TSTP Solution File: GRP526-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 10:42:08 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of clauses : 102 ( 57 unt; 0 nHn; 48 RR)
% Number of literals : 165 ( 164 equ; 66 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 204 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(A,divide(divide(A,B),divide(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(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
inverse(inverse(X_18)) = divide(divide(B,B),inverse(X_18)),
inference(subst,[],[inverse:[bind(A,$fot(inverse(X_18)))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_2,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_3,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_5,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_5:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_7,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_8,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_9,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_12,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(divide(B,B),X_18) = divide(divide(B,B),inverse(X_18)),
inference(subst,[],[refute_0_13:[bind(A,$fot(divide(B,B))),bind(B,$fot(X_18))]]) ).
cnf(refute_0_15,plain,
( multiply(divide(B,B),X_18) != divide(divide(B,B),inverse(X_18))
| divide(divide(B,B),inverse(X_18)) = multiply(divide(B,B),X_18) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(divide(B,B),X_18))),bind(Y,$fot(divide(divide(B,B),inverse(X_18))))]]) ).
cnf(refute_0_16,plain,
divide(divide(B,B),inverse(X_18)) = multiply(divide(B,B),X_18),
inference(resolve,[$cnf( $equal(multiply(divide(B,B),X_18),divide(divide(B,B),inverse(X_18))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( divide(divide(B,B),inverse(X_18)) != multiply(divide(B,B),X_18)
| inverse(inverse(X_18)) != divide(divide(B,B),inverse(X_18))
| inverse(inverse(X_18)) = multiply(divide(B,B),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_18)),divide(divide(B,B),inverse(X_18))) ),[1],$fot(multiply(divide(B,B),X_18))]]) ).
cnf(refute_0_18,plain,
( inverse(inverse(X_18)) != divide(divide(B,B),inverse(X_18))
| inverse(inverse(X_18)) = multiply(divide(B,B),X_18) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),inverse(X_18)),multiply(divide(B,B),X_18)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(inverse(X_18)) = multiply(divide(B,B),X_18),
inference(resolve,[$cnf( $equal(inverse(inverse(X_18)),divide(divide(B,B),inverse(X_18))) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
inverse(inverse(X_22)) = multiply(divide(inverse(B),inverse(B)),X_22),
inference(subst,[],[refute_0_19:[bind(B,$fot(inverse(B))),bind(X_18,$fot(X_22))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(B),B) = divide(inverse(B),inverse(B)),
inference(subst,[],[refute_0_13:[bind(A,$fot(inverse(B)))]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(B),B) != divide(inverse(B),inverse(B))
| divide(inverse(B),inverse(B)) = multiply(inverse(B),B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(inverse(B),B))),bind(Y,$fot(divide(inverse(B),inverse(B))))]]) ).
cnf(refute_0_23,plain,
divide(inverse(B),inverse(B)) = multiply(inverse(B),B),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),divide(inverse(B),inverse(B))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( divide(inverse(B),inverse(B)) != multiply(inverse(B),B)
| inverse(inverse(X_22)) != multiply(divide(inverse(B),inverse(B)),X_22)
| inverse(inverse(X_22)) = multiply(multiply(inverse(B),B),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_22)),multiply(divide(inverse(B),inverse(B)),X_22)) ),[1,0],$fot(multiply(inverse(B),B))]]) ).
cnf(refute_0_25,plain,
( inverse(inverse(X_22)) != multiply(divide(inverse(B),inverse(B)),X_22)
| inverse(inverse(X_22)) = multiply(multiply(inverse(B),B),X_22) ),
inference(resolve,[$cnf( $equal(divide(inverse(B),inverse(B)),multiply(inverse(B),B)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
inverse(inverse(X_22)) = multiply(multiply(inverse(B),B),X_22),
inference(resolve,[$cnf( $equal(inverse(inverse(X_22)),multiply(divide(inverse(B),inverse(B)),X_22)) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
( inverse(inverse(X_22)) != multiply(multiply(inverse(B),B),X_22)
| multiply(multiply(inverse(B),B),X_22) = inverse(inverse(X_22)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(inverse(X_22)))),bind(Y,$fot(multiply(multiply(inverse(B),B),X_22)))]]) ).
cnf(refute_0_28,plain,
multiply(multiply(inverse(B),B),X_22) = inverse(inverse(X_22)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_22)),multiply(multiply(inverse(B),B),X_22)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiply(multiply(inverse(b2),b2),a2) = inverse(inverse(a2)),
inference(subst,[],[refute_0_28:[bind(B,$fot(b2)),bind(X_22,$fot(a2))]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(inverse(b2),b2),a2) != inverse(inverse(a2))
| inverse(inverse(a2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).
