TSTP Solution File: GRP529-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP529-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:42:09 EDT 2022
% Result : Unsatisfiable 0.18s 0.36s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 28
% Syntax : Number of clauses : 109 ( 59 unt; 0 nHn; 54 RR)
% Number of literals : 181 ( 180 equ; 74 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 : 209 ( 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_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(refute_0_0,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,$fot(X_6))]]) ).
cnf(refute_0_1,plain,
inverse(X_5) = divide(divide(B,B),X_5),
inference(subst,[],[inverse:[bind(A,$fot(X_5))]]) ).
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( inverse(X_5) != divide(divide(B,B),X_5)
| divide(divide(B,B),X_5) = inverse(X_5) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_5))),bind(Y,$fot(divide(divide(B,B),X_5)))]]) ).
cnf(refute_0_6,plain,
divide(divide(B,B),X_5) = inverse(X_5),
inference(resolve,[$cnf( $equal(inverse(X_5),divide(divide(B,B),X_5)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( divide(divide(B,B),X_5) != inverse(X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)) != X_6
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = X_6 ),
introduced(tautology,[equality,[$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_8,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( $equal(divide(divide(B,B),X_5),inverse(X_5)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = X_6,
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),divide(divide(B,B),X_5)),X_6) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_11,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(divide(B,B),divide(X_5,X_6)) = inverse(divide(X_5,X_6)),
inference(subst,[],[refute_0_11:[bind(A,$fot(divide(X_5,X_6)))]]) ).
cnf(refute_0_13,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,[$fot(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5))]]) ).
cnf(refute_0_14,plain,
( multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) != multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)
| divide(divide(B,B),divide(X_5,X_6)) != inverse(divide(X_5,X_6))
| multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) = multiply(inverse(divide(X_5,X_6)),X_5) ),
introduced(tautology,[equality,[$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_15,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( $equal(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) = multiply(inverse(divide(X_5,X_6)),X_5),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(X_5,X_6)),inverse(divide(X_5,X_6))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_11:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_18,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_19,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_20,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_23,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_26,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),
inference(subst,[],[refute_0_26:[bind(A,$fot(divide(divide(B,B),divide(X_5,X_6)))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_28,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(divide(divide(B,B),divide(X_5,X_6)),X_5) != multiply(inverse(divide(X_5,X_6)),X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(inverse(divide(X_5,X_6)),X_5) ),
inference(subst,[],[refute_0_29:[bind(X,$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_31,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( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),multiply(divide(divide(B,B),divide(X_5,X_6)),X_5)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) = multiply(inverse(divide(X_5,X_6)),X_5),
inference(resolve,[$cnf( $equal(multiply(divide(divide(B,B),divide(X_5,X_6)),X_5),multiply(inverse(divide(X_5,X_6)),X_5)) )],[refute_0_16,refute_0_31]) ).
cnf(refute_0_33,plain,
( divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != X_6
| divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)) != multiply(inverse(divide(X_5,X_6)),X_5)
| multiply(inverse(divide(X_5,X_6)),X_5) = X_6 ),
introduced(tautology,[equality,[$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_34,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( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),multiply(inverse(divide(X_5,X_6)),X_5)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(inverse(divide(X_5,X_6)),X_5) = X_6,
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),divide(X_5,X_6)),inverse(X_5)),X_6) )],[refute_0_9,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(inverse(divide(X_5,divide(X_5,X_27))),X_5) = divide(X_5,X_27),
inference(subst,[],[refute_0_35:[bind(X_6,$fot(divide(X_5,X_27)))]]) ).
cnf(refute_0_37,plain,
divide(divide(B,divide(B,C)),divide(B,B)) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(B))]]) ).
cnf(refute_0_38,plain,
multiply(inverse(divide(inverse(divide(X_1,X_1)),X_13)),inverse(divide(X_1,X_1))) = X_13,
inference(subst,[],[refute_0_35:[bind(X_5,$fot(inverse(divide(X_1,X_1)))),bind(X_6,$fot(X_13))]]) ).
