TSTP Solution File: CAT004-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Fri Jul 15 00:04:32 EDT 2022
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 35
% Syntax : Number of clauses : 109 ( 29 unt; 0 nHn; 106 RR)
% Number of literals : 245 ( 244 equ; 137 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_domain1,axiom,
( codomain(X) != domain(Y)
| domain(compose(X,Y)) = domain(X) ) ).
cnf(codomain_domain2,axiom,
( codomain(X) != domain(Y)
| codomain(compose(X,Y)) = codomain(Y) ) ).
cnf(star_property,axiom,
( codomain(X) != domain(Y)
| codomain(Y) != domain(Z)
| compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ).
cnf(epimorphism1,hypothesis,
( codomain(a) != domain(X)
| compose(a,X) != Y
| codomain(a) != domain(Z)
| compose(a,Z) != Y
| X = Z ) ).
cnf(epimorphism2,hypothesis,
( codomain(b) != domain(X)
| compose(b,X) != Y
| codomain(b) != domain(Z)
| compose(b,Z) != Y
| X = Z ) ).
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b) ).
cnf(codomain_of_ab_equals_domain_of_h,hypothesis,
codomain(compose(a,b)) = domain(h) ).
cnf(codomain_of_ab_equals_domain_of_g,hypothesis,
codomain(compose(a,b)) = domain(g) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g ).
cnf(refute_0_0,plain,
( codomain(b) != domain(X)
| codomain(b) != domain(Z)
| compose(b,X) != compose(b,X)
| compose(b,Z) != compose(b,X)
| X = Z ),
inference(subst,[],[epimorphism2:[bind(Y,$fot(compose(b,X)))]]) ).
cnf(refute_0_1,plain,
compose(b,X) = compose(b,X),
introduced(tautology,[refl,[$fot(compose(b,X))]]) ).
cnf(refute_0_2,plain,
( codomain(b) != domain(X)
| codomain(b) != domain(Z)
| compose(b,Z) != compose(b,X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(b,X),compose(b,X)) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( codomain(b) != domain(Z)
| codomain(b) != domain(h)
| compose(b,Z) != compose(b,h)
| h = Z ),
inference(subst,[],[refute_0_2:[bind(X,$fot(h))]]) ).
cnf(refute_0_4,plain,
( codomain(a) != domain(X)
| codomain(a) != domain(Z)
| compose(a,X) != compose(a,X)
| compose(a,Z) != compose(a,X)
| X = Z ),
inference(subst,[],[epimorphism1:[bind(Y,$fot(compose(a,X)))]]) ).
cnf(refute_0_5,plain,
compose(a,X) = compose(a,X),
introduced(tautology,[refl,[$fot(compose(a,X))]]) ).
cnf(refute_0_6,plain,
( codomain(a) != domain(X)
| codomain(a) != domain(Z)
| compose(a,Z) != compose(a,X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(a,X),compose(a,X)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( codomain(a) != domain(Z)
| codomain(a) != domain(compose(b,h))
| compose(a,Z) != compose(a,compose(b,h))
| compose(b,h) = Z ),
inference(subst,[],[refute_0_6:[bind(X,$fot(compose(b,h)))]]) ).
cnf(refute_0_8,plain,
( codomain(X_128) != domain(b)
| codomain(b) != domain(X_130)
| compose(X_128,compose(b,X_130)) = compose(compose(X_128,b),X_130) ),
inference(subst,[],[star_property:[bind(X,$fot(X_128)),bind(Y,$fot(b)),bind(Z,$fot(X_130))]]) ).
cnf(refute_0_9,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_11,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( codomain(a) != domain(b)
| domain(b) = codomain(a) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(domain(b)))]]) ).
cnf(refute_0_13,plain,
domain(b) = codomain(a),
inference(resolve,[$cnf( $equal(codomain(a),domain(b)) )],[codomain_of_a_equals_domain_of_b,refute_0_12]) ).