cnf(refute_0_31,plain,
( inverse(inverse(a2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),inverse(inverse(a2))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(inverse(a2)) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_31,prove_these_axioms_2]) ).
cnf(refute_0_33,plain,
inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9))),
inference(subst,[],[inverse:[bind(A,$fot(divide(divide(divide(B,B),X_9),divide(X_10,X_9))))]]) ).
cnf(refute_0_34,plain,
divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = X_10,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(B,B))),bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_35,plain,
( divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != X_10
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9)))
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9)))) ),[1],$fot(X_10)]]) ).
cnf(refute_0_36,plain,
( inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9)))
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9))),X_10) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),divide(divide(B,B),divide(divide(divide(B,B),X_9),divide(X_10,X_9)))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
divide(divide(B,B),X_9) = inverse(X_9),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_39,plain,
divide(divide(divide(B,B),X_9),divide(X_10,X_9)) = divide(divide(divide(B,B),X_9),divide(X_10,X_9)),
introduced(tautology,[refl,[$fot(divide(divide(divide(B,B),X_9),divide(X_10,X_9)))]]) ).
cnf(refute_0_40,plain,
( divide(divide(B,B),X_9) != inverse(X_9)
| divide(divide(divide(B,B),X_9),divide(X_10,X_9)) != divide(divide(divide(B,B),X_9),divide(X_10,X_9))
| divide(divide(divide(B,B),X_9),divide(X_10,X_9)) = divide(inverse(X_9),divide(X_10,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(B,B),X_9),divide(X_10,X_9)),divide(divide(divide(B,B),X_9),divide(X_10,X_9))) ),[1,0],$fot(inverse(X_9))]]) ).
cnf(refute_0_41,plain,
( divide(divide(B,B),X_9) != inverse(X_9)
| divide(divide(divide(B,B),X_9),divide(X_10,X_9)) = divide(inverse(X_9),divide(X_10,X_9)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),X_9),divide(X_10,X_9)),divide(divide(divide(B,B),X_9),divide(X_10,X_9))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
divide(divide(divide(B,B),X_9),divide(X_10,X_9)) = divide(inverse(X_9),divide(X_10,X_9)),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_9),inverse(X_9)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),
introduced(tautology,[refl,[$fot(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))))]]) ).
cnf(refute_0_44,plain,
( divide(divide(divide(B,B),X_9),divide(X_10,X_9)) != divide(inverse(X_9),divide(X_10,X_9))
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9)))
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = inverse(divide(inverse(X_9),divide(X_10,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9)))) ),[1,0],$fot(divide(inverse(X_9),divide(X_10,X_9)))]]) ).
cnf(refute_0_45,plain,
( divide(divide(divide(B,B),X_9),divide(X_10,X_9)) != divide(inverse(X_9),divide(X_10,X_9))
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = inverse(divide(inverse(X_9),divide(X_10,X_9))) ),
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) = inverse(divide(inverse(X_9),divide(X_10,X_9))),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),X_9),divide(X_10,X_9)),divide(inverse(X_9),divide(X_10,X_9))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != X_10
| inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != inverse(divide(inverse(X_9),divide(X_10,X_9)))
| inverse(divide(inverse(X_9),divide(X_10,X_9))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),X_10) ),[0],$fot(inverse(divide(inverse(X_9),divide(X_10,X_9))))]]) ).
cnf(refute_0_48,plain,
( inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))) != X_10
| inverse(divide(inverse(X_9),divide(X_10,X_9))) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),inverse(divide(inverse(X_9),divide(X_10,X_9)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
inverse(divide(inverse(X_9),divide(X_10,X_9))) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_9),divide(X_10,X_9))),X_10) )],[refute_0_37,refute_0_48]) ).
cnf(refute_0_50,plain,
inverse(divide(inverse(X_9),divide(X_9,X_9))) = X_9,
inference(subst,[],[refute_0_49:[bind(X_10,$fot(X_9))]]) ).
cnf(refute_0_51,plain,
divide(X_9,divide(divide(X_9,X_9),divide(X_10,X_9))) = X_10,
inference(subst,[],[single_axiom:[bind(A,$fot(X_9)),bind(B,$fot(X_9)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_52,plain,
inverse(divide(X_10,X_9)) = divide(divide(X_9,X_9),divide(X_10,X_9)),
inference(subst,[],[inverse:[bind(A,$fot(divide(X_10,X_9))),bind(B,$fot(X_9))]]) ).
