TSTP Solution File: GRP536-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP536-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 0.18s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of clauses : 94 ( 51 unt; 0 nHn; 44 RR)
% Number of literals : 156 ( 155 equ; 64 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 : 173 ( 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_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(refute_0_0,plain,
divide(divide(A,divide(divide(A,divide(divide(A,C),X_4)),C)),divide(divide(A,C),X_4)) = C,
inference(subst,[],[single_axiom:[bind(B,$fot(divide(divide(A,C),X_4)))]]) ).
cnf(refute_0_1,plain,
divide(divide(A,divide(divide(A,C),X_4)),C) = X_4,
inference(subst,[],[single_axiom:[bind(B,$fot(C)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_2,plain,
( divide(divide(A,divide(divide(A,C),X_4)),C) != X_4
| divide(divide(A,divide(divide(A,divide(divide(A,C),X_4)),C)),divide(divide(A,C),X_4)) != C
| divide(divide(A,X_4),divide(divide(A,C),X_4)) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,divide(divide(A,divide(divide(A,C),X_4)),C)),divide(divide(A,C),X_4)),C) ),[0,0,1],$fot(X_4)]]) ).
cnf(refute_0_3,plain,
( divide(divide(A,divide(divide(A,divide(divide(A,C),X_4)),C)),divide(divide(A,C),X_4)) != C
| divide(divide(A,X_4),divide(divide(A,C),X_4)) = C ),
inference(resolve,[$cnf( $equal(divide(divide(A,divide(divide(A,C),X_4)),C),X_4) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
divide(divide(A,X_4),divide(divide(A,C),X_4)) = C,
inference(resolve,[$cnf( $equal(divide(divide(A,divide(divide(A,divide(divide(A,C),X_4)),C)),divide(divide(A,C),X_4)),C) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(divide(X_34,X_35),divide(divide(X_34,X_34),X_35)) = X_34,
inference(subst,[],[refute_0_4:[bind(A,$fot(X_34)),bind(C,$fot(X_34)),bind(X_4,$fot(X_35))]]) ).
cnf(refute_0_6,plain,
identity = divide(X_34,X_34),
inference(subst,[],[identity:[bind(A,$fot(X_34))]]) ).
cnf(refute_0_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( identity != divide(X_34,X_34)
| divide(X_34,X_34) = identity ),
inference(subst,[],[refute_0_9:[bind(X,$fot(identity)),bind(Y,$fot(divide(X_34,X_34)))]]) ).
cnf(refute_0_11,plain,
divide(X_34,X_34) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X_34,X_34)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( divide(X_34,X_34) != identity
| divide(divide(X_34,X_35),divide(divide(X_34,X_34),X_35)) != X_34
| divide(divide(X_34,X_35),divide(identity,X_35)) = X_34 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_34,X_35),divide(divide(X_34,X_34),X_35)),X_34) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_13,plain,
( divide(divide(X_34,X_35),divide(divide(X_34,X_34),X_35)) != X_34
| divide(divide(X_34,X_35),divide(identity,X_35)) = X_34 ),
inference(resolve,[$cnf( $equal(divide(X_34,X_34),identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
divide(divide(X_34,X_35),divide(identity,X_35)) = X_34,
inference(resolve,[$cnf( $equal(divide(divide(X_34,X_35),divide(divide(X_34,X_34),X_35)),X_34) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_16,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_16:[bind(A,$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( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_9:[bind(X,$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( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
divide(divide(X_34,X_35),inverse(X_35)) = multiply(divide(X_34,X_35),X_35),
inference(subst,[],[refute_0_26:[bind(A,$fot(divide(X_34,X_35))),bind(B,$fot(X_35))]]) ).
cnf(refute_0_28,plain,
( identity != divide(A,A)
| divide(A,A) = identity ),
inference(subst,[],[refute_0_9:[bind(X,$fot(identity)),bind(Y,$fot(divide(A,A)))]]) ).
