product(identity,X_50,X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(identity)),bind(Y,$fot(X_50)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_76,plain,
( ~ product(identity,X_50,X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(identity,X_50,X_50) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ product(identity,X_61,multiply(identity,X_61))
| multiply(identity,X_61) = X_61 ),
inference(subst,[],[refute_0_76:[bind(X_50,$fot(X_61)),bind(X_53,$fot(multiply(identity,X_61)))]]) ).
cnf(refute_0_78,plain,
multiply(identity,X_61) = X_61,
inference(resolve,[$cnf( product(identity,X_61,multiply(identity,X_61)) )],[refute_0_73,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(identity,X_167) = X_167,
inference(subst,[],[refute_0_78:[bind(X_61,$fot(X_167))]]) ).
cnf(refute_0_80,plain,
( multiply(identity,X_167) != X_167
| ~ product(multiply(identity,X_167),X_283,X_284)
| product(X_167,X_283,X_284) ),
introduced(tautology,[equality,[$cnf( product(multiply(identity,X_167),X_283,X_284) ),[0],$fot(X_167)]]) ).
cnf(refute_0_81,plain,
( ~ product(multiply(identity,X_167),X_283,X_284)
| product(X_167,X_283,X_284) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_167),X_167) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ product(inverse(X_167),X_284,X_283)
| product(X_167,X_283,X_284) ),
inference(resolve,[$cnf( product(multiply(identity,X_167),X_283,X_284) )],[refute_0_72,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ product(inverse(X_287),X_289,multiply(inverse(X_287),X_289))
| product(X_287,multiply(inverse(X_287),X_289),X_289) ),
inference(subst,[],[refute_0_82:[bind(X_167,$fot(X_287)),bind(X_283,$fot(multiply(inverse(X_287),X_289))),bind(X_284,$fot(X_289))]]) ).
cnf(refute_0_84,plain,
product(X_287,multiply(inverse(X_287),X_289),X_289),
inference(resolve,[$cnf( product(inverse(X_287),X_289,multiply(inverse(X_287),X_289)) )],[refute_0_57,refute_0_83]) ).
cnf(refute_0_85,plain,
product(X_290,multiply(inverse(X_290),X_291),X_291),
inference(subst,[],[refute_0_84:[bind(X_287,$fot(X_290)),bind(X_289,$fot(X_291))]]) ).
cnf(refute_0_86,plain,
product(X_290,identity,multiply(X_291,inverse(multiply(inverse(X_290),X_291)))),
inference(resolve,[$cnf( product(X_290,multiply(inverse(X_290),X_291),X_291) )],[refute_0_85,refute_0_56]) ).
cnf(refute_0_87,plain,
product(multiply(X_166,inverse(identity)),identity,multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))),
inference(subst,[],[refute_0_86:[bind(X_290,$fot(multiply(X_166,inverse(identity)))),bind(X_291,$fot(X_297))]]) ).
cnf(refute_0_88,plain,
X_166 = multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))),
inference(resolve,[$cnf( product(multiply(X_166,inverse(identity)),identity,multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))) )],[refute_0_87,refute_0_33]) ).
cnf(refute_0_89,plain,
multiply(X_166,identity) = X_166,
inference(subst,[],[refute_0_22:[bind(X_64,$fot(X_166))]]) ).
cnf(refute_0_90,plain,
product(inverse(identity),identity,inverse(identity)),
inference(subst,[],[right_identity:[bind(X,$fot(inverse(identity)))]]) ).
cnf(refute_0_91,plain,
product(inverse(X_52),X_52,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_52))]]) ).
cnf(refute_0_92,plain,
( ~ product(inverse(X_52),X_52,X_53)
| ~ product(inverse(X_52),X_52,identity)
| X_53 = identity ),
inference(subst,[],[total_function2:[bind(W,$fot(identity)),bind(X,$fot(inverse(X_52))),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_93,plain,
( ~ product(inverse(X_52),X_52,X_53)
| X_53 = identity ),
inference(resolve,[$cnf( product(inverse(X_52),X_52,identity) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ product(inverse(identity),identity,inverse(identity))
| inverse(identity) = identity ),
inference(subst,[],[refute_0_93:[bind(X_52,$fot(identity)),bind(X_53,$fot(inverse(identity)))]]) ).