cnf(refute_0_14,plain,
( codomain(X_128) != codomain(a)
| domain(b) != codomain(a)
| codomain(X_128) = domain(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(X_128),domain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_15,plain,
( codomain(X_128) != codomain(a)
| codomain(X_128) = domain(b) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( codomain(X_128) != codomain(a)
| codomain(b) != domain(X_130)
| compose(X_128,compose(b,X_130)) = compose(compose(X_128,b),X_130) ),
inference(resolve,[$cnf( $equal(codomain(X_128),domain(b)) )],[refute_0_15,refute_0_8]) ).
cnf(refute_0_17,plain,
( codomain(a) != codomain(a)
| codomain(b) != domain(X_130)
| compose(a,compose(b,X_130)) = compose(compose(a,b),X_130) ),
inference(subst,[],[refute_0_16:[bind(X_128,$fot(a))]]) ).
cnf(refute_0_18,plain,
codomain(a) = codomain(a),
introduced(tautology,[refl,[$fot(codomain(a))]]) ).
cnf(refute_0_19,plain,
( codomain(b) != domain(X_130)
| compose(a,compose(b,X_130)) = compose(compose(a,b),X_130) ),
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( codomain(b) != domain(h)
| compose(a,compose(b,h)) = compose(compose(a,b),h) ),
inference(subst,[],[refute_0_19:[bind(X_130,$fot(h))]]) ).
cnf(refute_0_21,plain,
( codomain(compose(a,b)) != domain(g)
| codomain(compose(a,b)) != domain(h)
| domain(h) = domain(g) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(compose(a,b)),domain(g)) ),[0],$fot(domain(h))]]) ).
cnf(refute_0_22,plain,
( codomain(compose(a,b)) != domain(g)
| domain(h) = domain(g) ),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),domain(h)) )],[codomain_of_ab_equals_domain_of_h,refute_0_21]) ).
cnf(refute_0_23,plain,
domain(h) = domain(g),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),domain(g)) )],[codomain_of_ab_equals_domain_of_g,refute_0_22]) ).
cnf(refute_0_24,plain,
( codomain(X_10) != domain(b)
| codomain(compose(X_10,b)) = codomain(b) ),
inference(subst,[],[codomain_domain2:[bind(X,$fot(X_10)),bind(Y,$fot(b))]]) ).
cnf(refute_0_25,plain,
( codomain(X_10) != codomain(a)
| domain(b) != codomain(a)
| codomain(X_10) = domain(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(X_10),domain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_26,plain,
( codomain(X_10) != codomain(a)
| codomain(X_10) = domain(b) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_13,refute_0_25]) ).
cnf(refute_0_27,plain,
( codomain(X_10) != codomain(a)
| codomain(compose(X_10,b)) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(X_10),domain(b)) )],[refute_0_26,refute_0_24]) ).
cnf(refute_0_28,plain,
( codomain(a) != codomain(a)
| codomain(compose(a,b)) = codomain(b) ),
inference(subst,[],[refute_0_27:[bind(X_10,$fot(a))]]) ).
cnf(refute_0_29,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_18,refute_0_28]) ).
cnf(refute_0_30,plain,
( codomain(compose(a,b)) != codomain(b)
| codomain(compose(a,b)) != domain(g)
| domain(g) = codomain(b) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(compose(a,b)),codomain(b)) ),[0],$fot(domain(g))]]) ).
cnf(refute_0_31,plain,
( codomain(compose(a,b)) != codomain(b)
| domain(g) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),domain(g)) )],[codomain_of_ab_equals_domain_of_g,refute_0_30]) ).
cnf(refute_0_32,plain,
domain(g) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),codomain(b)) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( domain(g) != codomain(b)
| domain(h) != domain(g)
| domain(h) = codomain(b) ),
introduced(tautology,[equality,[$cnf( $equal(domain(h),domain(g)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_34,plain,
( domain(h) != domain(g)
| domain(h) = codomain(b) ),
inference(resolve,[$cnf( $equal(domain(g),codomain(b)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
domain(h) = codomain(b),
inference(resolve,[$cnf( $equal(domain(h),domain(g)) )],[refute_0_23,refute_0_34]) ).