cnf(refute_0_29,plain,
divide(A,A) = identity,
inference(resolve,[$cnf( $equal(identity,divide(A,A)) )],[identity,refute_0_28]) ).
cnf(refute_0_30,plain,
divide(B,B) = identity,
inference(subst,[],[refute_0_29:[bind(A,$fot(B))]]) ).
cnf(refute_0_31,plain,
divide(divide(B,B),A) = divide(divide(B,B),A),
introduced(tautology,[refl,[$fot(divide(divide(B,B),A))]]) ).
cnf(refute_0_32,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_33,plain,
( divide(B,B) != identity
| divide(divide(B,B),A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(divide(B,B),A)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
divide(divide(B,B),A) = divide(identity,A),
inference(resolve,[$cnf( $equal(divide(B,B),identity) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( divide(divide(B,B),A) != divide(identity,A)
| inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) ),[1],$fot(divide(identity,A))]]) ).
cnf(refute_0_36,plain,
( inverse(A) != divide(divide(B,B),A)
| inverse(A) = divide(identity,A) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),A),divide(identity,A)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
inverse(A) = divide(identity,A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_36]) ).
cnf(refute_0_38,plain,
( inverse(A) != divide(identity,A)
| divide(identity,A) = inverse(A) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(identity,A)))]]) ).
cnf(refute_0_39,plain,
divide(identity,A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(identity,A)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
divide(identity,X_35) = inverse(X_35),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_41,plain,
divide(divide(X_34,X_35),divide(identity,X_35)) = divide(divide(X_34,X_35),divide(identity,X_35)),
introduced(tautology,[refl,[$fot(divide(divide(X_34,X_35),divide(identity,X_35)))]]) ).
cnf(refute_0_42,plain,
( divide(divide(X_34,X_35),divide(identity,X_35)) != divide(divide(X_34,X_35),divide(identity,X_35))
| divide(identity,X_35) != inverse(X_35)
| divide(divide(X_34,X_35),divide(identity,X_35)) = divide(divide(X_34,X_35),inverse(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_34,X_35),divide(identity,X_35)),divide(divide(X_34,X_35),divide(identity,X_35))) ),[1,1],$fot(inverse(X_35))]]) ).
cnf(refute_0_43,plain,
( divide(identity,X_35) != inverse(X_35)
| divide(divide(X_34,X_35),divide(identity,X_35)) = divide(divide(X_34,X_35),inverse(X_35)) ),
inference(resolve,[$cnf( $equal(divide(divide(X_34,X_35),divide(identity,X_35)),divide(divide(X_34,X_35),divide(identity,X_35))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
divide(divide(X_34,X_35),divide(identity,X_35)) = divide(divide(X_34,X_35),inverse(X_35)),
inference(resolve,[$cnf( $equal(divide(identity,X_35),inverse(X_35)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_46,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_9,refute_0_45]) ).
cnf(refute_0_47,plain,
( divide(divide(X_34,X_35),divide(identity,X_35)) != divide(divide(X_34,X_35),inverse(X_35))
| divide(divide(X_34,X_35),inverse(X_35)) != multiply(divide(X_34,X_35),X_35)
| divide(divide(X_34,X_35),divide(identity,X_35)) = multiply(divide(X_34,X_35),X_35) ),
inference(subst,[],[refute_0_46:[bind(X,$fot(divide(divide(X_34,X_35),divide(identity,X_35)))),bind(Y,$fot(divide(divide(X_34,X_35),inverse(X_35)))),bind(Z,$fot(multiply(divide(X_34,X_35),X_35)))]]) ).
