TSTP Solution File: GRP530-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP530-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 10:42:10 EDT 2022
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 33
% Syntax : Number of clauses : 127 ( 69 unt; 0 nHn; 59 RR)
% Number of literals : 210 ( 209 equ; 85 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 250 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,divide(B,C)),divide(A,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(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
inverse(A) = divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A),
inference(subst,[],[inverse:[bind(B,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_1,plain,
inverse(divide(X_1,X_1)) = divide(divide(X_1,X_1),divide(X_1,X_1)),
inference(subst,[],[inverse:[bind(A,$fot(divide(X_1,X_1))),bind(B,$fot(X_1))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( inverse(divide(X_1,X_1)) != divide(divide(X_1,X_1),divide(X_1,X_1))
| divide(divide(X_1,X_1),divide(X_1,X_1)) = inverse(divide(X_1,X_1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(divide(X_1,X_1)))),bind(Y,$fot(divide(divide(X_1,X_1),divide(X_1,X_1))))]]) ).
cnf(refute_0_6,plain,
divide(divide(X_1,X_1),divide(X_1,X_1)) = inverse(divide(X_1,X_1)),
inference(resolve,[$cnf( $equal(inverse(divide(X_1,X_1)),divide(divide(X_1,X_1),divide(X_1,X_1))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( divide(divide(X_1,X_1),divide(X_1,X_1)) != inverse(divide(X_1,X_1))
| inverse(A) != divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)
| inverse(A) = divide(inverse(divide(X_1,X_1)),A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)) ),[1,0],$fot(inverse(divide(X_1,X_1)))]]) ).
cnf(refute_0_8,plain,
( inverse(A) != divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)
| inverse(A) = divide(inverse(divide(X_1,X_1)),A) ),
inference(resolve,[$cnf( $equal(divide(divide(X_1,X_1),divide(X_1,X_1)),inverse(divide(X_1,X_1))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
inverse(A) = divide(inverse(divide(X_1,X_1)),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
inverse(inverse(X_19)) = divide(inverse(divide(X_1,X_1)),inverse(X_19)),
inference(subst,[],[refute_0_9:[bind(A,$fot(inverse(X_19)))]]) ).
cnf(refute_0_11,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_12,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_11]) ).
cnf(refute_0_13,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_12:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_14,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_15,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_16,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_19,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(inverse(divide(X_1,X_1)),X_19) = divide(inverse(divide(X_1,X_1)),inverse(X_19)),
inference(subst,[],[refute_0_20:[bind(A,$fot(inverse(divide(X_1,X_1)))),bind(B,$fot(X_19))]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(divide(X_1,X_1)),X_19) != divide(inverse(divide(X_1,X_1)),inverse(X_19))
| divide(inverse(divide(X_1,X_1)),inverse(X_19)) = multiply(inverse(divide(X_1,X_1)),X_19) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(inverse(divide(X_1,X_1)),X_19))),bind(Y,$fot(divide(inverse(divide(X_1,X_1)),inverse(X_19))))]]) ).
cnf(refute_0_23,plain,
divide(inverse(divide(X_1,X_1)),inverse(X_19)) = multiply(inverse(divide(X_1,X_1)),X_19),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_1,X_1)),X_19),divide(inverse(divide(X_1,X_1)),inverse(X_19))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( divide(inverse(divide(X_1,X_1)),inverse(X_19)) != multiply(inverse(divide(X_1,X_1)),X_19)
| inverse(inverse(X_19)) != divide(inverse(divide(X_1,X_1)),inverse(X_19))
| inverse(inverse(X_19)) = multiply(inverse(divide(X_1,X_1)),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_19)),divide(inverse(divide(X_1,X_1)),inverse(X_19))) ),[1],$fot(multiply(inverse(divide(X_1,X_1)),X_19))]]) ).
