%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP534-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 10:42:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 41
% Syntax : Number of clauses : 154 ( 83 unt; 0 nHn; 84 RR)
% Number of literals : 255 ( 254 equ; 104 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 197 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,divide(divide(A,B),C)),B) = C ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)) ).
cnf(inverse,axiom,
inverse(A) = divide(divide(B,B),A) ).
cnf(identity,axiom,
identity = divide(A,A) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
divide(divide(identity,divide(divide(identity,X_3),X_4)),X_3) = X_4,
inference(subst,[],[single_axiom:[bind(A,$fot(identity)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( identity != divide(A,A)
| divide(A,A) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(divide(A,A)))]]) ).
cnf(refute_0_5,plain,
divide(A,A) = identity,
inference(resolve,[$cnf( $equal(identity,divide(A,A)) )],[identity,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(B,B) = identity,
inference(subst,[],[refute_0_5:[bind(A,$fot(B))]]) ).
cnf(refute_0_7,plain,
divide(divide(B,B),A) = divide(divide(B,B),A),
introduced(tautology,[refl,[$fot(divide(divide(B,B),A))]]) ).
cnf(refute_0_8,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_9,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(divide(B,B),A) = divide(identity,A),
inference(resolve,[$cnf( $equal(divide(B,B),identity) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( divide(divide(B,B),A) != divide(identity,A)
| inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) ),[1],$fot(divide(identity,A))]]) ).
cnf(refute_0_12,plain,
( inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(identity,A)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
inverse(A) = divide(identity,A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_12]) ).
cnf(refute_0_14,plain,
inverse(X_3) = divide(identity,X_3),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_15,plain,
( inverse(X_3) != divide(identity,X_3)
| divide(identity,X_3) = inverse(X_3) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(divide(identity,X_3)))]]) ).
cnf(refute_0_16,plain,
divide(identity,X_3) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),divide(identity,X_3)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( divide(divide(identity,divide(divide(identity,X_3),X_4)),X_3) != X_4
| divide(identity,X_3) != inverse(X_3)
| divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(divide(identity,X_3),X_4)),X_3),X_4) ),[0,0,1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_18,plain,
( divide(divide(identity,divide(divide(identity,X_3),X_4)),X_3) != X_4
| divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = X_4 ),
inference(resolve,[$cnf( $equal(divide(identity,X_3),inverse(X_3)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(divide(identity,X_3),X_4)),X_3),X_4) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( inverse(A) != divide(identity,A)
| divide(identity,A) = inverse(A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(identity,A)))]]) ).
cnf(refute_0_21,plain,
divide(identity,A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(identity,A)) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
divide(identity,divide(inverse(X_3),X_4)) = inverse(divide(inverse(X_3),X_4)),
inference(subst,[],[refute_0_21:[bind(A,$fot(divide(inverse(X_3),X_4)))]]) ).
cnf(refute_0_23,plain,
divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = divide(divide(identity,divide(inverse(X_3),X_4)),X_3),
introduced(tautology,[refl,[$fot(divide(divide(identity,divide(inverse(X_3),X_4)),X_3))]]) ).
cnf(refute_0_24,plain,
( divide(divide(identity,divide(inverse(X_3),X_4)),X_3) != divide(divide(identity,divide(inverse(X_3),X_4)),X_3)
| divide(identity,divide(inverse(X_3),X_4)) != inverse(divide(inverse(X_3),X_4))
| divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = divide(inverse(divide(inverse(X_3),X_4)),X_3) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(inverse(X_3),X_4)),X_3),divide(divide(identity,divide(inverse(X_3),X_4)),X_3)) ),[1,0],$fot(inverse(divide(inverse(X_3),X_4)))]]) ).
