TSTP Solution File: GRP538-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP538-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 10:42:13 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of clauses : 94 ( 51 unt; 0 nHn; 50 RR)
% Number of literals : 155 ( 154 equ; 63 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,B),divide(divide(A,C),B)) = C ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)) ).
cnf(inverse,axiom,
inverse(A) = divide(divide(B,B),A) ).
cnf(identity,axiom,
identity = divide(A,A) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( identity != divide(A,A)
| divide(A,A) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(divide(A,A)))]]) ).
cnf(refute_0_4,plain,
divide(A,A) = identity,
inference(resolve,[$cnf( $equal(identity,divide(A,A)) )],[identity,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(B,B) = identity,
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_6,plain,
divide(divide(B,B),A) = divide(divide(B,B),A),
introduced(tautology,[refl,[$fot(divide(divide(B,B),A))]]) ).
cnf(refute_0_7,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_8,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(divide(B,B),A) = divide(identity,A),
inference(resolve,[$cnf( $equal(divide(B,B),identity) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( divide(divide(B,B),A) != divide(identity,A)
| inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) ),[1],$fot(divide(identity,A))]]) ).
cnf(refute_0_11,plain,
( inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(identity,A)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
inverse(A) = divide(identity,A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_11]) ).
cnf(refute_0_13,plain,
inverse(inverse(X_10)) = divide(identity,inverse(X_10)),
inference(subst,[],[refute_0_12:[bind(A,$fot(inverse(X_10)))]]) ).
cnf(refute_0_14,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_15,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_14]) ).
cnf(refute_0_16,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_15:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_17,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_18,plain,
( divide(A,divide(divide(C,C),B)) != divide(A,divide(divide(C,C),B))
| divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_19,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_22,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(identity,X_10) = divide(identity,inverse(X_10)),
inference(subst,[],[refute_0_23:[bind(A,$fot(identity)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_25,plain,
( multiply(identity,X_10) != divide(identity,inverse(X_10))
| divide(identity,inverse(X_10)) = multiply(identity,X_10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(identity,X_10))),bind(Y,$fot(divide(identity,inverse(X_10))))]]) ).
cnf(refute_0_26,plain,
divide(identity,inverse(X_10)) = multiply(identity,X_10),
inference(resolve,[$cnf( $equal(multiply(identity,X_10),divide(identity,inverse(X_10))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( divide(identity,inverse(X_10)) != multiply(identity,X_10)
| inverse(inverse(X_10)) != divide(identity,inverse(X_10))
| inverse(inverse(X_10)) = multiply(identity,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_10)),divide(identity,inverse(X_10))) ),[1],$fot(multiply(identity,X_10))]]) ).
cnf(refute_0_28,plain,
( inverse(inverse(X_10)) != divide(identity,inverse(X_10))
| inverse(inverse(X_10)) = multiply(identity,X_10) ),
inference(resolve,[$cnf( $equal(divide(identity,inverse(X_10)),multiply(identity,X_10)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
inverse(inverse(X_10)) = multiply(identity,X_10),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),divide(identity,inverse(X_10))) )],[refute_0_13,refute_0_28]) ).
cnf(refute_0_30,plain,
divide(divide(X_3,X_3),divide(divide(X_3,X_4),X_3)) = X_4,
inference(subst,[],[single_axiom:[bind(A,$fot(X_3)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_31,plain,
identity = divide(X_3,X_3),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_32,plain,
( identity != divide(X_3,X_3)
| divide(X_3,X_3) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(divide(X_3,X_3)))]]) ).
cnf(refute_0_33,plain,
divide(X_3,X_3) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X_3,X_3)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( divide(X_3,X_3) != identity
| divide(divide(X_3,X_3),divide(divide(X_3,X_4),X_3)) != X_4
| divide(identity,divide(divide(X_3,X_4),X_3)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,X_3),divide(divide(X_3,X_4),X_3)),X_4) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_35,plain,
( divide(divide(X_3,X_3),divide(divide(X_3,X_4),X_3)) != X_4
| divide(identity,divide(divide(X_3,X_4),X_3)) = X_4 ),
inference(resolve,[$cnf( $equal(divide(X_3,X_3),identity) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
divide(identity,divide(divide(X_3,X_4),X_3)) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_3,X_3),divide(divide(X_3,X_4),X_3)),X_4) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
( inverse(A) != divide(identity,A)
| divide(identity,A) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(identity,A)))]]) ).