cnf(refute_0_25,plain,
( inverse(inverse(X_19)) != divide(inverse(divide(X_1,X_1)),inverse(X_19))
| inverse(inverse(X_19)) = multiply(inverse(divide(X_1,X_1)),X_19) ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_1,X_1)),inverse(X_19)),multiply(inverse(divide(X_1,X_1)),X_19)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
inverse(inverse(X_19)) = multiply(inverse(divide(X_1,X_1)),X_19),
inference(resolve,[$cnf( $equal(inverse(inverse(X_19)),divide(inverse(divide(X_1,X_1)),inverse(X_19))) )],[refute_0_10,refute_0_25]) ).
cnf(refute_0_27,plain,
inverse(divide(divide(X_5,X_6),X_5)) = divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)),
inference(subst,[],[inverse:[bind(A,$fot(divide(divide(X_5,X_6),X_5))),bind(B,$fot(divide(X_5,X_6)))]]) ).
cnf(refute_0_28,plain,
divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)) = X_6,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(X_5,X_6))),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_29,plain,
( divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)) != X_6
| inverse(divide(divide(X_5,X_6),X_5)) != divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5))
| inverse(divide(divide(X_5,X_6),X_5)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(X_5,X_6),X_5)),divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5))) ),[1],$fot(X_6)]]) ).
cnf(refute_0_30,plain,
( inverse(divide(divide(X_5,X_6),X_5)) != divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5))
| inverse(divide(divide(X_5,X_6),X_5)) = X_6 ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)),X_6) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
inverse(divide(divide(X_5,X_6),X_5)) = X_6,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_5,X_6),X_5)),divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(divide(divide(X_12,X_12),X_12)) = X_12,
inference(subst,[],[refute_0_31:[bind(X_5,$fot(X_12)),bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_33,plain,
inverse(X_12) = divide(divide(X_12,X_12),X_12),
inference(subst,[],[inverse:[bind(A,$fot(X_12)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_34,plain,
( inverse(X_12) != divide(divide(X_12,X_12),X_12)
| divide(divide(X_12,X_12),X_12) = inverse(X_12) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_12))),bind(Y,$fot(divide(divide(X_12,X_12),X_12)))]]) ).
cnf(refute_0_35,plain,
divide(divide(X_12,X_12),X_12) = inverse(X_12),
inference(resolve,[$cnf( $equal(inverse(X_12),divide(divide(X_12,X_12),X_12)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( divide(divide(X_12,X_12),X_12) != inverse(X_12)
| inverse(divide(divide(X_12,X_12),X_12)) != X_12
| inverse(inverse(X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(X_12,X_12),X_12)),X_12) ),[0,0],$fot(inverse(X_12))]]) ).
cnf(refute_0_37,plain,
( inverse(divide(divide(X_12,X_12),X_12)) != X_12
| inverse(inverse(X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,X_12),X_12),inverse(X_12)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_12,X_12),X_12)),X_12) )],[refute_0_32,refute_0_37]) ).
cnf(refute_0_39,plain,
inverse(inverse(X_19)) = X_19,
inference(subst,[],[refute_0_38:[bind(X_12,$fot(X_19))]]) ).
cnf(refute_0_40,plain,
( inverse(inverse(X_19)) != X_19
| inverse(inverse(X_19)) != multiply(inverse(divide(X_1,X_1)),X_19)
| X_19 = multiply(inverse(divide(X_1,X_1)),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_19)),multiply(inverse(divide(X_1,X_1)),X_19)) ),[0],$fot(X_19)]]) ).
cnf(refute_0_41,plain,
( inverse(inverse(X_19)) != multiply(inverse(divide(X_1,X_1)),X_19)
| X_19 = multiply(inverse(divide(X_1,X_1)),X_19) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_19)),X_19) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
X_19 = multiply(inverse(divide(X_1,X_1)),X_19),
inference(resolve,[$cnf( $equal(inverse(inverse(X_19)),multiply(inverse(divide(X_1,X_1)),X_19)) )],[refute_0_26,refute_0_41]) ).
cnf(refute_0_43,plain,
inverse(multiply(inverse(X_25),X_25)) = divide(divide(B,B),multiply(inverse(X_25),X_25)),
inference(subst,[],[inverse:[bind(A,$fot(multiply(inverse(X_25),X_25)))]]) ).
cnf(refute_0_44,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)) = X_6,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(B,B))),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_45,plain,
inverse(X_5) = divide(divide(B,B),X_5),
inference(subst,[],[inverse:[bind(A,$fot(X_5))]]) ).