cnf(refute_0_25,plain,
( divide(identity,divide(inverse(X_3),X_4)) != inverse(divide(inverse(X_3),X_4))
| divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = divide(inverse(divide(inverse(X_3),X_4)),X_3) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(inverse(X_3),X_4)),X_3),divide(divide(identity,divide(inverse(X_3),X_4)),X_3)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
divide(divide(identity,divide(inverse(X_3),X_4)),X_3) = divide(inverse(divide(inverse(X_3),X_4)),X_3),
inference(resolve,[$cnf( $equal(divide(identity,divide(inverse(X_3),X_4)),inverse(divide(inverse(X_3),X_4))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( divide(divide(identity,divide(inverse(X_3),X_4)),X_3) != X_4
| divide(divide(identity,divide(inverse(X_3),X_4)),X_3) != divide(inverse(divide(inverse(X_3),X_4)),X_3)
| divide(inverse(divide(inverse(X_3),X_4)),X_3) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(inverse(X_3),X_4)),X_3),X_4) ),[0],$fot(divide(inverse(divide(inverse(X_3),X_4)),X_3))]]) ).
cnf(refute_0_28,plain,
( divide(divide(identity,divide(inverse(X_3),X_4)),X_3) != X_4
| divide(inverse(divide(inverse(X_3),X_4)),X_3) = X_4 ),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(inverse(X_3),X_4)),X_3),divide(inverse(divide(inverse(X_3),X_4)),X_3)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
divide(inverse(divide(inverse(X_3),X_4)),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(inverse(X_3),X_4)),X_3),X_4) )],[refute_0_19,refute_0_28]) ).
cnf(refute_0_30,plain,
divide(inverse(divide(inverse(divide(inverse(X_4),X_6)),X_4)),divide(inverse(X_4),X_6)) = X_4,
inference(subst,[],[refute_0_29:[bind(X_3,$fot(divide(inverse(X_4),X_6)))]]) ).
cnf(refute_0_31,plain,
divide(inverse(divide(inverse(X_4),X_6)),X_4) = X_6,
inference(subst,[],[refute_0_29:[bind(X_3,$fot(X_4)),bind(X_4,$fot(X_6))]]) ).
cnf(refute_0_32,plain,
( divide(inverse(divide(inverse(X_4),X_6)),X_4) != X_6
| divide(inverse(divide(inverse(divide(inverse(X_4),X_6)),X_4)),divide(inverse(X_4),X_6)) != X_4
| divide(inverse(X_6),divide(inverse(X_4),X_6)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(divide(inverse(divide(inverse(X_4),X_6)),X_4)),divide(inverse(X_4),X_6)),X_4) ),[0,0,0],$fot(X_6)]]) ).
cnf(refute_0_33,plain,
( divide(inverse(divide(inverse(divide(inverse(X_4),X_6)),X_4)),divide(inverse(X_4),X_6)) != X_4
| divide(inverse(X_6),divide(inverse(X_4),X_6)) = X_4 ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(inverse(X_4),X_6)),X_4),X_6) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
divide(inverse(X_6),divide(inverse(X_4),X_6)) = X_4,
inference(resolve,[$cnf( $equal(divide(inverse(divide(inverse(divide(inverse(X_4),X_6)),X_4)),divide(inverse(X_4),X_6)),X_4) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
divide(inverse(identity),divide(inverse(X_10),identity)) = X_10,
inference(subst,[],[refute_0_34:[bind(X_4,$fot(X_10)),bind(X_6,$fot(identity))]]) ).
cnf(refute_0_36,plain,
identity = divide(identity,identity),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_37,plain,
inverse(identity) = divide(identity,identity),
inference(subst,[],[refute_0_13:[bind(A,$fot(identity))]]) ).
cnf(refute_0_38,plain,
( inverse(identity) != divide(identity,identity)
| divide(identity,identity) = inverse(identity) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(identity))),bind(Y,$fot(divide(identity,identity)))]]) ).