cnf(refute_0_39,plain,
inverse(A) = divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A),
inference(subst,[],[inverse:[bind(B,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_40,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_41,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_42,plain,
divide(divide(X_1,X_1),divide(X_1,X_1)) = inverse(divide(X_1,X_1)),
inference(resolve,[$cnf( $equal(inverse(divide(X_1,X_1)),divide(divide(X_1,X_1),divide(X_1,X_1))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( divide(divide(X_1,X_1),divide(X_1,X_1)) != inverse(divide(X_1,X_1))
| inverse(A) != divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)
| inverse(A) = divide(inverse(divide(X_1,X_1)),A) ),
introduced(tautology,[equality,[$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_44,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( $equal(divide(divide(X_1,X_1),divide(X_1,X_1)),inverse(divide(X_1,X_1))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(A) = divide(inverse(divide(X_1,X_1)),A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(divide(X_1,X_1),divide(X_1,X_1)),A)) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
inverse(X_13) = divide(inverse(divide(X_1,X_1)),X_13),
inference(subst,[],[refute_0_45:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_47,plain,
( inverse(X_13) != divide(inverse(divide(X_1,X_1)),X_13)
| divide(inverse(divide(X_1,X_1)),X_13) = inverse(X_13) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_13))),bind(Y,$fot(divide(inverse(divide(X_1,X_1)),X_13)))]]) ).
cnf(refute_0_48,plain,
divide(inverse(divide(X_1,X_1)),X_13) = inverse(X_13),
inference(resolve,[$cnf( $equal(inverse(X_13),divide(inverse(divide(X_1,X_1)),X_13)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( multiply(inverse(divide(inverse(divide(X_1,X_1)),X_13)),inverse(divide(X_1,X_1))) != X_13
| divide(inverse(divide(X_1,X_1)),X_13) != inverse(X_13)
| multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(inverse(divide(X_1,X_1)),X_13)),inverse(divide(X_1,X_1))),X_13) ),[0,0,0],$fot(inverse(X_13))]]) ).
cnf(refute_0_50,plain,
( multiply(inverse(divide(inverse(divide(X_1,X_1)),X_13)),inverse(divide(X_1,X_1))) != X_13
| multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = X_13 ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(X_1,X_1)),X_13),inverse(X_13)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(inverse(divide(X_1,X_1)),X_13)),inverse(divide(X_1,X_1))),X_13) )],[refute_0_38,refute_0_50]) ).
cnf(refute_0_52,plain,
inverse(divide(divide(X_5,X_6),X_5)) = divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)),
inference(subst,[],[inverse:[bind(A,$fot(divide(divide(X_5,X_6),X_5))),bind(B,$fot(divide(X_5,X_6)))]]) ).
cnf(refute_0_53,plain,
divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)) = X_6,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(X_5,X_6))),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_54,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_55,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( $equal(divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5)),X_6) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
inverse(divide(divide(X_5,X_6),X_5)) = X_6,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_5,X_6),X_5)),divide(divide(divide(X_5,X_6),divide(X_5,X_6)),divide(divide(X_5,X_6),X_5))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
inverse(divide(divide(X_10,X_10),X_10)) = X_10,
inference(subst,[],[refute_0_56:[bind(X_5,$fot(X_10)),bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_58,plain,
inverse(X_10) = divide(divide(X_10,X_10),X_10),
inference(subst,[],[inverse:[bind(A,$fot(X_10)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_59,plain,
( inverse(X_10) != divide(divide(X_10,X_10),X_10)
| divide(divide(X_10,X_10),X_10) = inverse(X_10) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_10))),bind(Y,$fot(divide(divide(X_10,X_10),X_10)))]]) ).
cnf(refute_0_60,plain,
divide(divide(X_10,X_10),X_10) = inverse(X_10),
inference(resolve,[$cnf( $equal(inverse(X_10),divide(divide(X_10,X_10),X_10)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( divide(divide(X_10,X_10),X_10) != inverse(X_10)
| inverse(divide(divide(X_10,X_10),X_10)) != X_10
| inverse(inverse(X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(X_10,X_10),X_10)),X_10) ),[0,0],$fot(inverse(X_10))]]) ).
cnf(refute_0_62,plain,
( inverse(divide(divide(X_10,X_10),X_10)) != X_10
| inverse(inverse(X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(divide(X_10,X_10),X_10),inverse(X_10)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
inverse(inverse(X_10)) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(divide(X_10,X_10),X_10)),X_10) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
inverse(inverse(X_13)) = X_13,
inference(subst,[],[refute_0_63:[bind(X_10,$fot(X_13))]]) ).
cnf(refute_0_65,plain,
multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))))]]) ).