cnf(refute_0_46,plain,
( inverse(X_5) != divide(divide(B,B),X_5)
| divide(divide(B,B),X_5) = inverse(X_5) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_5))),bind(Y,$fot(divide(divide(B,B),X_5)))]]) ).
cnf(refute_0_47,plain,
divide(divide(B,B),X_5) = inverse(X_5),
inference(resolve,[$cnf( $equal(inverse(X_5),divide(divide(B,B),X_5)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( divide(divide(B,B),X_5) != inverse(X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)) != X_6
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)),X_6) ),[0,1],$fot(inverse(X_5))]]) ).
cnf(refute_0_49,plain,
( divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)) != X_6
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = X_6 ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_5),inverse(X_5)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = X_6,
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)),X_6) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
divide(divide(B,B),divide(X_5,X_6)) = inverse(divide(X_5,X_6)),
inference(subst,[],[refute_0_12:[bind(A,$fot(divide(X_5,X_6)))]]) ).
cnf(refute_0_52,plain,
multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) = multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),
introduced(tautology,[refl,[$fot(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5))]]) ).
cnf(refute_0_53,plain,
( multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) != multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)
| divide(divide(B,B),divide(X_5,X_6)) != inverse(divide(X_5,X_6))
| multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) = multiply(inverse(divide(X_5,X_6)),X_5) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)) ),[1,0],$fot(inverse(divide(X_5,X_6)))]]) ).
cnf(refute_0_54,plain,
( divide(divide(B,B),divide(X_5,X_6)) != inverse(divide(X_5,X_6))
| multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) = multiply(inverse(divide(X_5,X_6)),X_5) ),
inference(resolve,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) = multiply(inverse(divide(X_5,X_6)),X_5),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(X_5,X_6)),inverse(divide(X_5,X_6))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_57,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_20,refute_0_56]) ).
cnf(refute_0_58,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),
inference(subst,[],[refute_0_57:[bind(A,$fot(divide(divide(B,B),divide(X_5,X_6)))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_59,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_60,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) != multiply(inverse(divide(X_5,X_6)),X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(inverse(divide(X_5,X_6)),X_5) ),
inference(subst,[],[refute_0_60:[bind(X,$fot(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)))),bind(Y,$fot(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5))),bind(Z,$fot(multiply(inverse(divide(X_5,X_6)),X_5)))]]) ).
cnf(refute_0_62,plain,
( multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) != multiply(inverse(divide(X_5,X_6)),X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(inverse(divide(X_5,X_6)),X_5) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(inverse(divide(X_5,X_6)),X_5),
inference(resolve,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),multiply(inverse(divide(X_5,X_6)),X_5)) )],[refute_0_55,refute_0_62]) ).
cnf(refute_0_64,plain,
( divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != X_6
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != multiply(inverse(divide(X_5,X_6)),X_5)
| multiply(inverse(divide(X_5,X_6)),X_5) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),X_6) ),[0],$fot(multiply(inverse(divide(X_5,X_6)),X_5))]]) ).
cnf(refute_0_65,plain,
( divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != X_6
| multiply(inverse(divide(X_5,X_6)),X_5) = X_6 ),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),multiply(inverse(divide(X_5,X_6)),X_5)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(inverse(divide(X_5,X_6)),X_5) = X_6,
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),X_6) )],[refute_0_50,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(divide(inverse(divide(X_1,X_1)),X_15)),inverse(divide(X_1,X_1))) = X_15,
inference(subst,[],[refute_0_66:[bind(X_5,$fot(inverse(divide(X_1,X_1)))),bind(X_6,$fot(X_15))]]) ).
cnf(refute_0_68,plain,
inverse(X_15) = divide(inverse(divide(X_1,X_1)),X_15),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_69,plain,
( inverse(X_15) != divide(inverse(divide(X_1,X_1)),X_15)
| divide(inverse(divide(X_1,X_1)),X_15) = inverse(X_15) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_15))),bind(Y,$fot(divide(inverse(divide(X_1,X_1)),X_15)))]]) ).
