TSTP Solution File: GRP031-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 10:32:33 EDT 2022
% Result : Unsatisfiable 0.48s 0.67s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of clauses : 76 ( 39 unt; 0 nHn; 42 RR)
% Number of literals : 133 ( 72 equ; 59 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(left_identity,hypothesis,
product(identity,A,A) ).
cnf(left_inverse,hypothesis,
product(inverse(A),A,identity) ).
cnf(prove_a_has_an_inverse,negated_conjecture,
~ product(a,A,identity) ).
cnf(refute_0_0,plain,
~ product(a,inverse(a),identity),
inference(subst,[],[prove_a_has_an_inverse:[bind(A,$fot(inverse(a)))]]) ).
cnf(refute_0_1,plain,
product(inverse(inverse(X_212)),inverse(X_212),identity),
inference(subst,[],[left_inverse:[bind(A,$fot(inverse(X_212)))]]) ).
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,[$cnf( product(X_51,X_52,multiply(X_51,X_52)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(multiply(X_92,identity),identity,multiply(X_92,identity))
| multiply(X_92,identity) = multiply(multiply(X_92,identity),identity) ),
inference(subst,[],[refute_0_4:[bind(X_51,$fot(multiply(X_92,identity))),bind(X_52,$fot(identity)),bind(X_53,$fot(multiply(X_92,identity)))]]) ).
cnf(refute_0_6,plain,
product(X_91,identity,multiply(X_91,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_91)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_7,plain,
product(identity,identity,identity),
inference(subst,[],[left_identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_87,identity,X_86)
| ~ product(identity,identity,identity)
| product(X_86,identity,X_86) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_86)),bind(V,$fot(identity)),bind(W,$fot(X_86)),bind(X,$fot(X_87)),bind(Y,$fot(identity)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_87,identity,X_86)
| product(X_86,identity,X_86) ),
inference(resolve,[$cnf( product(identity,identity,identity) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product(X_91,identity,multiply(X_91,identity))
| product(multiply(X_91,identity),identity,multiply(X_91,identity)) ),
inference(subst,[],[refute_0_9:[bind(X_86,$fot(multiply(X_91,identity))),bind(X_87,$fot(X_91))]]) ).
cnf(refute_0_11,plain,
product(multiply(X_91,identity),identity,multiply(X_91,identity)),
inference(resolve,[$cnf( product(X_91,identity,multiply(X_91,identity)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
product(multiply(X_92,identity),identity,multiply(X_92,identity)),
inference(subst,[],[refute_0_11:[bind(X_91,$fot(X_92))]]) ).
cnf(refute_0_13,plain,
multiply(X_92,identity) = multiply(multiply(X_92,identity),identity),
inference(resolve,[$cnf( product(multiply(X_92,identity),identity,multiply(X_92,identity)) )],[refute_0_12,refute_0_5]) ).
cnf(refute_0_14,plain,
multiply(inverse(inverse(X_210)),identity) = multiply(multiply(inverse(inverse(X_210)),identity),identity),
inference(subst,[],[refute_0_13:[bind(X_92,$fot(inverse(inverse(X_210))))]]) ).
cnf(refute_0_15,plain,
( ~ product(identity,X_209,multiply(inverse(inverse(X_209)),identity))
| multiply(inverse(inverse(X_209)),identity) = multiply(identity,X_209) ),
inference(subst,[],[refute_0_4:[bind(X_51,$fot(identity)),bind(X_52,$fot(X_209)),bind(X_53,$fot(multiply(inverse(inverse(X_209)),identity)))]]) ).
cnf(refute_0_16,plain,
product(inverse(inverse(X_208)),identity,multiply(inverse(inverse(X_208)),identity)),
inference(subst,[],[total_function1:[bind(X,$fot(inverse(inverse(X_208)))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_17,plain,
product(inverse(X_206),X_206,identity),
inference(subst,[],[left_inverse:[bind(A,$fot(X_206))]]) ).
cnf(refute_0_18,plain,
product(inverse(X_191),X_191,identity),
inference(subst,[],[left_inverse:[bind(A,$fot(X_191))]]) ).
cnf(refute_0_19,plain,
( ~ product(X_191,X_192,X_188)
| ~ product(inverse(X_191),X_188,X_189)
| ~ product(inverse(X_191),X_191,identity)
| product(identity,X_192,X_189) ),
inference(subst,[],[associativity2:[bind(U,$fot(identity)),bind(V,$fot(X_188)),bind(W,$fot(X_189)),bind(X,$fot(inverse(X_191))),bind(Y,$fot(X_191)),bind(Z,$fot(X_192))]]) ).
cnf(refute_0_20,plain,
( ~ product(X_191,X_192,X_188)
| ~ product(inverse(X_191),X_188,X_189)
| product(identity,X_192,X_189) ),
inference(resolve,[$cnf( product(inverse(X_191),X_191,identity) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ product(inverse(X_206),X_206,identity)
| ~ product(inverse(inverse(X_206)),identity,X_204)
| product(identity,X_206,X_204) ),
inference(subst,[],[refute_0_20:[bind(X_188,$fot(identity)),bind(X_189,$fot(X_204)),bind(X_191,$fot(inverse(X_206))),bind(X_192,$fot(X_206))]]) ).