cnf(refute_0_53,plain,
( inverse(divide(X_10,X_9)) != divide(divide(X_9,X_9),divide(X_10,X_9))
| divide(divide(X_9,X_9),divide(X_10,X_9)) = inverse(divide(X_10,X_9)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(divide(X_10,X_9)))),bind(Y,$fot(divide(divide(X_9,X_9),divide(X_10,X_9))))]]) ).
cnf(refute_0_54,plain,
divide(divide(X_9,X_9),divide(X_10,X_9)) = inverse(divide(X_10,X_9)),
inference(resolve,[$cnf( $equal(inverse(divide(X_10,X_9)),divide(divide(X_9,X_9),divide(X_10,X_9))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( divide(X_9,divide(divide(X_9,X_9),divide(X_10,X_9))) != X_10
| divide(divide(X_9,X_9),divide(X_10,X_9)) != inverse(divide(X_10,X_9))
| divide(X_9,inverse(divide(X_10,X_9))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_9,divide(divide(X_9,X_9),divide(X_10,X_9))),X_10) ),[0,1],$fot(inverse(divide(X_10,X_9)))]]) ).
cnf(refute_0_56,plain,
( divide(X_9,divide(divide(X_9,X_9),divide(X_10,X_9))) != X_10
| divide(X_9,inverse(divide(X_10,X_9))) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(X_9,X_9),divide(X_10,X_9)),inverse(divide(X_10,X_9))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
divide(X_9,inverse(divide(X_10,X_9))) = X_10,
inference(resolve,[$cnf( $equal(divide(X_9,divide(divide(X_9,X_9),divide(X_10,X_9))),X_10) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_59,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_13,refute_0_58]) ).
cnf(refute_0_60,plain,
divide(X_9,inverse(divide(X_10,X_9))) = multiply(X_9,divide(X_10,X_9)),
inference(subst,[],[refute_0_59:[bind(A,$fot(X_9)),bind(B,$fot(divide(X_10,X_9)))]]) ).
cnf(refute_0_61,plain,
( divide(X_9,inverse(divide(X_10,X_9))) != X_10
| divide(X_9,inverse(divide(X_10,X_9))) != multiply(X_9,divide(X_10,X_9))
| multiply(X_9,divide(X_10,X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_9,inverse(divide(X_10,X_9))),X_10) ),[0],$fot(multiply(X_9,divide(X_10,X_9)))]]) ).
cnf(refute_0_62,plain,
( divide(X_9,inverse(divide(X_10,X_9))) != X_10
| multiply(X_9,divide(X_10,X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(X_9,inverse(divide(X_10,X_9))),multiply(X_9,divide(X_10,X_9))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(X_9,divide(X_10,X_9)) = X_10,
inference(resolve,[$cnf( $equal(divide(X_9,inverse(divide(X_10,X_9))),X_10) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(X_12,divide(divide(B,B),X_12)) = divide(B,B),
inference(subst,[],[refute_0_63:[bind(X_10,$fot(divide(B,B))),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_65,plain,
inverse(X_12) = divide(divide(B,B),X_12),
inference(subst,[],[inverse:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_66,plain,
( inverse(X_12) != divide(divide(B,B),X_12)
| divide(divide(B,B),X_12) = inverse(X_12) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(X_12))),bind(Y,$fot(divide(divide(B,B),X_12)))]]) ).
cnf(refute_0_67,plain,
divide(divide(B,B),X_12) = inverse(X_12),
inference(resolve,[$cnf( $equal(inverse(X_12),divide(divide(B,B),X_12)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( multiply(X_12,divide(divide(B,B),X_12)) != divide(B,B)
| divide(divide(B,B),X_12) != inverse(X_12)
| multiply(X_12,inverse(X_12)) = divide(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_12,divide(divide(B,B),X_12)),divide(B,B)) ),[0,1],$fot(inverse(X_12))]]) ).
cnf(refute_0_69,plain,
( multiply(X_12,divide(divide(B,B),X_12)) != divide(B,B)
| multiply(X_12,inverse(X_12)) = divide(B,B) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_12),inverse(X_12)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(X_12,inverse(X_12)) = divide(B,B),
inference(resolve,[$cnf( $equal(multiply(X_12,divide(divide(B,B),X_12)),divide(B,B)) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_30,inverse(X_30)) = divide(X_9,X_9),
inference(subst,[],[refute_0_70:[bind(B,$fot(X_9)),bind(X_12,$fot(X_30))]]) ).
cnf(refute_0_72,plain,
( multiply(X_30,inverse(X_30)) != divide(X_9,X_9)
| divide(X_9,X_9) = multiply(X_30,inverse(X_30)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(X_30,inverse(X_30)))),bind(Y,$fot(divide(X_9,X_9)))]]) ).