cnf(refute_0_70,plain,
divide(inverse(divide(X_1,X_1)),X_15) = inverse(X_15),
inference(resolve,[$cnf( $equal(inverse(X_15),divide(inverse(divide(X_1,X_1)),X_15)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( multiply(inverse(divide(inverse(divide(X_1,X_1)),X_15)),inverse(divide(X_1,X_1))) != X_15
| divide(inverse(divide(X_1,X_1)),X_15) != inverse(X_15)
| multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = X_15 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(inverse(divide(X_1,X_1)),X_15)),inverse(divide(X_1,X_1))),X_15) ),[0,0,0],$fot(inverse(X_15))]]) ).
cnf(refute_0_72,plain,
( multiply(inverse(divide(inverse(divide(X_1,X_1)),X_15)),inverse(divide(X_1,X_1))) != X_15
| multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = X_15 ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_1,X_1)),X_15),inverse(X_15)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = X_15,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(inverse(divide(X_1,X_1)),X_15)),inverse(divide(X_1,X_1))),X_15) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
inverse(inverse(X_15)) = X_15,
inference(subst,[],[refute_0_38:[bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_75,plain,
multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))))]]) ).
cnf(refute_0_76,plain,
( multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) != multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1)))
| inverse(inverse(X_15)) != X_15
| multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = multiply(X_15,inverse(divide(X_1,X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))),multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1)))) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_77,plain,
( inverse(inverse(X_15)) != X_15
| multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = multiply(X_15,inverse(divide(X_1,X_1))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))),multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) = multiply(X_15,inverse(divide(X_1,X_1))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_15)),X_15) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
( multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) != X_15
| multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) != multiply(X_15,inverse(divide(X_1,X_1)))
| multiply(X_15,inverse(divide(X_1,X_1))) = X_15 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))),X_15) ),[0],$fot(multiply(X_15,inverse(divide(X_1,X_1))))]]) ).
cnf(refute_0_80,plain,
( multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))) != X_15
| multiply(X_15,inverse(divide(X_1,X_1))) = X_15 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))),multiply(X_15,inverse(divide(X_1,X_1)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(X_15,inverse(divide(X_1,X_1))) = X_15,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_15)),inverse(divide(X_1,X_1))),X_15) )],[refute_0_73,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(X_15,inverse(divide(inverse(X_19),inverse(X_19)))) = X_15,
inference(subst,[],[refute_0_81:[bind(X_1,$fot(inverse(X_19)))]]) ).
cnf(refute_0_83,plain,
multiply(inverse(X_19),X_19) = divide(inverse(X_19),inverse(X_19)),
inference(subst,[],[refute_0_20:[bind(A,$fot(inverse(X_19))),bind(B,$fot(X_19))]]) ).
cnf(refute_0_84,plain,
( multiply(inverse(X_19),X_19) != divide(inverse(X_19),inverse(X_19))
| divide(inverse(X_19),inverse(X_19)) = multiply(inverse(X_19),X_19) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(inverse(X_19),X_19))),bind(Y,$fot(divide(inverse(X_19),inverse(X_19))))]]) ).
cnf(refute_0_85,plain,
divide(inverse(X_19),inverse(X_19)) = multiply(inverse(X_19),X_19),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),X_19),divide(inverse(X_19),inverse(X_19))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( multiply(X_15,inverse(divide(inverse(X_19),inverse(X_19)))) != X_15
| divide(inverse(X_19),inverse(X_19)) != multiply(inverse(X_19),X_19)
| multiply(X_15,inverse(multiply(inverse(X_19),X_19))) = X_15 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_15,inverse(divide(inverse(X_19),inverse(X_19)))),X_15) ),[0,1,0],$fot(multiply(inverse(X_19),X_19))]]) ).