cnf(refute_0_39,plain,
divide(identity,identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),divide(identity,identity)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( divide(identity,identity) != inverse(identity)
| identity != divide(identity,identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,divide(identity,identity)) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_41,plain,
( identity != divide(identity,identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(divide(identity,identity),inverse(identity)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,divide(identity,identity)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_44,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( divide(inverse(identity),divide(inverse(X_10),identity)) != X_10
| inverse(identity) != identity
| divide(identity,divide(inverse(X_10),identity)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(inverse(identity),divide(inverse(X_10),identity)),X_10) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_46,plain,
( divide(inverse(identity),divide(inverse(X_10),identity)) != X_10
| divide(identity,divide(inverse(X_10),identity)) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
divide(identity,divide(inverse(X_10),identity)) = X_10,
inference(resolve,[$cnf( $equal(divide(inverse(identity),divide(inverse(X_10),identity)),X_10) )],[refute_0_35,refute_0_46]) ).
cnf(refute_0_48,plain,
divide(identity,divide(inverse(X_10),identity)) = inverse(divide(inverse(X_10),identity)),
inference(subst,[],[refute_0_21:[bind(A,$fot(divide(inverse(X_10),identity)))]]) ).
cnf(refute_0_49,plain,
( divide(identity,divide(inverse(X_10),identity)) != X_10
| divide(identity,divide(inverse(X_10),identity)) != inverse(divide(inverse(X_10),identity))
| inverse(divide(inverse(X_10),identity)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(divide(identity,divide(inverse(X_10),identity)),X_10) ),[0],$fot(inverse(divide(inverse(X_10),identity)))]]) ).
cnf(refute_0_50,plain,
( divide(identity,divide(inverse(X_10),identity)) != X_10
| inverse(divide(inverse(X_10),identity)) = X_10 ),
inference(resolve,[$cnf( $equal(divide(identity,divide(inverse(X_10),identity)),inverse(divide(inverse(X_10),identity))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
inverse(divide(inverse(X_10),identity)) = X_10,
inference(resolve,[$cnf( $equal(divide(identity,divide(inverse(X_10),identity)),X_10) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
inverse(divide(inverse(divide(inverse(X_12),identity)),identity)) = divide(inverse(X_12),identity),
inference(subst,[],[refute_0_51:[bind(X_10,$fot(divide(inverse(X_12),identity)))]]) ).
cnf(refute_0_53,plain,
inverse(divide(inverse(X_12),identity)) = X_12,
inference(subst,[],[refute_0_51:[bind(X_10,$fot(X_12))]]) ).
cnf(refute_0_54,plain,
( inverse(divide(inverse(X_12),identity)) != X_12
| inverse(divide(inverse(divide(inverse(X_12),identity)),identity)) != divide(inverse(X_12),identity)
| inverse(divide(X_12,identity)) = divide(inverse(X_12),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(divide(inverse(X_12),identity)),identity)),divide(inverse(X_12),identity)) ),[0,0,0],$fot(X_12)]]) ).
cnf(refute_0_55,plain,
( inverse(divide(inverse(divide(inverse(X_12),identity)),identity)) != divide(inverse(X_12),identity)
| inverse(divide(X_12,identity)) = divide(inverse(X_12),identity) ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_12),identity)),X_12) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
inverse(divide(X_12,identity)) = divide(inverse(X_12),identity),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(divide(inverse(X_12),identity)),identity)),divide(inverse(X_12),identity)) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
( inverse(divide(X_12,identity)) != divide(inverse(X_12),identity)
| divide(inverse(X_12),identity) = inverse(divide(X_12,identity)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(divide(X_12,identity)))),bind(Y,$fot(divide(inverse(X_12),identity)))]]) ).
cnf(refute_0_58,plain,
divide(inverse(X_12),identity) = inverse(divide(X_12,identity)),
inference(resolve,[$cnf( $equal(inverse(divide(X_12,identity)),divide(inverse(X_12),identity)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
divide(inverse(X_10),identity) = inverse(divide(X_10,identity)),
inference(subst,[],[refute_0_58:[bind(X_12,$fot(X_10))]]) ).