cnf(refute_0_95,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( product(inverse(identity),identity,inverse(identity)) )],[refute_0_90,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(X_166,inverse(identity)) = multiply(X_166,inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(X_166,inverse(identity)))]]) ).
cnf(refute_0_97,plain,
( multiply(X_166,inverse(identity)) != multiply(X_166,inverse(identity))
| inverse(identity) != identity
| multiply(X_166,inverse(identity)) = multiply(X_166,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_166,inverse(identity)),multiply(X_166,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_98,plain,
( inverse(identity) != identity
| multiply(X_166,inverse(identity)) = multiply(X_166,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_166,inverse(identity)),multiply(X_166,inverse(identity))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(X_166,inverse(identity)) = multiply(X_166,identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_101,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_50,refute_0_100]) ).
cnf(refute_0_102,plain,
( multiply(X_166,identity) != X_166
| multiply(X_166,inverse(identity)) != multiply(X_166,identity)
| multiply(X_166,inverse(identity)) = X_166 ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(multiply(X_166,inverse(identity)))),bind(Y0,$fot(multiply(X_166,identity))),bind(Z0,$fot(X_166))]]) ).
cnf(refute_0_103,plain,
( multiply(X_166,identity) != X_166
| multiply(X_166,inverse(identity)) = X_166 ),
inference(resolve,[$cnf( $equal(multiply(X_166,inverse(identity)),multiply(X_166,identity)) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(X_166,inverse(identity)) = X_166,
inference(resolve,[$cnf( $equal(multiply(X_166,identity),X_166) )],[refute_0_89,refute_0_103]) ).
cnf(refute_0_105,plain,
inverse(multiply(X_166,inverse(identity))) = inverse(multiply(X_166,inverse(identity))),
introduced(tautology,[refl,[$fot(inverse(multiply(X_166,inverse(identity))))]]) ).
cnf(refute_0_106,plain,
( multiply(X_166,inverse(identity)) != X_166
| inverse(multiply(X_166,inverse(identity))) != inverse(multiply(X_166,inverse(identity)))
| inverse(multiply(X_166,inverse(identity))) = inverse(X_166) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_166,inverse(identity))),inverse(multiply(X_166,inverse(identity)))) ),[1,0],$fot(X_166)]]) ).
cnf(refute_0_107,plain,
( multiply(X_166,inverse(identity)) != X_166
| inverse(multiply(X_166,inverse(identity))) = inverse(X_166) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_166,inverse(identity))),inverse(multiply(X_166,inverse(identity)))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
inverse(multiply(X_166,inverse(identity))) = inverse(X_166),
inference(resolve,[$cnf( $equal(multiply(X_166,inverse(identity)),X_166) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(inverse(multiply(X_166,inverse(identity))),X_297) = multiply(inverse(multiply(X_166,inverse(identity))),X_297),
introduced(tautology,[refl,[$fot(multiply(inverse(multiply(X_166,inverse(identity))),X_297))]]) ).
cnf(refute_0_110,plain,
( multiply(inverse(multiply(X_166,inverse(identity))),X_297) != multiply(inverse(multiply(X_166,inverse(identity))),X_297)
| inverse(multiply(X_166,inverse(identity))) != inverse(X_166)
| multiply(inverse(multiply(X_166,inverse(identity))),X_297) = multiply(inverse(X_166),X_297) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_166,inverse(identity))),X_297),multiply(inverse(multiply(X_166,inverse(identity))),X_297)) ),[1,0],$fot(inverse(X_166))]]) ).