cnf(refute_0_66,plain,
( multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) != multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1)))
| inverse(inverse(X_13)) != X_13
| multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = multiply(X_13,inverse(divide(X_1,X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))),multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1)))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_67,plain,
( inverse(inverse(X_13)) != X_13
| multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = multiply(X_13,inverse(divide(X_1,X_1))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))),multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) = multiply(X_13,inverse(divide(X_1,X_1))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_13)),X_13) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) != X_13
| multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) != multiply(X_13,inverse(divide(X_1,X_1)))
| multiply(X_13,inverse(divide(X_1,X_1))) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))),X_13) ),[0],$fot(multiply(X_13,inverse(divide(X_1,X_1))))]]) ).
cnf(refute_0_70,plain,
( multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))) != X_13
| multiply(X_13,inverse(divide(X_1,X_1))) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))),multiply(X_13,inverse(divide(X_1,X_1)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_13,inverse(divide(X_1,X_1))) = X_13,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),inverse(divide(X_1,X_1))),X_13) )],[refute_0_51,refute_0_70]) ).
cnf(refute_0_72,plain,
multiply(X_16,inverse(X_10)) = divide(X_16,inverse(inverse(X_10))),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_16)),bind(B,$fot(inverse(X_10)))]]) ).
cnf(refute_0_73,plain,
( multiply(X_16,inverse(X_10)) != divide(X_16,inverse(inverse(X_10)))
| inverse(inverse(X_10)) != X_10
| multiply(X_16,inverse(X_10)) = divide(X_16,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_16,inverse(X_10)),divide(X_16,inverse(inverse(X_10)))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_74,plain,
( multiply(X_16,inverse(X_10)) != divide(X_16,inverse(inverse(X_10)))
| multiply(X_16,inverse(X_10)) = divide(X_16,X_10) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_63,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(X_16,inverse(X_10)) = divide(X_16,X_10),
inference(resolve,[$cnf( $equal(multiply(X_16,inverse(X_10)),divide(X_16,inverse(inverse(X_10)))) )],[refute_0_72,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(X_13,inverse(divide(X_1,X_1))) = divide(X_13,divide(X_1,X_1)),
inference(subst,[],[refute_0_75:[bind(X_10,$fot(divide(X_1,X_1))),bind(X_16,$fot(X_13))]]) ).
cnf(refute_0_77,plain,
( multiply(X_13,inverse(divide(X_1,X_1))) != X_13
| multiply(X_13,inverse(divide(X_1,X_1))) != divide(X_13,divide(X_1,X_1))
| divide(X_13,divide(X_1,X_1)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_13,inverse(divide(X_1,X_1))),X_13) ),[0],$fot(divide(X_13,divide(X_1,X_1)))]]) ).
cnf(refute_0_78,plain,
( multiply(X_13,inverse(divide(X_1,X_1))) != X_13
| divide(X_13,divide(X_1,X_1)) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(X_13,inverse(divide(X_1,X_1))),divide(X_13,divide(X_1,X_1))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
divide(X_13,divide(X_1,X_1)) = X_13,
inference(resolve,[$cnf( $equal(multiply(X_13,inverse(divide(X_1,X_1))),X_13) )],[refute_0_71,refute_0_78]) ).
cnf(refute_0_80,plain,
divide(divide(B,divide(B,C)),divide(B,B)) = divide(B,divide(B,C)),
inference(subst,[],[refute_0_79:[bind(X_1,$fot(B)),bind(X_13,$fot(divide(B,divide(B,C))))]]) ).
cnf(refute_0_81,plain,
( divide(divide(B,divide(B,C)),divide(B,B)) != C
| divide(divide(B,divide(B,C)),divide(B,B)) != divide(B,divide(B,C))
| divide(B,divide(B,C)) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(B,divide(B,C)),divide(B,B)),C) ),[0],$fot(divide(B,divide(B,C)))]]) ).
cnf(refute_0_82,plain,
( divide(divide(B,divide(B,C)),divide(B,B)) != C
| divide(B,divide(B,C)) = C ),
inference(resolve,[$cnf( $equal(divide(divide(B,divide(B,C)),divide(B,B)),divide(B,divide(B,C))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
divide(B,divide(B,C)) = C,
inference(resolve,[$cnf( $equal(divide(divide(B,divide(B,C)),divide(B,B)),C) )],[refute_0_37,refute_0_82]) ).