cnf(refute_0_36,plain,
( codomain(b) != codomain(b)
| domain(h) != codomain(b)
| codomain(b) = domain(h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(b),domain(h)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_37,plain,
( codomain(b) != codomain(b)
| codomain(b) = domain(h) ),
inference(resolve,[$cnf( $equal(domain(h),codomain(b)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,h)) = compose(compose(a,b),h) ),
inference(resolve,[$cnf( $equal(codomain(b),domain(h)) )],[refute_0_37,refute_0_20]) ).
cnf(refute_0_39,plain,
codomain(b) = codomain(b),
introduced(tautology,[refl,[$fot(codomain(b))]]) ).
cnf(refute_0_40,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
( codomain(b) != domain(g)
| compose(a,compose(b,g)) = compose(compose(a,b),g) ),
inference(subst,[],[refute_0_19:[bind(X_130,$fot(g))]]) ).
cnf(refute_0_42,plain,
( codomain(b) != codomain(b)
| domain(g) != codomain(b)
| codomain(b) = domain(g) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(b),domain(g)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_43,plain,
( codomain(b) != codomain(b)
| codomain(b) = domain(g) ),
inference(resolve,[$cnf( $equal(domain(g),codomain(b)) )],[refute_0_32,refute_0_42]) ).
cnf(refute_0_44,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,g)) = compose(compose(a,b),g) ),
inference(resolve,[$cnf( $equal(codomain(b),domain(g)) )],[refute_0_43,refute_0_41]) ).
cnf(refute_0_45,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
( compose(a,compose(b,g)) != compose(compose(a,b),g)
| compose(compose(a,b),g) = compose(a,compose(b,g)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(compose(a,compose(b,g)))),bind(Y0,$fot(compose(compose(a,b),g)))]]) ).
cnf(refute_0_47,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(compose(a,b),g)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_49,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_11,refute_0_48]) ).
cnf(refute_0_50,plain,
( compose(compose(a,b),g) != compose(a,compose(b,g))
| compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(compose(a,b),h) = compose(a,compose(b,g)) ),
inference(subst,[],[refute_0_49:[bind(X0,$fot(compose(compose(a,b),h))),bind(Y0,$fot(compose(compose(a,b),g))),bind(Z0,$fot(compose(a,compose(b,g))))]]) ).
cnf(refute_0_51,plain,
( compose(compose(a,b),g) != compose(a,compose(b,g))
| compose(compose(a,b),h) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(compose(a,b),g)) )],[ab_h_equals_ab_g,refute_0_50]) ).
cnf(refute_0_52,plain,
compose(compose(a,b),h) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(compose(a,b),g),compose(a,compose(b,g))) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),h)
| compose(compose(a,b),h) != compose(a,compose(b,g))
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) ),[0],$fot(compose(compose(a,b),h))]]) ).
cnf(refute_0_54,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),h)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(a,compose(b,g))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(compose(a,b),h)) )],[refute_0_40,refute_0_54]) ).
cnf(refute_0_56,plain,
( compose(a,Z) != compose(a,compose(b,g))
| compose(a,compose(b,h)) != compose(a,compose(b,g))
| compose(a,Z) = compose(a,compose(b,h)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,Z),compose(a,compose(b,h))) ),[1],$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_57,plain,
( compose(a,Z) != compose(a,compose(b,g))
| compose(a,Z) = compose(a,compose(b,h)) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( codomain(a) != domain(Z)
| codomain(a) != domain(compose(b,h))
| compose(a,Z) != compose(a,compose(b,g))
| compose(b,h) = Z ),
inference(resolve,[$cnf( $equal(compose(a,Z),compose(a,compose(b,h))) )],[refute_0_57,refute_0_7]) ).