cnf(refute_0_38,plain,
divide(identity,A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(identity,A)) )],[refute_0_12,refute_0_37]) ).
cnf(refute_0_39,plain,
divide(identity,divide(divide(X_3,X_4),X_3)) = inverse(divide(divide(X_3,X_4),X_3)),
inference(subst,[],[refute_0_38:[bind(A,$fot(divide(divide(X_3,X_4),X_3)))]]) ).
cnf(refute_0_40,plain,
( divide(identity,divide(divide(X_3,X_4),X_3)) != X_4
| divide(identity,divide(divide(X_3,X_4),X_3)) != inverse(divide(divide(X_3,X_4),X_3))
| inverse(divide(divide(X_3,X_4),X_3)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(identity,divide(divide(X_3,X_4),X_3)),X_4) ),[0],$fot(inverse(divide(divide(X_3,X_4),X_3)))]]) ).
cnf(refute_0_41,plain,
( divide(identity,divide(divide(X_3,X_4),X_3)) != X_4
| inverse(divide(divide(X_3,X_4),X_3)) = X_4 ),
inference(resolve,[$cnf( $equal(divide(identity,divide(divide(X_3,X_4),X_3)),inverse(divide(divide(X_3,X_4),X_3))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
inverse(divide(divide(X_3,X_4),X_3)) = X_4,
inference(resolve,[$cnf( $equal(divide(identity,divide(divide(X_3,X_4),X_3)),X_4) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
inverse(divide(divide(X_6,X_6),X_6)) = X_6,
inference(subst,[],[refute_0_42:[bind(X_3,$fot(X_6)),bind(X_4,$fot(X_6))]]) ).
cnf(refute_0_44,plain,
identity = divide(X_6,X_6),
inference(subst,[],[identity:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_45,plain,
( identity != divide(X_6,X_6)
| divide(X_6,X_6) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(divide(X_6,X_6)))]]) ).
cnf(refute_0_46,plain,
divide(X_6,X_6) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X_6,X_6)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( divide(X_6,X_6) != identity
| inverse(divide(divide(X_6,X_6),X_6)) != X_6
| inverse(divide(identity,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(X_6,X_6),X_6)),X_6) ),[0,0,0],$fot(identity)]]) ).
cnf(refute_0_48,plain,
( inverse(divide(divide(X_6,X_6),X_6)) != X_6
| inverse(divide(identity,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(divide(X_6,X_6),identity) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
inverse(divide(identity,X_6)) = X_6,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_6,X_6),X_6)),X_6) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
divide(identity,X_6) = inverse(X_6),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_51,plain,
inverse(divide(identity,X_6)) = inverse(divide(identity,X_6)),
introduced(tautology,[refl,[$fot(inverse(divide(identity,X_6)))]]) ).
cnf(refute_0_52,plain,
( divide(identity,X_6) != inverse(X_6)
| inverse(divide(identity,X_6)) != inverse(divide(identity,X_6))
| inverse(divide(identity,X_6)) = inverse(inverse(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(identity,X_6)),inverse(divide(identity,X_6))) ),[1,0],$fot(inverse(X_6))]]) ).
cnf(refute_0_53,plain,
( divide(identity,X_6) != inverse(X_6)
| inverse(divide(identity,X_6)) = inverse(inverse(X_6)) ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,X_6)),inverse(divide(identity,X_6))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
inverse(divide(identity,X_6)) = inverse(inverse(X_6)),
inference(resolve,[$cnf( $equal(divide(identity,X_6),inverse(X_6)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( inverse(divide(identity,X_6)) != X_6
| inverse(divide(identity,X_6)) != inverse(inverse(X_6))
| inverse(inverse(X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(identity,X_6)),X_6) ),[0],$fot(inverse(inverse(X_6)))]]) ).
cnf(refute_0_56,plain,
( inverse(divide(identity,X_6)) != X_6
| inverse(inverse(X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(inverse(divide(identity,X_6)),inverse(inverse(X_6))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
inverse(inverse(X_6)) = X_6,
inference(resolve,[$cnf( $equal(inverse(divide(identity,X_6)),X_6) )],[refute_0_49,refute_0_56]) ).