cnf(refute_0_60,plain,
inverse(divide(inverse(X_10),identity)) = inverse(divide(inverse(X_10),identity)),
introduced(tautology,[refl,[$fot(inverse(divide(inverse(X_10),identity)))]]) ).
cnf(refute_0_61,plain,
( divide(inverse(X_10),identity) != inverse(divide(X_10,identity))
| inverse(divide(inverse(X_10),identity)) != inverse(divide(inverse(X_10),identity))
| inverse(divide(inverse(X_10),identity)) = inverse(inverse(divide(X_10,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_10),identity)),inverse(divide(inverse(X_10),identity))) ),[1,0],$fot(inverse(divide(X_10,identity)))]]) ).
cnf(refute_0_62,plain,
( divide(inverse(X_10),identity) != inverse(divide(X_10,identity))
| inverse(divide(inverse(X_10),identity)) = inverse(inverse(divide(X_10,identity))) ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_10),identity)),inverse(divide(inverse(X_10),identity))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
inverse(divide(inverse(X_10),identity)) = inverse(inverse(divide(X_10,identity))),
inference(resolve,[$cnf( $equal(divide(inverse(X_10),identity),inverse(divide(X_10,identity))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( inverse(divide(inverse(X_10),identity)) != X_10
| inverse(divide(inverse(X_10),identity)) != inverse(inverse(divide(X_10,identity)))
| inverse(inverse(divide(X_10,identity))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_10),identity)),X_10) ),[0],$fot(inverse(inverse(divide(X_10,identity))))]]) ).
cnf(refute_0_65,plain,
( inverse(divide(inverse(X_10),identity)) != X_10
| inverse(inverse(divide(X_10,identity))) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_10),identity)),inverse(inverse(divide(X_10,identity)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
inverse(inverse(divide(X_10,identity))) = X_10,
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_10),identity)),X_10) )],[refute_0_51,refute_0_65]) ).
cnf(refute_0_67,plain,
inverse(inverse(divide(multiply(identity,X_4),identity))) = multiply(identity,X_4),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(multiply(identity,X_4)))]]) ).
cnf(refute_0_68,plain,
divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3) = X_4,
inference(subst,[],[single_axiom:[bind(A,$fot(X_3)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_69,plain,
identity = divide(X_3,X_3),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_70,plain,
( identity != divide(X_3,X_3)
| divide(X_3,X_3) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(divide(X_3,X_3)))]]) ).
cnf(refute_0_71,plain,
divide(X_3,X_3) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X_3,X_3)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( divide(X_3,X_3) != identity
| divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3) != X_4
| divide(divide(X_3,divide(identity,X_4)),X_3) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3),X_4) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_73,plain,
( divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3) != X_4
| divide(divide(X_3,divide(identity,X_4)),X_3) = X_4 ),
inference(resolve,[$cnf( $equal(divide(X_3,X_3),identity) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
divide(divide(X_3,divide(identity,X_4)),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3),X_4) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_76,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_75]) ).
cnf(refute_0_77,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_76:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_78,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_79,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_80,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_83,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_83]) ).
cnf(refute_0_85,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_86,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
divide(X_3,inverse(X_4)) = multiply(X_3,X_4),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_88,plain,
divide(identity,X_4) = inverse(X_4),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_4))]]) ).
cnf(refute_0_89,plain,
divide(X_3,divide(identity,X_4)) = divide(X_3,divide(identity,X_4)),
introduced(tautology,[refl,[$fot(divide(X_3,divide(identity,X_4)))]]) ).
cnf(refute_0_90,plain,
( divide(X_3,divide(identity,X_4)) != divide(X_3,divide(identity,X_4))
| divide(identity,X_4) != inverse(X_4)
| divide(X_3,divide(identity,X_4)) = divide(X_3,inverse(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_3,divide(identity,X_4)),divide(X_3,divide(identity,X_4))) ),[1,1],$fot(inverse(X_4))]]) ).