cnf(refute_0_87,plain,
( multiply(X_15,inverse(divide(inverse(X_19),inverse(X_19)))) != X_15
| multiply(X_15,inverse(multiply(inverse(X_19),X_19))) = X_15 ),
inference(resolve,[$cnf( $equal(divide(inverse(X_19),inverse(X_19)),multiply(inverse(X_19),X_19)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(X_15,inverse(multiply(inverse(X_19),X_19))) = X_15,
inference(resolve,[$cnf( $equal(multiply(X_15,inverse(divide(inverse(X_19),inverse(X_19)))),X_15) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(X_18,inverse(X_12)) = divide(X_18,inverse(inverse(X_12))),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_18)),bind(B,$fot(inverse(X_12)))]]) ).
cnf(refute_0_90,plain,
( multiply(X_18,inverse(X_12)) != divide(X_18,inverse(inverse(X_12)))
| inverse(inverse(X_12)) != X_12
| multiply(X_18,inverse(X_12)) = divide(X_18,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_18,inverse(X_12)),divide(X_18,inverse(inverse(X_12)))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_91,plain,
( multiply(X_18,inverse(X_12)) != divide(X_18,inverse(inverse(X_12)))
| multiply(X_18,inverse(X_12)) = divide(X_18,X_12) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_12)),X_12) )],[refute_0_38,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(X_18,inverse(X_12)) = divide(X_18,X_12),
inference(resolve,[$cnf( $equal(multiply(X_18,inverse(X_12)),divide(X_18,inverse(inverse(X_12)))) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(X_15,inverse(multiply(inverse(X_19),X_19))) = divide(X_15,multiply(inverse(X_19),X_19)),
inference(subst,[],[refute_0_92:[bind(X_12,$fot(multiply(inverse(X_19),X_19))),bind(X_18,$fot(X_15))]]) ).
cnf(refute_0_94,plain,
( multiply(X_15,inverse(multiply(inverse(X_19),X_19))) != X_15
| multiply(X_15,inverse(multiply(inverse(X_19),X_19))) != divide(X_15,multiply(inverse(X_19),X_19))
| divide(X_15,multiply(inverse(X_19),X_19)) = X_15 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_15,inverse(multiply(inverse(X_19),X_19))),X_15) ),[0],$fot(divide(X_15,multiply(inverse(X_19),X_19)))]]) ).
cnf(refute_0_95,plain,
( multiply(X_15,inverse(multiply(inverse(X_19),X_19))) != X_15
| divide(X_15,multiply(inverse(X_19),X_19)) = X_15 ),
inference(resolve,[$cnf( $equal(multiply(X_15,inverse(multiply(inverse(X_19),X_19))),divide(X_15,multiply(inverse(X_19),X_19))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
divide(X_15,multiply(inverse(X_19),X_19)) = X_15,
inference(resolve,[$cnf( $equal(multiply(X_15,inverse(multiply(inverse(X_19),X_19))),X_15) )],[refute_0_88,refute_0_95]) ).
cnf(refute_0_97,plain,
divide(divide(B,B),multiply(inverse(X_25),X_25)) = divide(B,B),
inference(subst,[],[refute_0_96:[bind(X_15,$fot(divide(B,B))),bind(X_19,$fot(X_25))]]) ).
cnf(refute_0_98,plain,
( divide(divide(B,B),multiply(inverse(X_25),X_25)) != divide(B,B)
| inverse(multiply(inverse(X_25),X_25)) != divide(divide(B,B),multiply(inverse(X_25),X_25))
| inverse(multiply(inverse(X_25),X_25)) = divide(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_25),X_25)),divide(divide(B,B),multiply(inverse(X_25),X_25))) ),[1],$fot(divide(B,B))]]) ).
cnf(refute_0_99,plain,
( inverse(multiply(inverse(X_25),X_25)) != divide(divide(B,B),multiply(inverse(X_25),X_25))
| inverse(multiply(inverse(X_25),X_25)) = divide(B,B) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),multiply(inverse(X_25),X_25)),divide(B,B)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
inverse(multiply(inverse(X_25),X_25)) = divide(B,B),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_25),X_25)),divide(divide(B,B),multiply(inverse(X_25),X_25))) )],[refute_0_43,refute_0_99]) ).
cnf(refute_0_101,plain,
inverse(multiply(inverse(X_29),X_29)) = divide(X_1,X_1),
inference(subst,[],[refute_0_100:[bind(B,$fot(X_1)),bind(X_25,$fot(X_29))]]) ).
