%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CAT001-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n032.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 00:04:30 EDT 2022

% Result   : Unsatisfiable 2.24s 2.41s
% Output   : CNFRefutation 2.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   33
% Syntax   : Number of clauses     :  124 (  45 unt;   0 nHn; 109 RR)
%            Number of literals    :  228 ( 167 equ; 106 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   74 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(codomain_has_elements,axiom,
    ( ~ there_exists(codomain(X))
    | there_exists(X) ) ).

cnf(composition_implies_domain,axiom,
    ( ~ there_exists(compose(X,Y))
    | there_exists(domain(X)) ) ).

cnf(domain_codomain_composition1,axiom,
    ( ~ there_exists(compose(X,Y))
    | domain(X) = codomain(Y) ) ).

cnf(associativity_of_compose,axiom,
    compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ).

cnf(compose_domain,axiom,
    compose(X,domain(X)) = X ).

cnf(monomorphism,hypothesis,
    ( compose(compose(a,b),X) != Y
    | compose(compose(a,b),Z) != Y
    | X = Z ) ).

cnf(assume_bh_exists,hypothesis,
    there_exists(compose(b,h)) ).

cnf(bh_equals_bg,hypothesis,
    compose(b,h) = compose(b,g) ).

cnf(prove_h_equals_g,negated_conjecture,
    h != g ).

cnf(refute_0_0,plain,
    compose(h,domain(h)) = h,
    inference(subst,[],[compose_domain:[bind(X,$fot(h))]]) ).

cnf(refute_0_1,plain,
    ( ~ there_exists(compose(g,domain(h)))
    | domain(g) = codomain(domain(h)) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(g)),bind(Y,$fot(domain(h)))]]) ).

cnf(refute_0_2,plain,
    ( ~ there_exists(codomain(compose(g,domain(h))))
    | there_exists(compose(g,domain(h))) ),
    inference(subst,[],[codomain_has_elements:[bind(X,$fot(compose(g,domain(h))))]]) ).

cnf(refute_0_3,plain,
    ( ~ there_exists(compose(b,compose(g,domain(h))))
    | domain(b) = codomain(compose(g,domain(h))) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(compose(g,domain(h))))]]) ).

cnf(refute_0_4,plain,
    compose(b,compose(h,X_9)) = compose(compose(b,h),X_9),
    inference(subst,[],[associativity_of_compose:[bind(X,$fot(b)),bind(Y,$fot(h)),bind(Z,$fot(X_9))]]) ).

cnf(refute_0_5,plain,
    ( compose(b,compose(h,X_9)) != compose(compose(b,h),X_9)
    | compose(b,h) != compose(b,g)
    | compose(b,compose(h,X_9)) = compose(compose(b,g),X_9) ),
    introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,X_9)),compose(compose(b,h),X_9)) ),[1,0],$fot(compose(b,g))]]) ).

cnf(refute_0_6,plain,
    ( compose(b,compose(h,X_9)) != compose(compose(b,h),X_9)
    | compose(b,compose(h,X_9)) = compose(compose(b,g),X_9) ),
    inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_5]) ).

cnf(refute_0_7,plain,
    compose(b,compose(h,X_9)) = compose(compose(b,g),X_9),
    inference(resolve,[$cnf( $equal(compose(b,compose(h,X_9)),compose(compose(b,h),X_9)) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_9,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_10,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( compose(X,compose(Y,Z)) != compose(compose(X,Y),Z)
    | compose(compose(X,Y),Z) = compose(X,compose(Y,Z)) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(compose(X,compose(Y,Z)))),bind(Y0,$fot(compose(compose(X,Y),Z)))]]) ).

cnf(refute_0_12,plain,
    compose(compose(X,Y),Z) = compose(X,compose(Y,Z)),
    inference(resolve,[$cnf( $equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z)) )],[associativity_of_compose,refute_0_11]) ).

cnf(refute_0_13,plain,
    compose(compose(b,g),X_9) = compose(b,compose(g,X_9)),
    inference(subst,[],[refute_0_12:[bind(X,$fot(b)),bind(Y,$fot(g)),bind(Z,$fot(X_9))]]) ).

cnf(refute_0_14,plain,
    ( compose(b,compose(h,X_9)) != compose(compose(b,g),X_9)
    | compose(compose(b,g),X_9) != compose(b,compose(g,X_9))
    | compose(b,compose(h,X_9)) = compose(b,compose(g,X_9)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(compose(b,compose(h,X_9)),compose(b,compose(g,X_9))) ),[0],$fot(compose(compose(b,g),X_9))]]) ).

cnf(refute_0_15,plain,
    ( compose(b,compose(h,X_9)) != compose(compose(b,g),X_9)
    | compose(b,compose(h,X_9)) = compose(b,compose(g,X_9)) ),
    inference(resolve,[$cnf( $equal(compose(compose(b,g),X_9),compose(b,compose(g,X_9))) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    compose(b,compose(h,X_9)) = compose(b,compose(g,X_9)),
    inference(resolve,[$cnf( $equal(compose(b,compose(h,X_9)),compose(compose(b,g),X_9)) )],[refute_0_7,refute_0_15]) ).

cnf(refute_0_17,plain,
    compose(b,compose(h,domain(h))) = compose(b,compose(g,domain(h))),
    inference(subst,[],[refute_0_16:[bind(X_9,$fot(domain(h)))]]) ).