cnf(refute_0_84,plain,
divide(X_5,divide(X_5,X_27)) = X_27,
inference(subst,[],[refute_0_83:[bind(B,$fot(X_5)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_85,plain,
( multiply(inverse(divide(X_5,divide(X_5,X_27))),X_5) != divide(X_5,X_27)
| divide(X_5,divide(X_5,X_27)) != X_27
| multiply(inverse(X_27),X_5) = divide(X_5,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_5,divide(X_5,X_27))),X_5),divide(X_5,X_27)) ),[0,0,0],$fot(X_27)]]) ).
cnf(refute_0_86,plain,
( multiply(inverse(divide(X_5,divide(X_5,X_27))),X_5) != divide(X_5,X_27)
| multiply(inverse(X_27),X_5) = divide(X_5,X_27) ),
inference(resolve,[$cnf( $equal(divide(X_5,divide(X_5,X_27)),X_27) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(X_27),X_5) = divide(X_5,X_27),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_5,divide(X_5,X_27))),X_5),divide(X_5,X_27)) )],[refute_0_36,refute_0_86]) ).
cnf(refute_0_88,plain,
multiply(inverse(a1),a1) = divide(a1,a1),
inference(subst,[],[refute_0_87:[bind(X_27,$fot(a1)),bind(X_5,$fot(a1))]]) ).
cnf(refute_0_89,plain,
( multiply(inverse(a1),a1) != divide(a1,a1)
| divide(a1,a1) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) ),[0],$fot(divide(a1,a1))]]) ).
cnf(refute_0_90,plain,
( divide(a1,a1) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),divide(a1,a1)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(inverse(b1),b1) = divide(b1,b1),
inference(subst,[],[refute_0_87:[bind(X_27,$fot(b1)),bind(X_5,$fot(b1))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(b1),b1) != divide(b1,b1)
| divide(a1,a1) != divide(b1,b1)
| divide(a1,a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(a1,a1),multiply(inverse(b1),b1)) ),[1],$fot(divide(b1,b1))]]) ).
cnf(refute_0_93,plain,
( divide(a1,a1) != divide(b1,b1)
| divide(a1,a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b1),b1),divide(b1,b1)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( divide(a1,a1) != divide(b1,b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(divide(a1,a1),multiply(inverse(b1),b1)) )],[refute_0_93,refute_0_90]) ).
cnf(refute_0_95,plain,
divide(a1,a1) != divide(b1,b1),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_94,prove_these_axioms_1]) ).
cnf(refute_0_96,plain,
divide(X_26,divide(X_26,divide(X_1,X_1))) = divide(X_1,X_1),
inference(subst,[],[refute_0_83:[bind(B,$fot(X_26)),bind(C,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_97,plain,
divide(X_26,divide(X_1,X_1)) = X_26,
inference(subst,[],[refute_0_79:[bind(X_13,$fot(X_26))]]) ).
cnf(refute_0_98,plain,
( divide(X_26,divide(X_1,X_1)) != X_26
| divide(X_26,divide(X_26,divide(X_1,X_1))) != divide(X_1,X_1)
| divide(X_26,X_26) = divide(X_1,X_1) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_26,divide(X_26,divide(X_1,X_1))),divide(X_1,X_1)) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_99,plain,
( divide(X_26,divide(X_26,divide(X_1,X_1))) != divide(X_1,X_1)
| divide(X_26,X_26) = divide(X_1,X_1) ),
inference(resolve,[$cnf( $equal(divide(X_26,divide(X_1,X_1)),X_26) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
divide(X_26,X_26) = divide(X_1,X_1),
inference(resolve,[$cnf( $equal(divide(X_26,divide(X_26,divide(X_1,X_1))),divide(X_1,X_1)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
( divide(X_26,X_26) != divide(X_1,X_1)
| divide(X_1,X_1) = divide(X_26,X_26) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(divide(X_26,X_26))),bind(Y,$fot(divide(X_1,X_1)))]]) ).
cnf(refute_0_102,plain,
divide(X_1,X_1) = divide(X_26,X_26),
inference(resolve,[$cnf( $equal(divide(X_26,X_26),divide(X_1,X_1)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
divide(a1,a1) = divide(b1,b1),
inference(subst,[],[refute_0_102:[bind(X_1,$fot(a1)),bind(X_26,$fot(b1))]]) ).
cnf(refute_0_104,plain,
$false,
inference(resolve,[$cnf( $equal(divide(a1,a1),divide(b1,b1)) )],[refute_0_103,refute_0_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP529-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:17:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.36
% 0.18/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.38
%------------------------------------------------------------------------------