%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP537-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 10:42:12 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 22
% Syntax : Number of clauses : 70 ( 37 unt; 0 nHn; 36 RR)
% Number of literals : 117 ( 116 equ; 49 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 : 109 ( 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_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(refute_0_0,plain,
divide(divide(X_4,X_3),divide(divide(X_4,X_4),X_3)) = X_4,
inference(subst,[],[single_axiom:[bind(A,$fot(X_4)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_1,plain,
identity = divide(X_4,X_4),
inference(subst,[],[identity:[bind(A,$fot(X_4))]]) ).
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( identity != divide(X_4,X_4)
| divide(X_4,X_4) = identity ),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(divide(X_4,X_4)))]]) ).
cnf(refute_0_6,plain,
divide(X_4,X_4) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X_4,X_4)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( divide(X_4,X_4) != identity
| divide(divide(X_4,X_3),divide(divide(X_4,X_4),X_3)) != X_4
| divide(divide(X_4,X_3),divide(identity,X_3)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_4,X_3),divide(divide(X_4,X_4),X_3)),X_4) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_8,plain,
( divide(divide(X_4,X_3),divide(divide(X_4,X_4),X_3)) != X_4
| divide(divide(X_4,X_3),divide(identity,X_3)) = X_4 ),
inference(resolve,[$cnf( $equal(divide(X_4,X_4),identity) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(divide(X_4,X_3),divide(identity,X_3)) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_4,X_3),divide(divide(X_4,X_4),X_3)),X_4) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_4:[bind(X,$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( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_11:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_13,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_14,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_15,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_18,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_18]) ).
cnf(refute_0_20,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_21,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
divide(divide(X_4,X_3),inverse(X_3)) = multiply(divide(X_4,X_3),X_3),
inference(subst,[],[refute_0_21:[bind(A,$fot(divide(X_4,X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_23,plain,
( identity != divide(A,A)
| divide(A,A) = identity ),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity)),bind(Y,$fot(divide(A,A)))]]) ).
cnf(refute_0_24,plain,
divide(A,A) = identity,
inference(resolve,[$cnf( $equal(identity,divide(A,A)) )],[identity,refute_0_23]) ).
cnf(refute_0_25,plain,
divide(B,B) = identity,
inference(subst,[],[refute_0_24:[bind(A,$fot(B))]]) ).
cnf(refute_0_26,plain,
divide(divide(B,B),A) = divide(divide(B,B),A),
introduced(tautology,[refl,[$fot(divide(divide(B,B),A))]]) ).
cnf(refute_0_27,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_28,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
divide(divide(B,B),A) = divide(identity,A),
inference(resolve,[$cnf( $equal(divide(B,B),identity) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( divide(divide(B,B),A) != divide(identity,A)
| inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) ),[1],$fot(divide(identity,A))]]) ).
cnf(refute_0_31,plain,
( inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(identity,A)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
inverse(A) = divide(identity,A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_31]) ).
cnf(refute_0_33,plain,
( inverse(A) != divide(identity,A)
| divide(identity,A) = inverse(A) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(identity,A)))]]) ).
cnf(refute_0_34,plain,
divide(identity,A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(identity,A)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
divide(identity,X_3) = inverse(X_3),
inference(subst,[],[refute_0_34:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_36,plain,
divide(divide(X_4,X_3),divide(identity,X_3)) = divide(divide(X_4,X_3),divide(identity,X_3)),
introduced(tautology,[refl,[$fot(divide(divide(X_4,X_3),divide(identity,X_3)))]]) ).
cnf(refute_0_37,plain,
( divide(divide(X_4,X_3),divide(identity,X_3)) != divide(divide(X_4,X_3),divide(identity,X_3))
| divide(identity,X_3) != inverse(X_3)
| divide(divide(X_4,X_3),divide(identity,X_3)) = divide(divide(X_4,X_3),inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_4,X_3),divide(identity,X_3)),divide(divide(X_4,X_3),divide(identity,X_3))) ),[1,1],$fot(inverse(X_3))]]) ).
cnf(refute_0_38,plain,
( divide(identity,X_3) != inverse(X_3)
| divide(divide(X_4,X_3),divide(identity,X_3)) = divide(divide(X_4,X_3),inverse(X_3)) ),
inference(resolve,[$cnf( $equal(divide(divide(X_4,X_3),divide(identity,X_3)),divide(divide(X_4,X_3),divide(identity,X_3))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
divide(divide(X_4,X_3),divide(identity,X_3)) = divide(divide(X_4,X_3),inverse(X_3)),
inference(resolve,[$cnf( $equal(divide(identity,X_3),inverse(X_3)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_41,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_40]) ).