cnf(refute_0_22,plain,
( ~ product(inverse(inverse(X_206)),identity,X_204)
| product(identity,X_206,X_204) ),
inference(resolve,[$cnf( product(inverse(X_206),X_206,identity) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ product(inverse(inverse(X_208)),identity,multiply(inverse(inverse(X_208)),identity))
| product(identity,X_208,multiply(inverse(inverse(X_208)),identity)) ),
inference(subst,[],[refute_0_22:[bind(X_204,$fot(multiply(inverse(inverse(X_208)),identity))),bind(X_206,$fot(X_208))]]) ).
cnf(refute_0_24,plain,
product(identity,X_208,multiply(inverse(inverse(X_208)),identity)),
inference(resolve,[$cnf( product(inverse(inverse(X_208)),identity,multiply(inverse(inverse(X_208)),identity)) )],[refute_0_16,refute_0_23]) ).
cnf(refute_0_25,plain,
product(identity,X_209,multiply(inverse(inverse(X_209)),identity)),
inference(subst,[],[refute_0_24:[bind(X_208,$fot(X_209))]]) ).
cnf(refute_0_26,plain,
multiply(inverse(inverse(X_209)),identity) = multiply(identity,X_209),
inference(resolve,[$cnf( product(identity,X_209,multiply(inverse(inverse(X_209)),identity)) )],[refute_0_25,refute_0_15]) ).
cnf(refute_0_27,plain,
product(identity,X_54,multiply(identity,X_54)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(X_54))]]) ).
cnf(refute_0_28,plain,
product(identity,X_50,X_50),
inference(subst,[],[left_identity:[bind(A,$fot(X_50))]]) ).
cnf(refute_0_29,plain,
( ~ product(identity,X_50,X_50)
| ~ product(identity,X_50,X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(identity)),bind(Y,$fot(X_50)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_30,plain,
( ~ product(identity,X_50,X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(identity,X_50,X_50) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ product(identity,X_54,multiply(identity,X_54))
| multiply(identity,X_54) = X_54 ),
inference(subst,[],[refute_0_30:[bind(X_50,$fot(X_54)),bind(X_53,$fot(multiply(identity,X_54)))]]) ).
cnf(refute_0_32,plain,
multiply(identity,X_54) = X_54,
inference(resolve,[$cnf( product(identity,X_54,multiply(identity,X_54)) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(identity,X_209) = X_209,
inference(subst,[],[refute_0_32:[bind(X_54,$fot(X_209))]]) ).
cnf(refute_0_34,plain,
( multiply(identity,X_209) != X_209
| multiply(inverse(inverse(X_209)),identity) != multiply(identity,X_209)
| multiply(inverse(inverse(X_209)),identity) = X_209 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_209)),identity),multiply(identity,X_209)) ),[1],$fot(X_209)]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(inverse(X_209)),identity) != multiply(identity,X_209)
| multiply(inverse(inverse(X_209)),identity) = X_209 ),
inference(resolve,[$cnf( $equal(multiply(identity,X_209),X_209) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(inverse(inverse(X_209)),identity) = X_209,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_209)),identity),multiply(identity,X_209)) )],[refute_0_26,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(inverse(inverse(X_210)),identity) = X_210,
inference(subst,[],[refute_0_36:[bind(X_209,$fot(X_210))]]) ).
cnf(refute_0_38,plain,
( multiply(inverse(inverse(X_210)),identity) != X_210
| multiply(inverse(inverse(X_210)),identity) != multiply(multiply(inverse(inverse(X_210)),identity),identity)
| X_210 = multiply(multiply(inverse(inverse(X_210)),identity),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),multiply(multiply(inverse(inverse(X_210)),identity),identity)) ),[0],$fot(X_210)]]) ).
cnf(refute_0_39,plain,
( multiply(inverse(inverse(X_210)),identity) != multiply(multiply(inverse(inverse(X_210)),identity),identity)
| X_210 = multiply(multiply(inverse(inverse(X_210)),identity),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),X_210) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
X_210 = multiply(multiply(inverse(inverse(X_210)),identity),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),multiply(multiply(inverse(inverse(X_210)),identity),identity)) )],[refute_0_14,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(inverse(inverse(X_210)),identity) != X_210
| multiply(inverse(inverse(X_210)),identity) != multiply(multiply(inverse(inverse(X_210)),identity),identity)
| multiply(inverse(inverse(X_210)),identity) = multiply(X_210,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),multiply(multiply(inverse(inverse(X_210)),identity),identity)) ),[1,0],$fot(X_210)]]) ).
cnf(refute_0_42,plain,
( multiply(inverse(inverse(X_210)),identity) != multiply(multiply(inverse(inverse(X_210)),identity),identity)
| multiply(inverse(inverse(X_210)),identity) = multiply(X_210,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),X_210) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(inverse(inverse(X_210)),identity) = multiply(X_210,identity),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),multiply(multiply(inverse(inverse(X_210)),identity),identity)) )],[refute_0_14,refute_0_42]) ).