cnf(refute_0_91,plain,
( divide(identity,X_4) != inverse(X_4)
| divide(X_3,divide(identity,X_4)) = divide(X_3,inverse(X_4)) ),
inference(resolve,[$cnf( $equal(divide(X_3,divide(identity,X_4)),divide(X_3,divide(identity,X_4))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
divide(X_3,divide(identity,X_4)) = divide(X_3,inverse(X_4)),
inference(resolve,[$cnf( $equal(divide(identity,X_4),inverse(X_4)) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_94,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_93]) ).
cnf(refute_0_95,plain,
( divide(X_3,divide(identity,X_4)) != divide(X_3,inverse(X_4))
| divide(X_3,inverse(X_4)) != multiply(X_3,X_4)
| divide(X_3,divide(identity,X_4)) = multiply(X_3,X_4) ),
inference(subst,[],[refute_0_94:[bind(X,$fot(divide(X_3,divide(identity,X_4)))),bind(Y,$fot(divide(X_3,inverse(X_4)))),bind(Z,$fot(multiply(X_3,X_4)))]]) ).
cnf(refute_0_96,plain,
( divide(X_3,inverse(X_4)) != multiply(X_3,X_4)
| divide(X_3,divide(identity,X_4)) = multiply(X_3,X_4) ),
inference(resolve,[$cnf( $equal(divide(X_3,divide(identity,X_4)),divide(X_3,inverse(X_4))) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
divide(X_3,divide(identity,X_4)) = multiply(X_3,X_4),
inference(resolve,[$cnf( $equal(divide(X_3,inverse(X_4)),multiply(X_3,X_4)) )],[refute_0_87,refute_0_96]) ).
cnf(refute_0_98,plain,
divide(divide(X_3,divide(identity,X_4)),X_3) = divide(divide(X_3,divide(identity,X_4)),X_3),
introduced(tautology,[refl,[$fot(divide(divide(X_3,divide(identity,X_4)),X_3))]]) ).
cnf(refute_0_99,plain,
( divide(X_3,divide(identity,X_4)) != multiply(X_3,X_4)
| divide(divide(X_3,divide(identity,X_4)),X_3) != divide(divide(X_3,divide(identity,X_4)),X_3)
| divide(divide(X_3,divide(identity,X_4)),X_3) = divide(multiply(X_3,X_4),X_3) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),divide(divide(X_3,divide(identity,X_4)),X_3)) ),[1,0],$fot(multiply(X_3,X_4))]]) ).
cnf(refute_0_100,plain,
( divide(X_3,divide(identity,X_4)) != multiply(X_3,X_4)
| divide(divide(X_3,divide(identity,X_4)),X_3) = divide(multiply(X_3,X_4),X_3) ),
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),divide(divide(X_3,divide(identity,X_4)),X_3)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
divide(divide(X_3,divide(identity,X_4)),X_3) = divide(multiply(X_3,X_4),X_3),
inference(resolve,[$cnf( $equal(divide(X_3,divide(identity,X_4)),multiply(X_3,X_4)) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
( divide(divide(X_3,divide(identity,X_4)),X_3) != X_4
| divide(divide(X_3,divide(identity,X_4)),X_3) != divide(multiply(X_3,X_4),X_3)
| divide(multiply(X_3,X_4),X_3) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),X_4) ),[0],$fot(divide(multiply(X_3,X_4),X_3))]]) ).
cnf(refute_0_103,plain,
( divide(divide(X_3,divide(identity,X_4)),X_3) != X_4
| divide(multiply(X_3,X_4),X_3) = X_4 ),
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),divide(multiply(X_3,X_4),X_3)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
divide(multiply(X_3,X_4),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),X_4) )],[refute_0_74,refute_0_103]) ).