cnf(refute_0_42,plain,
( divide(divide(X_4,X_3),divide(identity,X_3)) != divide(divide(X_4,X_3),inverse(X_3))
| divide(divide(X_4,X_3),inverse(X_3)) != multiply(divide(X_4,X_3),X_3)
| divide(divide(X_4,X_3),divide(identity,X_3)) = multiply(divide(X_4,X_3),X_3) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(divide(divide(X_4,X_3),divide(identity,X_3)))),bind(Y,$fot(divide(divide(X_4,X_3),inverse(X_3)))),bind(Z,$fot(multiply(divide(X_4,X_3),X_3)))]]) ).
cnf(refute_0_43,plain,
( divide(divide(X_4,X_3),inverse(X_3)) != multiply(divide(X_4,X_3),X_3)
| divide(divide(X_4,X_3),divide(identity,X_3)) = multiply(divide(X_4,X_3),X_3) ),
inference(resolve,[$cnf( $equal(divide(divide(X_4,X_3),divide(identity,X_3)),divide(divide(X_4,X_3),inverse(X_3))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
divide(divide(X_4,X_3),divide(identity,X_3)) = multiply(divide(X_4,X_3),X_3),
inference(resolve,[$cnf( $equal(divide(divide(X_4,X_3),inverse(X_3)),multiply(divide(X_4,X_3),X_3)) )],[refute_0_22,refute_0_43]) ).
cnf(refute_0_45,plain,
( divide(divide(X_4,X_3),divide(identity,X_3)) != X_4
| divide(divide(X_4,X_3),divide(identity,X_3)) != multiply(divide(X_4,X_3),X_3)
| multiply(divide(X_4,X_3),X_3) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_4,X_3),divide(identity,X_3)),X_4) ),[0],$fot(multiply(divide(X_4,X_3),X_3))]]) ).
cnf(refute_0_46,plain,
( divide(divide(X_4,X_3),divide(identity,X_3)) != X_4
| multiply(divide(X_4,X_3),X_3) = X_4 ),
inference(resolve,[$cnf( $equal(divide(divide(X_4,X_3),divide(identity,X_3)),multiply(divide(X_4,X_3),X_3)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(divide(X_4,X_3),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_4,X_3),divide(identity,X_3)),X_4) )],[refute_0_9,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(divide(identity,X_5),X_5) = identity,
inference(subst,[],[refute_0_47:[bind(X_3,$fot(X_5)),bind(X_4,$fot(identity))]]) ).
cnf(refute_0_49,plain,
inverse(X_5) = divide(identity,X_5),
inference(subst,[],[refute_0_32:[bind(A,$fot(X_5))]]) ).
cnf(refute_0_50,plain,
( inverse(X_5) != divide(identity,X_5)
| divide(identity,X_5) = inverse(X_5) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_5))),bind(Y,$fot(divide(identity,X_5)))]]) ).
cnf(refute_0_51,plain,
divide(identity,X_5) = inverse(X_5),
inference(resolve,[$cnf( $equal(inverse(X_5),divide(identity,X_5)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiply(divide(identity,X_5),X_5) != identity
| divide(identity,X_5) != inverse(X_5)
| multiply(inverse(X_5),X_5) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(identity,X_5),X_5),identity) ),[0,0],$fot(inverse(X_5))]]) ).
cnf(refute_0_53,plain,
( multiply(divide(identity,X_5),X_5) != identity
| multiply(inverse(X_5),X_5) = identity ),
inference(resolve,[$cnf( $equal(divide(identity,X_5),inverse(X_5)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(X_5),X_5) = identity,
inference(resolve,[$cnf( $equal(multiply(divide(identity,X_5),X_5),identity) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(inverse(a1),a1) = identity,
inference(subst,[],[refute_0_54:[bind(X_5,$fot(a1))]]) ).
cnf(refute_0_56,plain,
( multiply(inverse(a1),a1) != identity
| identity != 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(identity)]]) ).
cnf(refute_0_57,plain,
( identity != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(inverse(b1),b1) = identity,
inference(subst,[],[refute_0_54:[bind(X_5,$fot(b1))]]) ).
cnf(refute_0_59,plain,
( multiply(inverse(b1),b1) != identity
| identity != identity
| identity = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,multiply(inverse(b1),b1)) ),[1],$fot(identity)]]) ).
cnf(refute_0_60,plain,
( identity != identity
| identity = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(b1),b1),identity) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( identity != identity
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(identity,multiply(inverse(b1),b1)) )],[refute_0_60,refute_0_57]) ).
cnf(refute_0_62,plain,
identity != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_61,prove_these_axioms_1]) ).
cnf(refute_0_63,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_64,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_63,refute_0_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP537-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.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 : Tue Jun 14 07:47:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------