cnf(refute_0_44,plain,
( multiply(inverse(inverse(X_210)),identity) != X_210
| multiply(inverse(inverse(X_210)),identity) != multiply(X_210,identity)
| X_210 = multiply(X_210,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),multiply(X_210,identity)) ),[0],$fot(X_210)]]) ).
cnf(refute_0_45,plain,
( multiply(inverse(inverse(X_210)),identity) != multiply(X_210,identity)
| X_210 = multiply(X_210,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),X_210) )],[refute_0_37,refute_0_44]) ).
cnf(refute_0_46,plain,
X_210 = multiply(X_210,identity),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),multiply(X_210,identity)) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_48,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_49,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( X_210 != multiply(X_210,identity)
| multiply(X_210,identity) = X_210 ),
inference(subst,[],[refute_0_49:[bind(X0,$fot(X_210)),bind(Y0,$fot(multiply(X_210,identity)))]]) ).
cnf(refute_0_51,plain,
multiply(X_210,identity) = X_210,
inference(resolve,[$cnf( $equal(X_210,multiply(X_210,identity)) )],[refute_0_46,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(inverse(inverse(X_210)),identity) = inverse(inverse(X_210)),
inference(subst,[],[refute_0_51:[bind(X_210,$fot(inverse(inverse(X_210))))]]) ).
cnf(refute_0_53,plain,
multiply(multiply(inverse(inverse(X_210)),identity),identity) = multiply(inverse(inverse(X_210)),identity),
inference(subst,[],[refute_0_51:[bind(X_210,$fot(multiply(inverse(inverse(X_210)),identity)))]]) ).
cnf(refute_0_54,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_55,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(multiply(inverse(inverse(X_210)),identity),identity) != multiply(inverse(inverse(X_210)),identity)
| multiply(inverse(inverse(X_210)),identity) != inverse(inverse(X_210))
| multiply(multiply(inverse(inverse(X_210)),identity),identity) = inverse(inverse(X_210)) ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(multiply(multiply(inverse(inverse(X_210)),identity),identity))),bind(Y0,$fot(multiply(inverse(inverse(X_210)),identity))),bind(Z0,$fot(inverse(inverse(X_210))))]]) ).
cnf(refute_0_57,plain,
( multiply(inverse(inverse(X_210)),identity) != inverse(inverse(X_210))
| multiply(multiply(inverse(inverse(X_210)),identity),identity) = inverse(inverse(X_210)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_210)),identity),identity),multiply(inverse(inverse(X_210)),identity)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(multiply(inverse(inverse(X_210)),identity),identity) = inverse(inverse(X_210)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_210)),identity),inverse(inverse(X_210))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
( X_210 != multiply(multiply(inverse(inverse(X_210)),identity),identity)
| multiply(multiply(inverse(inverse(X_210)),identity),identity) != inverse(inverse(X_210))
| X_210 = inverse(inverse(X_210)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_210,inverse(inverse(X_210))) ),[0],$fot(multiply(multiply(inverse(inverse(X_210)),identity),identity))]]) ).
cnf(refute_0_60,plain,
( X_210 != multiply(multiply(inverse(inverse(X_210)),identity),identity)
| X_210 = inverse(inverse(X_210)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_210)),identity),identity),inverse(inverse(X_210))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
X_210 = inverse(inverse(X_210)),
inference(resolve,[$cnf( $equal(X_210,multiply(multiply(inverse(inverse(X_210)),identity),identity)) )],[refute_0_40,refute_0_60]) ).
cnf(refute_0_62,plain,
X_212 = inverse(inverse(X_212)),
inference(subst,[],[refute_0_61:[bind(X_210,$fot(X_212))]]) ).
cnf(refute_0_63,plain,
( X_212 != inverse(inverse(X_212))
| inverse(inverse(X_212)) = X_212 ),
inference(subst,[],[refute_0_49:[bind(X0,$fot(X_212)),bind(Y0,$fot(inverse(inverse(X_212))))]]) ).
cnf(refute_0_64,plain,
inverse(inverse(X_212)) = X_212,
inference(resolve,[$cnf( $equal(X_212,inverse(inverse(X_212))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( inverse(inverse(X_212)) != X_212
| ~ product(inverse(inverse(X_212)),inverse(X_212),identity)
| product(X_212,inverse(X_212),identity) ),
introduced(tautology,[equality,[$cnf( product(inverse(inverse(X_212)),inverse(X_212),identity) ),[0],$fot(X_212)]]) ).
cnf(refute_0_66,plain,
( ~ product(inverse(inverse(X_212)),inverse(X_212),identity)
| product(X_212,inverse(X_212),identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_212)),X_212) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
product(X_212,inverse(X_212),identity),
inference(resolve,[$cnf( product(inverse(inverse(X_212)),inverse(X_212),identity) )],[refute_0_1,refute_0_66]) ).
cnf(refute_0_68,plain,
product(a,inverse(a),identity),
inference(subst,[],[refute_0_67:[bind(X_212,$fot(a))]]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( product(a,inverse(a),identity) )],[refute_0_68,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n010.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 05:16:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.67
% 0.48/0.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.67
%------------------------------------------------------------------------------