cnf(refute_0_111,plain,
( inverse(multiply(X_166,inverse(identity))) != inverse(X_166)
| multiply(inverse(multiply(X_166,inverse(identity))),X_297) = multiply(inverse(X_166),X_297) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_166,inverse(identity))),X_297),multiply(inverse(multiply(X_166,inverse(identity))),X_297)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(inverse(multiply(X_166,inverse(identity))),X_297) = multiply(inverse(X_166),X_297),
inference(resolve,[$cnf( $equal(inverse(multiply(X_166,inverse(identity))),inverse(X_166)) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) = inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))]]) ).
cnf(refute_0_114,plain,
( multiply(inverse(multiply(X_166,inverse(identity))),X_297) != multiply(inverse(X_166),X_297)
| inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) != inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))
| inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) = inverse(multiply(inverse(X_166),X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)),inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) ),[1,0],$fot(multiply(inverse(X_166),X_297))]]) ).
cnf(refute_0_115,plain,
( multiply(inverse(multiply(X_166,inverse(identity))),X_297) != multiply(inverse(X_166),X_297)
| inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) = inverse(multiply(inverse(X_166),X_297)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)),inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) = inverse(multiply(inverse(X_166),X_297)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_166,inverse(identity))),X_297),multiply(inverse(X_166),X_297)) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) = multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))),
introduced(tautology,[refl,[$fot(multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))))]]) ).
cnf(refute_0_118,plain,
( multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) != multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))
| inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) != inverse(multiply(inverse(X_166),X_297))
| multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) = multiply(X_297,inverse(multiply(inverse(X_166),X_297))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))),multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))) ),[1,1],$fot(inverse(multiply(inverse(X_166),X_297)))]]) ).
cnf(refute_0_119,plain,
( inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)) != inverse(multiply(inverse(X_166),X_297))
| multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) = multiply(X_297,inverse(multiply(inverse(X_166),X_297))) ),
inference(resolve,[$cnf( $equal(multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))),multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) = multiply(X_297,inverse(multiply(inverse(X_166),X_297))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)),inverse(multiply(inverse(X_166),X_297))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( X_166 != multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))
| multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))) != multiply(X_297,inverse(multiply(inverse(X_166),X_297)))
| X_166 = multiply(X_297,inverse(multiply(inverse(X_166),X_297))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_166,multiply(X_297,inverse(multiply(inverse(X_166),X_297)))) ),[0],$fot(multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))))]]) ).
cnf(refute_0_122,plain,
( X_166 != multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))
| X_166 = multiply(X_297,inverse(multiply(inverse(X_166),X_297))) ),
inference(resolve,[$cnf( $equal(multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297))),multiply(X_297,inverse(multiply(inverse(X_166),X_297)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
X_166 = multiply(X_297,inverse(multiply(inverse(X_166),X_297))),
inference(resolve,[$cnf( $equal(X_166,multiply(X_297,inverse(multiply(inverse(multiply(X_166,inverse(identity))),X_297)))) )],[refute_0_88,refute_0_122]) ).
cnf(refute_0_124,plain,
inverse(X_141) = multiply(X_299,inverse(multiply(inverse(inverse(X_141)),X_299))),
inference(subst,[],[refute_0_123:[bind(X_166,$fot(inverse(X_141))),bind(X_297,$fot(X_299))]]) ).
cnf(refute_0_125,plain,
( inverse(X_141) != multiply(X_299,inverse(multiply(inverse(inverse(X_141)),X_299)))
| inverse(inverse(X_141)) != X_141
| inverse(X_141) = multiply(X_299,inverse(multiply(X_141,X_299))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_141),multiply(X_299,inverse(multiply(inverse(inverse(X_141)),X_299)))) ),[1,1,0,0],$fot(X_141)]]) ).
cnf(refute_0_126,plain,
( inverse(X_141) != multiply(X_299,inverse(multiply(inverse(inverse(X_141)),X_299)))
| inverse(X_141) = multiply(X_299,inverse(multiply(X_141,X_299))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_141)),X_141) )],[refute_0_52,refute_0_125]) ).