cnf(refute_0_58,plain,
inverse(inverse(X_10)) = X_10,
inference(subst,[],[refute_0_57:[bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_59,plain,
( inverse(inverse(X_10)) != X_10
| inverse(inverse(X_10)) != multiply(identity,X_10)
| X_10 = multiply(identity,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_10)),multiply(identity,X_10)) ),[0],$fot(X_10)]]) ).
cnf(refute_0_60,plain,
( inverse(inverse(X_10)) != multiply(identity,X_10)
| X_10 = multiply(identity,X_10) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
X_10 = multiply(identity,X_10),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),multiply(identity,X_10)) )],[refute_0_29,refute_0_60]) ).
cnf(refute_0_62,plain,
( X_10 != multiply(identity,X_10)
| multiply(identity,X_10) = X_10 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_10)),bind(Y,$fot(multiply(identity,X_10)))]]) ).
cnf(refute_0_63,plain,
multiply(identity,X_10) = X_10,
inference(resolve,[$cnf( $equal(X_10,multiply(identity,X_10)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(identity,a2) = a2,
inference(subst,[],[refute_0_63:[bind(X_10,$fot(a2))]]) ).
cnf(refute_0_65,plain,
identity = divide(inverse(X_10),inverse(X_10)),
inference(subst,[],[identity:[bind(A,$fot(inverse(X_10)))]]) ).
cnf(refute_0_66,plain,
multiply(inverse(X_10),X_10) = divide(inverse(X_10),inverse(X_10)),
inference(subst,[],[refute_0_23:[bind(A,$fot(inverse(X_10))),bind(B,$fot(X_10))]]) ).
cnf(refute_0_67,plain,
( multiply(inverse(X_10),X_10) != divide(inverse(X_10),inverse(X_10))
| divide(inverse(X_10),inverse(X_10)) = multiply(inverse(X_10),X_10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(inverse(X_10),X_10))),bind(Y,$fot(divide(inverse(X_10),inverse(X_10))))]]) ).
cnf(refute_0_68,plain,
divide(inverse(X_10),inverse(X_10)) = multiply(inverse(X_10),X_10),
inference(resolve,[$cnf( $equal(multiply(inverse(X_10),X_10),divide(inverse(X_10),inverse(X_10))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( divide(inverse(X_10),inverse(X_10)) != multiply(inverse(X_10),X_10)
| identity != divide(inverse(X_10),inverse(X_10))
| identity = multiply(inverse(X_10),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(identity,divide(inverse(X_10),inverse(X_10))) ),[1],$fot(multiply(inverse(X_10),X_10))]]) ).
cnf(refute_0_70,plain,
( identity != divide(inverse(X_10),inverse(X_10))
| identity = multiply(inverse(X_10),X_10) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_10),inverse(X_10)),multiply(inverse(X_10),X_10)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
identity = multiply(inverse(X_10),X_10),
inference(resolve,[$cnf( $equal(identity,divide(inverse(X_10),inverse(X_10))) )],[refute_0_65,refute_0_70]) ).
cnf(refute_0_72,plain,
( identity != multiply(inverse(X_10),X_10)
| multiply(inverse(X_10),X_10) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_10),X_10)))]]) ).
cnf(refute_0_73,plain,
multiply(inverse(X_10),X_10) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(X_10),X_10)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(b2),b2) = identity,
inference(subst,[],[refute_0_73:[bind(X_10,$fot(b2))]]) ).
cnf(refute_0_75,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(multiply(inverse(b2),b2),a2),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(b2),b2),a2))]]) ).
cnf(refute_0_76,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(b2),b2) != identity
| multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(b2),b2) != identity
| multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),identity) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_80,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(identity,a2)
| multiply(identity,a2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(subst,[],[refute_0_80:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(identity,a2))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_82,plain,
( multiply(identity,a2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(identity,a2)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_64,refute_0_82]) ).
cnf(refute_0_84,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_85,plain,
( a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_85,prove_these_axioms_2]) ).
cnf(refute_0_87,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_88,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_87,refute_0_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP538-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 14:57:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------