cnf(refute_0_105,plain,
divide(multiply(identity,X_4),identity) = X_4,
inference(subst,[],[refute_0_104:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_106,plain,
( divide(multiply(identity,X_4),identity) != X_4
| inverse(inverse(divide(multiply(identity,X_4),identity))) != multiply(identity,X_4)
| inverse(inverse(X_4)) = multiply(identity,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(divide(multiply(identity,X_4),identity))),multiply(identity,X_4)) ),[0,0,0],$fot(X_4)]]) ).
cnf(refute_0_107,plain,
( inverse(inverse(divide(multiply(identity,X_4),identity))) != multiply(identity,X_4)
| inverse(inverse(X_4)) = multiply(identity,X_4) ),
inference(resolve,[$cnf( $equal(divide(multiply(identity,X_4),identity),X_4) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
inverse(inverse(X_4)) = multiply(identity,X_4),
inference(resolve,[$cnf( $equal(inverse(inverse(divide(multiply(identity,X_4),identity))),multiply(identity,X_4)) )],[refute_0_67,refute_0_107]) ).
cnf(refute_0_109,plain,
( inverse(inverse(X_4)) != multiply(identity,X_4)
| multiply(identity,X_4) = inverse(inverse(X_4)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(inverse(inverse(X_4)))),bind(Y,$fot(multiply(identity,X_4)))]]) ).
cnf(refute_0_110,plain,
multiply(identity,X_4) = inverse(inverse(X_4)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_4)),multiply(identity,X_4)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(identity,a2) = inverse(inverse(a2)),
inference(subst,[],[refute_0_110:[bind(X_4,$fot(a2))]]) ).
cnf(refute_0_112,plain,
identity = divide(inverse(X_16),inverse(X_16)),
inference(subst,[],[identity:[bind(A,$fot(inverse(X_16)))]]) ).
cnf(refute_0_113,plain,
multiply(inverse(X_16),X_16) = divide(inverse(X_16),inverse(X_16)),
inference(subst,[],[refute_0_84:[bind(A,$fot(inverse(X_16))),bind(B,$fot(X_16))]]) ).
cnf(refute_0_114,plain,
( multiply(inverse(X_16),X_16) != divide(inverse(X_16),inverse(X_16))
| divide(inverse(X_16),inverse(X_16)) = multiply(inverse(X_16),X_16) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(inverse(X_16),X_16))),bind(Y,$fot(divide(inverse(X_16),inverse(X_16))))]]) ).
cnf(refute_0_115,plain,
divide(inverse(X_16),inverse(X_16)) = multiply(inverse(X_16),X_16),
inference(resolve,[$cnf( $equal(multiply(inverse(X_16),X_16),divide(inverse(X_16),inverse(X_16))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( divide(inverse(X_16),inverse(X_16)) != multiply(inverse(X_16),X_16)
| identity != divide(inverse(X_16),inverse(X_16))
| identity = multiply(inverse(X_16),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(identity,divide(inverse(X_16),inverse(X_16))) ),[1],$fot(multiply(inverse(X_16),X_16))]]) ).
cnf(refute_0_117,plain,
( identity != divide(inverse(X_16),inverse(X_16))
| identity = multiply(inverse(X_16),X_16) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_16),inverse(X_16)),multiply(inverse(X_16),X_16)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
identity = multiply(inverse(X_16),X_16),
inference(resolve,[$cnf( $equal(identity,divide(inverse(X_16),inverse(X_16))) )],[refute_0_112,refute_0_117]) ).
cnf(refute_0_119,plain,
( identity != multiply(inverse(X_16),X_16)
| multiply(inverse(X_16),X_16) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_16),X_16)))]]) ).
cnf(refute_0_120,plain,
multiply(inverse(X_16),X_16) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(X_16),X_16)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(inverse(b2),b2) = identity,
inference(subst,[],[refute_0_120:[bind(X_16,$fot(b2))]]) ).
cnf(refute_0_122,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(multiply(inverse(b2),b2),a2),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(b2),b2),a2))]]) ).