cnf(refute_0_127,plain,
inverse(X_141) = multiply(X_299,inverse(multiply(X_141,X_299))),
inference(resolve,[$cnf( $equal(inverse(X_141),multiply(X_299,inverse(multiply(inverse(inverse(X_141)),X_299)))) )],[refute_0_124,refute_0_126]) ).
cnf(refute_0_128,plain,
inverse(multiply(X_163,X_141)) = multiply(inverse(X_141),inverse(multiply(multiply(X_163,X_141),inverse(X_141)))),
inference(subst,[],[refute_0_127:[bind(X_141,$fot(multiply(X_163,X_141))),bind(X_299,$fot(inverse(X_141)))]]) ).
cnf(refute_0_129,plain,
( multiply(multiply(X_163,X_141),inverse(X_141)) != X_163
| inverse(multiply(X_163,X_141)) != multiply(inverse(X_141),inverse(multiply(multiply(X_163,X_141),inverse(X_141))))
| inverse(multiply(X_163,X_141)) = multiply(inverse(X_141),inverse(X_163)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_163,X_141)),multiply(inverse(X_141),inverse(multiply(multiply(X_163,X_141),inverse(X_141))))) ),[1,1,0],$fot(X_163)]]) ).
cnf(refute_0_130,plain,
( inverse(multiply(X_163,X_141)) != multiply(inverse(X_141),inverse(multiply(multiply(X_163,X_141),inverse(X_141))))
| inverse(multiply(X_163,X_141)) = multiply(inverse(X_141),inverse(X_163)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_163,X_141),inverse(X_141)),X_163) )],[refute_0_62,refute_0_129]) ).
cnf(refute_0_131,plain,
inverse(multiply(X_163,X_141)) = multiply(inverse(X_141),inverse(X_163)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_163,X_141)),multiply(inverse(X_141),inverse(multiply(multiply(X_163,X_141),inverse(X_141))))) )],[refute_0_128,refute_0_130]) ).
cnf(refute_0_132,plain,
( inverse(multiply(X_163,X_141)) != multiply(inverse(X_141),inverse(X_163))
| multiply(inverse(X_141),inverse(X_163)) = inverse(multiply(X_163,X_141)) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(inverse(multiply(X_163,X_141)))),bind(Y0,$fot(multiply(inverse(X_141),inverse(X_163))))]]) ).
cnf(refute_0_133,plain,
multiply(inverse(X_141),inverse(X_163)) = inverse(multiply(X_163,X_141)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_163,X_141)),multiply(inverse(X_141),inverse(X_163))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(inverse(b),inverse(a)) = inverse(multiply(a,b)),
inference(subst,[],[refute_0_133:[bind(X_141,$fot(b)),bind(X_163,$fot(a))]]) ).
cnf(refute_0_135,plain,
( multiply(inverse(b),inverse(a)) != inverse(multiply(a,b))
| inverse(multiply(a,b)) != inverse(multiply(a,b))
| inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(multiply(a,b)),multiply(inverse(b),inverse(a))) ),[1],$fot(inverse(multiply(a,b)))]]) ).
cnf(refute_0_136,plain,
( inverse(multiply(a,b)) != inverse(multiply(a,b))
| inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b),inverse(a)),inverse(multiply(a,b))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
inverse(multiply(a,b)) != inverse(multiply(a,b)),
inference(resolve,[$cnf( $equal(inverse(multiply(a,b)),multiply(inverse(b),inverse(a))) )],[refute_0_136,prove_inverse_of_product_is_product_of_inverses]) ).
cnf(refute_0_138,plain,
inverse(multiply(a,b)) = inverse(multiply(a,b)),
introduced(tautology,[refl,[$fot(inverse(multiply(a,b)))]]) ).
cnf(refute_0_139,plain,
$false,
inference(resolve,[$cnf( $equal(inverse(multiply(a,b)),inverse(multiply(a,b))) )],[refute_0_138,refute_0_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 01:58:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48
% 0.20/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.49
%------------------------------------------------------------------------------