cnf(refute_0_48,plain,
( divide(divide(X_34,X_35),inverse(X_35)) != multiply(divide(X_34,X_35),X_35)
| divide(divide(X_34,X_35),divide(identity,X_35)) = multiply(divide(X_34,X_35),X_35) ),
inference(resolve,[$cnf( $equal(divide(divide(X_34,X_35),divide(identity,X_35)),divide(divide(X_34,X_35),inverse(X_35))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
divide(divide(X_34,X_35),divide(identity,X_35)) = multiply(divide(X_34,X_35),X_35),
inference(resolve,[$cnf( $equal(divide(divide(X_34,X_35),inverse(X_35)),multiply(divide(X_34,X_35),X_35)) )],[refute_0_27,refute_0_48]) ).
cnf(refute_0_50,plain,
( divide(divide(X_34,X_35),divide(identity,X_35)) != X_34
| divide(divide(X_34,X_35),divide(identity,X_35)) != multiply(divide(X_34,X_35),X_35)
| multiply(divide(X_34,X_35),X_35) = X_34 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_34,X_35),divide(identity,X_35)),X_34) ),[0],$fot(multiply(divide(X_34,X_35),X_35))]]) ).
cnf(refute_0_51,plain,
( divide(divide(X_34,X_35),divide(identity,X_35)) != X_34
| multiply(divide(X_34,X_35),X_35) = X_34 ),
inference(resolve,[$cnf( $equal(divide(divide(X_34,X_35),divide(identity,X_35)),multiply(divide(X_34,X_35),X_35)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(divide(X_34,X_35),X_35) = X_34,
inference(resolve,[$cnf( $equal(divide(divide(X_34,X_35),divide(identity,X_35)),X_34) )],[refute_0_14,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(divide(multiply(X_37,X_4),X_37),X_37) = multiply(X_37,X_4),
inference(subst,[],[refute_0_52:[bind(X_34,$fot(multiply(X_37,X_4))),bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_54,plain,
divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3) = X_4,
inference(subst,[],[single_axiom:[bind(A,$fot(X_3)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_55,plain,
identity = divide(X_3,X_3),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_56,plain,
( identity != divide(X_3,X_3)
| divide(X_3,X_3) = identity ),
inference(subst,[],[refute_0_9:[bind(X,$fot(identity)),bind(Y,$fot(divide(X_3,X_3)))]]) ).
cnf(refute_0_57,plain,
divide(X_3,X_3) = identity,
inference(resolve,[$cnf( $equal(identity,divide(X_3,X_3)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( divide(X_3,X_3) != identity
| divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3) != X_4
| divide(divide(X_3,divide(identity,X_4)),X_3) = X_4 ),
introduced(tautology,[equality,[$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_59,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( $equal(divide(X_3,X_3),identity) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
divide(divide(X_3,divide(identity,X_4)),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(divide(X_3,X_3),X_4)),X_3),X_4) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
divide(X_3,inverse(X_4)) = multiply(X_3,X_4),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_62,plain,
divide(identity,X_4) = inverse(X_4),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_4))]]) ).
cnf(refute_0_63,plain,
divide(X_3,divide(identity,X_4)) = divide(X_3,divide(identity,X_4)),
introduced(tautology,[refl,[$fot(divide(X_3,divide(identity,X_4)))]]) ).
cnf(refute_0_64,plain,
( divide(X_3,divide(identity,X_4)) != divide(X_3,divide(identity,X_4))
| divide(identity,X_4) != inverse(X_4)
| divide(X_3,divide(identity,X_4)) = divide(X_3,inverse(X_4)) ),
introduced(tautology,[equality,[$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_65,plain,
( divide(identity,X_4) != inverse(X_4)
| divide(X_3,divide(identity,X_4)) = divide(X_3,inverse(X_4)) ),
inference(resolve,[$cnf( $equal(divide(X_3,divide(identity,X_4)),divide(X_3,divide(identity,X_4))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
divide(X_3,divide(identity,X_4)) = divide(X_3,inverse(X_4)),
inference(resolve,[$cnf( $equal(divide(identity,X_4),inverse(X_4)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( divide(X_3,divide(identity,X_4)) != divide(X_3,inverse(X_4))
| divide(X_3,inverse(X_4)) != multiply(X_3,X_4)
| divide(X_3,divide(identity,X_4)) = multiply(X_3,X_4) ),
inference(subst,[],[refute_0_46:[bind(X,$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_68,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( $equal(divide(X_3,divide(identity,X_4)),divide(X_3,inverse(X_4))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
divide(X_3,divide(identity,X_4)) = multiply(X_3,X_4),
inference(resolve,[$cnf( $equal(divide(X_3,inverse(X_4)),multiply(X_3,X_4)) )],[refute_0_61,refute_0_68]) ).