cnf(refute_0_59,plain,
( codomain(X) != domain(h)
| domain(compose(X,h)) = domain(X) ),
inference(subst,[],[codomain_domain1:[bind(Y,$fot(h))]]) ).
cnf(refute_0_60,plain,
( codomain(X) != codomain(b)
| domain(h) != codomain(b)
| codomain(X) = domain(h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(X),domain(h)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_61,plain,
( codomain(X) != codomain(b)
| codomain(X) = domain(h) ),
inference(resolve,[$cnf( $equal(domain(h),codomain(b)) )],[refute_0_35,refute_0_60]) ).
cnf(refute_0_62,plain,
( codomain(X) != codomain(b)
| domain(compose(X,h)) = domain(X) ),
inference(resolve,[$cnf( $equal(codomain(X),domain(h)) )],[refute_0_61,refute_0_59]) ).
cnf(refute_0_63,plain,
( codomain(b) != codomain(b)
| domain(compose(b,h)) = domain(b) ),
inference(subst,[],[refute_0_62:[bind(X,$fot(b))]]) ).
cnf(refute_0_64,plain,
domain(compose(b,h)) = domain(b),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_39,refute_0_63]) ).
cnf(refute_0_65,plain,
( domain(b) != codomain(a)
| domain(compose(b,h)) != domain(b)
| domain(compose(b,h)) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(compose(b,h)),domain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_66,plain,
( domain(compose(b,h)) != domain(b)
| domain(compose(b,h)) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_13,refute_0_65]) ).
cnf(refute_0_67,plain,
domain(compose(b,h)) = codomain(a),
inference(resolve,[$cnf( $equal(domain(compose(b,h)),domain(b)) )],[refute_0_64,refute_0_66]) ).
cnf(refute_0_68,plain,
( codomain(a) != codomain(a)
| domain(compose(b,h)) != codomain(a)
| codomain(a) = domain(compose(b,h)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(a),domain(compose(b,h))) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_69,plain,
( codomain(a) != codomain(a)
| codomain(a) = domain(compose(b,h)) ),
inference(resolve,[$cnf( $equal(domain(compose(b,h)),codomain(a)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( codomain(a) != codomain(a)
| codomain(a) != domain(Z)
| compose(a,Z) != compose(a,compose(b,g))
| compose(b,h) = Z ),
inference(resolve,[$cnf( $equal(codomain(a),domain(compose(b,h))) )],[refute_0_69,refute_0_58]) ).
cnf(refute_0_71,plain,
( codomain(a) != domain(Z)
| compose(a,Z) != compose(a,compose(b,g))
| compose(b,h) = Z ),
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_18,refute_0_70]) ).
cnf(refute_0_72,plain,
( codomain(a) != domain(compose(b,g))
| compose(a,compose(b,g)) != compose(a,compose(b,g))
| compose(b,h) = compose(b,g) ),
inference(subst,[],[refute_0_71:[bind(Z,$fot(compose(b,g)))]]) ).
cnf(refute_0_73,plain,
compose(a,compose(b,g)) = compose(a,compose(b,g)),
introduced(tautology,[refl,[$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_74,plain,
( codomain(a) != domain(compose(b,g))
| compose(b,h) = compose(b,g) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(a,compose(b,g))) )],[refute_0_73,refute_0_72]) ).
cnf(refute_0_75,plain,
( codomain(X) != domain(g)
| domain(compose(X,g)) = domain(X) ),
inference(subst,[],[codomain_domain1:[bind(Y,$fot(g))]]) ).
cnf(refute_0_76,plain,
( codomain(X) != codomain(b)
| domain(g) != codomain(b)
| codomain(X) = domain(g) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(X),domain(g)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_77,plain,
( codomain(X) != codomain(b)
| codomain(X) = domain(g) ),
inference(resolve,[$cnf( $equal(domain(g),codomain(b)) )],[refute_0_32,refute_0_76]) ).