cnf(refute_0_73,plain,
divide(X_9,X_9) = multiply(X_30,inverse(X_30)),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(X_30)),divide(X_9,X_9)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( divide(X_9,X_9) != multiply(X_30,inverse(X_30))
| inverse(divide(inverse(X_9),divide(X_9,X_9))) != X_9
| inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_9),divide(X_9,X_9))),X_9) ),[0,0,1],$fot(multiply(X_30,inverse(X_30)))]]) ).
cnf(refute_0_75,plain,
( inverse(divide(inverse(X_9),divide(X_9,X_9))) != X_9
| inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = X_9 ),
inference(resolve,[$cnf( $equal(divide(X_9,X_9),multiply(X_30,inverse(X_30))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = X_9,
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_9),divide(X_9,X_9))),X_9) )],[refute_0_50,refute_0_75]) ).
cnf(refute_0_77,plain,
divide(C,divide(divide(C,B),divide(C,B))) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(C))]]) ).
cnf(refute_0_78,plain,
multiply(X_30,inverse(X_30)) = divide(divide(C,B),divide(C,B)),
inference(subst,[],[refute_0_70:[bind(B,$fot(divide(C,B))),bind(X_12,$fot(X_30))]]) ).
cnf(refute_0_79,plain,
( multiply(X_30,inverse(X_30)) != divide(divide(C,B),divide(C,B))
| divide(divide(C,B),divide(C,B)) = multiply(X_30,inverse(X_30)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(X_30,inverse(X_30)))),bind(Y,$fot(divide(divide(C,B),divide(C,B))))]]) ).
cnf(refute_0_80,plain,
divide(divide(C,B),divide(C,B)) = multiply(X_30,inverse(X_30)),
inference(resolve,[$cnf( $equal(multiply(X_30,inverse(X_30)),divide(divide(C,B),divide(C,B))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( divide(C,divide(divide(C,B),divide(C,B))) != C
| divide(divide(C,B),divide(C,B)) != multiply(X_30,inverse(X_30))
| divide(C,multiply(X_30,inverse(X_30))) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(C,divide(divide(C,B),divide(C,B))),C) ),[0,1],$fot(multiply(X_30,inverse(X_30)))]]) ).
cnf(refute_0_82,plain,
( divide(C,divide(divide(C,B),divide(C,B))) != C
| divide(C,multiply(X_30,inverse(X_30))) = C ),
inference(resolve,[$cnf( $equal(divide(divide(C,B),divide(C,B)),multiply(X_30,inverse(X_30))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
divide(C,multiply(X_30,inverse(X_30))) = C,
inference(resolve,[$cnf( $equal(divide(C,divide(divide(C,B),divide(C,B))),C) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
divide(inverse(X_9),multiply(X_30,inverse(X_30))) = inverse(X_9),
inference(subst,[],[refute_0_83:[bind(C,$fot(inverse(X_9)))]]) ).
cnf(refute_0_85,plain,
inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))),
introduced(tautology,[refl,[$fot(inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))))]]) ).
cnf(refute_0_86,plain,
( divide(inverse(X_9),multiply(X_30,inverse(X_30))) != inverse(X_9)
| inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) != inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30))))
| inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = inverse(inverse(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))),inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30))))) ),[1,0],$fot(inverse(X_9))]]) ).
cnf(refute_0_87,plain,
( divide(inverse(X_9),multiply(X_30,inverse(X_30))) != inverse(X_9)
| inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = inverse(inverse(X_9)) ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))),inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30))))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) = inverse(inverse(X_9)),
inference(resolve,[$cnf( $equal(divide(inverse(X_9),multiply(X_30,inverse(X_30))),inverse(X_9)) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) != X_9
| inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) != inverse(inverse(X_9))
| inverse(inverse(X_9)) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))),X_9) ),[0],$fot(inverse(inverse(X_9)))]]) ).
cnf(refute_0_90,plain,
( inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))) != X_9
| inverse(inverse(X_9)) = X_9 ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))),inverse(inverse(X_9))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
inverse(inverse(X_9)) = X_9,
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_9),multiply(X_30,inverse(X_30)))),X_9) )],[refute_0_76,refute_0_90]) ).
cnf(refute_0_92,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_91:[bind(X_9,$fot(a2))]]) ).
cnf(refute_0_93,plain,
( a2 != a2
| inverse(inverse(a2)) != a2
| inverse(inverse(a2)) = a2 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a2)),a2) ),[0,0,0],$fot(a2)]]) ).
cnf(refute_0_94,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_94,refute_0_32]) ).
cnf(refute_0_96,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_97,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_96,refute_0_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 09:49:15 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42
% 0.20/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.44
%------------------------------------------------------------------------------