cnf(refute_0_123,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(b2),b2) != identity
| multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_124,plain,
( multiply(inverse(b2),b2) != identity
| multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),identity) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(identity,a2)
| multiply(identity,a2) != inverse(inverse(a2))
| multiply(multiply(inverse(b2),b2),a2) = inverse(inverse(a2)) ),
inference(subst,[],[refute_0_94:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(identity,a2))),bind(Z,$fot(inverse(inverse(a2))))]]) ).
cnf(refute_0_127,plain,
( multiply(identity,a2) != inverse(inverse(a2))
| multiply(multiply(inverse(b2),b2),a2) = inverse(inverse(a2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(identity,a2)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(multiply(inverse(b2),b2),a2) = inverse(inverse(a2)),
inference(resolve,[$cnf( $equal(multiply(identity,a2),inverse(inverse(a2))) )],[refute_0_111,refute_0_127]) ).
cnf(refute_0_129,plain,
( multiply(multiply(inverse(b2),b2),a2) != inverse(inverse(a2))
| inverse(inverse(a2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).
cnf(refute_0_130,plain,
( inverse(inverse(a2)) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),inverse(inverse(a2))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
inverse(inverse(a2)) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_130,prove_these_axioms_2]) ).
cnf(refute_0_132,plain,
divide(multiply(inverse(X_4),X_4),inverse(X_4)) = X_4,
inference(subst,[],[refute_0_104:[bind(X_3,$fot(inverse(X_4)))]]) ).
cnf(refute_0_133,plain,
identity = multiply(inverse(X_4),X_4),
inference(subst,[],[refute_0_118:[bind(X_16,$fot(X_4))]]) ).
cnf(refute_0_134,plain,
( identity != multiply(inverse(X_4),X_4)
| multiply(inverse(X_4),X_4) = identity ),
inference(subst,[],[refute_0_3:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_4),X_4)))]]) ).
cnf(refute_0_135,plain,
multiply(inverse(X_4),X_4) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(inverse(X_4),X_4)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
( multiply(inverse(X_4),X_4) != identity
| divide(multiply(inverse(X_4),X_4),inverse(X_4)) != X_4
| divide(identity,inverse(X_4)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(inverse(X_4),X_4),inverse(X_4)),X_4) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_137,plain,
( divide(multiply(inverse(X_4),X_4),inverse(X_4)) != X_4
| divide(identity,inverse(X_4)) = X_4 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_4),X_4),identity) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
divide(identity,inverse(X_4)) = X_4,
inference(resolve,[$cnf( $equal(divide(multiply(inverse(X_4),X_4),inverse(X_4)),X_4) )],[refute_0_132,refute_0_137]) ).
cnf(refute_0_139,plain,
divide(identity,inverse(X_4)) = inverse(inverse(X_4)),
inference(subst,[],[refute_0_21:[bind(A,$fot(inverse(X_4)))]]) ).
cnf(refute_0_140,plain,
( divide(identity,inverse(X_4)) != X_4
| divide(identity,inverse(X_4)) != inverse(inverse(X_4))
| inverse(inverse(X_4)) = X_4 ),
introduced(tautology,[equality,[$cnf( $equal(divide(identity,inverse(X_4)),X_4) ),[0],$fot(inverse(inverse(X_4)))]]) ).
cnf(refute_0_141,plain,
( divide(identity,inverse(X_4)) != X_4
| inverse(inverse(X_4)) = X_4 ),
inference(resolve,[$cnf( $equal(divide(identity,inverse(X_4)),inverse(inverse(X_4))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
inverse(inverse(X_4)) = X_4,
inference(resolve,[$cnf( $equal(divide(identity,inverse(X_4)),X_4) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_142:[bind(X_4,$fot(a2))]]) ).
cnf(refute_0_144,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_145,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_145,refute_0_131]) ).
cnf(refute_0_147,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_148,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_147,refute_0_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP534-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.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 01:48:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36
% 0.20/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
%------------------------------------------------------------------------------