cnf(refute_0_78,plain,
( codomain(X) != codomain(b)
| domain(compose(X,g)) = domain(X) ),
inference(resolve,[$cnf( $equal(codomain(X),domain(g)) )],[refute_0_77,refute_0_75]) ).
cnf(refute_0_79,plain,
( codomain(b) != codomain(b)
| domain(compose(b,g)) = domain(b) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(b))]]) ).
cnf(refute_0_80,plain,
domain(compose(b,g)) = domain(b),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_39,refute_0_79]) ).
cnf(refute_0_81,plain,
( domain(b) != codomain(a)
| domain(compose(b,g)) != domain(b)
| domain(compose(b,g)) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(compose(b,g)),domain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_82,plain,
( domain(compose(b,g)) != domain(b)
| domain(compose(b,g)) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_13,refute_0_81]) ).
cnf(refute_0_83,plain,
domain(compose(b,g)) = codomain(a),
inference(resolve,[$cnf( $equal(domain(compose(b,g)),domain(b)) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
( codomain(a) != codomain(a)
| domain(compose(b,g)) != codomain(a)
| codomain(a) = domain(compose(b,g)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(a),domain(compose(b,g))) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_85,plain,
( codomain(a) != codomain(a)
| codomain(a) = domain(compose(b,g)) ),
inference(resolve,[$cnf( $equal(domain(compose(b,g)),codomain(a)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( codomain(a) != codomain(a)
| compose(b,h) = compose(b,g) ),
inference(resolve,[$cnf( $equal(codomain(a),domain(compose(b,g))) )],[refute_0_85,refute_0_74]) ).
cnf(refute_0_87,plain,
compose(b,h) = compose(b,g),
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_18,refute_0_86]) ).
cnf(refute_0_88,plain,
( compose(b,Z) != compose(b,g)
| compose(b,h) != compose(b,g)
| compose(b,Z) = compose(b,h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(b,Z),compose(b,h)) ),[1],$fot(compose(b,g))]]) ).
cnf(refute_0_89,plain,
( compose(b,Z) != compose(b,g)
| compose(b,Z) = compose(b,h) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( codomain(b) != domain(Z)
| codomain(b) != domain(h)
| compose(b,Z) != compose(b,g)
| h = Z ),
inference(resolve,[$cnf( $equal(compose(b,Z),compose(b,h)) )],[refute_0_89,refute_0_3]) ).
cnf(refute_0_91,plain,
( codomain(b) != codomain(b)
| codomain(b) != domain(Z)
| compose(b,Z) != compose(b,g)
| h = Z ),
inference(resolve,[$cnf( $equal(codomain(b),domain(h)) )],[refute_0_37,refute_0_90]) ).
cnf(refute_0_92,plain,
( codomain(b) != domain(Z)
| compose(b,Z) != compose(b,g)
| h = Z ),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_39,refute_0_91]) ).
cnf(refute_0_93,plain,
( codomain(b) != domain(g)
| compose(b,g) != compose(b,g)
| h = g ),
inference(subst,[],[refute_0_92:[bind(Z,$fot(g))]]) ).
cnf(refute_0_94,plain,
compose(b,g) = compose(b,g),
introduced(tautology,[refl,[$fot(compose(b,g))]]) ).
cnf(refute_0_95,plain,
( codomain(b) != domain(g)
| h = g ),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,g)) )],[refute_0_94,refute_0_93]) ).
cnf(refute_0_96,plain,
( codomain(b) != codomain(b)
| h = g ),
inference(resolve,[$cnf( $equal(codomain(b),domain(g)) )],[refute_0_43,refute_0_95]) ).
cnf(refute_0_97,plain,
h = g,
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_39,refute_0_96]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( $equal(h,g) )],[refute_0_97,prove_h_equals_g]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 : Sun May 29 15:36:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.52
% 0.18/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.53
%------------------------------------------------------------------------------