cnf(refute_0_102,plain,
( inverse(multiply(inverse(X_29),X_29)) != divide(X_1,X_1)
| divide(X_1,X_1) = inverse(multiply(inverse(X_29),X_29)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(multiply(inverse(X_29),X_29)))),bind(Y,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_103,plain,
divide(X_1,X_1) = inverse(multiply(inverse(X_29),X_29)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_29),X_29)),divide(X_1,X_1)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( X_19 != multiply(inverse(divide(X_1,X_1)),X_19)
| divide(X_1,X_1) != inverse(multiply(inverse(X_29),X_29))
| X_19 = multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(X_19,multiply(inverse(divide(X_1,X_1)),X_19)) ),[1,0,0],$fot(inverse(multiply(inverse(X_29),X_29)))]]) ).
cnf(refute_0_105,plain,
( X_19 != multiply(inverse(divide(X_1,X_1)),X_19)
| X_19 = multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) ),
inference(resolve,[$cnf( $equal(divide(X_1,X_1),inverse(multiply(inverse(X_29),X_29))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
X_19 = multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19),
inference(resolve,[$cnf( $equal(X_19,multiply(inverse(divide(X_1,X_1)),X_19)) )],[refute_0_42,refute_0_105]) ).
cnf(refute_0_107,plain,
inverse(inverse(multiply(inverse(X_29),X_29))) = multiply(inverse(X_29),X_29),
inference(subst,[],[refute_0_38:[bind(X_12,$fot(multiply(inverse(X_29),X_29)))]]) ).
cnf(refute_0_108,plain,
multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) = multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19))]]) ).
cnf(refute_0_109,plain,
( multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) != multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19)
| inverse(inverse(multiply(inverse(X_29),X_29))) != multiply(inverse(X_29),X_29)
| multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) = multiply(multiply(inverse(X_29),X_29),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19),multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19)) ),[1,0],$fot(multiply(inverse(X_29),X_29))]]) ).
cnf(refute_0_110,plain,
( inverse(inverse(multiply(inverse(X_29),X_29))) != multiply(inverse(X_29),X_29)
| multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) = multiply(multiply(inverse(X_29),X_29),X_19) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19),multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) = multiply(multiply(inverse(X_29),X_29),X_19),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(inverse(X_29),X_29))),multiply(inverse(X_29),X_29)) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
( X_19 != multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19)
| multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19) != multiply(multiply(inverse(X_29),X_29),X_19)
| X_19 = multiply(multiply(inverse(X_29),X_29),X_19) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_19,multiply(multiply(inverse(X_29),X_29),X_19)) ),[0],$fot(multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19))]]) ).
cnf(refute_0_113,plain,
( X_19 != multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19)
| X_19 = multiply(multiply(inverse(X_29),X_29),X_19) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19),multiply(multiply(inverse(X_29),X_29),X_19)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
X_19 = multiply(multiply(inverse(X_29),X_29),X_19),
inference(resolve,[$cnf( $equal(X_19,multiply(inverse(inverse(multiply(inverse(X_29),X_29))),X_19)) )],[refute_0_106,refute_0_113]) ).
cnf(refute_0_115,plain,
( X_19 != multiply(multiply(inverse(X_29),X_29),X_19)
| multiply(multiply(inverse(X_29),X_29),X_19) = X_19 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_19)),bind(Y,$fot(multiply(multiply(inverse(X_29),X_29),X_19)))]]) ).
cnf(refute_0_116,plain,
multiply(multiply(inverse(X_29),X_29),X_19) = X_19,
inference(resolve,[$cnf( $equal(X_19,multiply(multiply(inverse(X_29),X_29),X_19)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(subst,[],[refute_0_116:[bind(X_19,$fot(a2)),bind(X_29,$fot(b2))]]) ).
cnf(refute_0_118,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_119,plain,
( a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_119,prove_these_axioms_2]) ).
cnf(refute_0_121,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_122,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_121,refute_0_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP530-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 03:45:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.41
%------------------------------------------------------------------------------