cnf(refute_0_70,plain,
divide(divide(X_3,divide(identity,X_4)),X_3) = divide(divide(X_3,divide(identity,X_4)),X_3),
introduced(tautology,[refl,[$fot(divide(divide(X_3,divide(identity,X_4)),X_3))]]) ).
cnf(refute_0_71,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_72,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( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),divide(divide(X_3,divide(identity,X_4)),X_3)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
divide(divide(X_3,divide(identity,X_4)),X_3) = divide(multiply(X_3,X_4),X_3),
inference(resolve,[$cnf( $equal(divide(X_3,divide(identity,X_4)),multiply(X_3,X_4)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( divide(divide(X_3,divide(identity,X_4)),X_3) != X_4
| divide(divide(X_3,divide(identity,X_4)),X_3) != divide(multiply(X_3,X_4),X_3)
| divide(multiply(X_3,X_4),X_3) = X_4 ),
introduced(tautology,[equality,[$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_75,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( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),divide(multiply(X_3,X_4),X_3)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
divide(multiply(X_3,X_4),X_3) = X_4,
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(identity,X_4)),X_3),X_4) )],[refute_0_60,refute_0_75]) ).
cnf(refute_0_77,plain,
divide(multiply(X_37,X_4),X_37) = X_4,
inference(subst,[],[refute_0_76:[bind(X_3,$fot(X_37))]]) ).
cnf(refute_0_78,plain,
( multiply(divide(multiply(X_37,X_4),X_37),X_37) != multiply(X_37,X_4)
| divide(multiply(X_37,X_4),X_37) != X_4
| multiply(X_4,X_37) = multiply(X_37,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(multiply(X_37,X_4),X_37),X_37),multiply(X_37,X_4)) ),[0,0],$fot(X_4)]]) ).
cnf(refute_0_79,plain,
( multiply(divide(multiply(X_37,X_4),X_37),X_37) != multiply(X_37,X_4)
| multiply(X_4,X_37) = multiply(X_37,X_4) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_37,X_4),X_37),X_4) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(X_4,X_37) = multiply(X_37,X_4),
inference(resolve,[$cnf( $equal(multiply(divide(multiply(X_37,X_4),X_37),X_37),multiply(X_37,X_4)) )],[refute_0_53,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(X_4,X_37) != multiply(X_37,X_4)
| multiply(X_37,X_4) = multiply(X_4,X_37) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(multiply(X_4,X_37))),bind(Y,$fot(multiply(X_37,X_4)))]]) ).
cnf(refute_0_82,plain,
multiply(X_37,X_4) = multiply(X_4,X_37),
inference(resolve,[$cnf( $equal(multiply(X_4,X_37),multiply(X_37,X_4)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(b,a) = multiply(a,b),
inference(subst,[],[refute_0_82:[bind(X_37,$fot(b)),bind(X_4,$fot(a))]]) ).
cnf(refute_0_84,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),multiply(b,a)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_85,plain,
( multiply(a,b) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(b,a)) )],[refute_0_85,prove_these_axioms_4]) ).
cnf(refute_0_87,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_88,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_87,refute_0_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP536-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.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 13:03:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.37
% 0.18/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.38
%------------------------------------------------------------------------------