cnf(refute_0_18,plain,
    ( compose(b,compose(h,domain(h))) != compose(b,compose(g,domain(h)))
    | compose(h,domain(h)) != h
    | compose(b,h) = compose(b,compose(g,domain(h))) ),
    introduced(tautology,[equality,[$cnf( $equal(compose(b,compose(h,domain(h))),compose(b,compose(g,domain(h)))) ),[0,1],$fot(h)]]) ).

cnf(refute_0_19,plain,
    ( compose(b,compose(h,domain(h))) != compose(b,compose(g,domain(h)))
    | compose(b,h) = compose(b,compose(g,domain(h))) ),
    inference(resolve,[$cnf( $equal(compose(h,domain(h)),h) )],[refute_0_0,refute_0_18]) ).

cnf(refute_0_20,plain,
    compose(b,h) = compose(b,compose(g,domain(h))),
    inference(resolve,[$cnf( $equal(compose(b,compose(h,domain(h))),compose(b,compose(g,domain(h)))) )],[refute_0_17,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( compose(b,h) != compose(b,compose(g,domain(h)))
    | compose(b,h) != compose(b,g)
    | compose(b,g) = compose(b,compose(g,domain(h))) ),
    introduced(tautology,[equality,[$cnf( $equal(compose(b,h),compose(b,compose(g,domain(h)))) ),[0],$fot(compose(b,g))]]) ).

cnf(refute_0_22,plain,
    ( compose(b,h) != compose(b,compose(g,domain(h)))
    | compose(b,g) = compose(b,compose(g,domain(h))) ),
    inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_21]) ).

cnf(refute_0_23,plain,
    compose(b,g) = compose(b,compose(g,domain(h))),
    inference(resolve,[$cnf( $equal(compose(b,h),compose(b,compose(g,domain(h)))) )],[refute_0_20,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( compose(b,g) != compose(b,compose(g,domain(h)))
    | compose(b,compose(g,domain(h))) = compose(b,g) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(compose(b,g))),bind(Y0,$fot(compose(b,compose(g,domain(h)))))]]) ).

cnf(refute_0_25,plain,
    compose(b,compose(g,domain(h))) = compose(b,g),
    inference(resolve,[$cnf( $equal(compose(b,g),compose(b,compose(g,domain(h)))) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( compose(b,compose(g,domain(h))) != compose(b,g)
    | ~ there_exists(compose(b,g))
    | there_exists(compose(b,compose(g,domain(h)))) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(b,compose(g,domain(h)))) ),[0],$fot(compose(b,g))]]) ).

cnf(refute_0_27,plain,
    ( ~ there_exists(compose(b,g))
    | there_exists(compose(b,compose(g,domain(h)))) ),
    inference(resolve,[$cnf( $equal(compose(b,compose(g,domain(h))),compose(b,g)) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( ~ there_exists(compose(b,g))
    | domain(b) = codomain(compose(g,domain(h))) ),
    inference(resolve,[$cnf( there_exists(compose(b,compose(g,domain(h)))) )],[refute_0_27,refute_0_3]) ).

cnf(refute_0_29,plain,
    ( compose(b,h) != compose(b,g)
    | ~ there_exists(compose(b,h))
    | there_exists(compose(b,g)) ),
    introduced(tautology,[equality,[$cnf( there_exists(compose(b,h)) ),[0],$fot(compose(b,g))]]) ).

cnf(refute_0_30,plain,
    ( ~ there_exists(compose(b,h))
    | there_exists(compose(b,g)) ),
    inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_29]) ).

cnf(refute_0_31,plain,
    there_exists(compose(b,g)),
    inference(resolve,[$cnf( there_exists(compose(b,h)) )],[assume_bh_exists,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( ~ there_exists(compose(b,g))
    | domain(b) = codomain(g) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(g))]]) ).

cnf(refute_0_33,plain,
    domain(b) = codomain(g),
    inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( domain(b) != codomain(compose(g,domain(h)))
    | domain(b) != codomain(g)
    | codomain(g) = codomain(compose(g,domain(h))) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(compose(g,domain(h)))) ),[0],$fot(codomain(g))]]) ).

cnf(refute_0_35,plain,
    ( domain(b) != codomain(compose(g,domain(h)))
    | codomain(g) = codomain(compose(g,domain(h))) ),
    inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_33,refute_0_34]) ).

cnf(refute_0_36,plain,
    ( ~ there_exists(compose(b,g))
    | codomain(g) = codomain(compose(g,domain(h))) ),
    inference(resolve,[$cnf( $equal(domain(b),codomain(compose(g,domain(h)))) )],[refute_0_28,refute_0_35]) ).

cnf(refute_0_37,plain,
    codomain(g) = codomain(compose(g,domain(h))),
    inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_31,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( codomain(g) != codomain(compose(g,domain(h)))
    | codomain(compose(g,domain(h))) = codomain(g) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(codomain(g))),bind(Y0,$fot(codomain(compose(g,domain(h)))))]]) ).

cnf(refute_0_39,plain,
    codomain(compose(g,domain(h))) = codomain(g),
    inference(resolve,[$cnf( $equal(codomain(g),codomain(compose(g,domain(h)))) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( codomain(compose(g,domain(h))) != codomain(g)
    | ~ there_exists(codomain(g))
    | there_exists(codomain(compose(g,domain(h)))) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(compose(g,domain(h)))) ),[0],$fot(codomain(g))]]) ).

cnf(refute_0_41,plain,
    ( ~ there_exists(codomain(g))
    | there_exists(codomain(compose(g,domain(h)))) ),
    inference(resolve,[$cnf( $equal(codomain(compose(g,domain(h))),codomain(g)) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    ( ~ there_exists(codomain(g))
    | there_exists(compose(g,domain(h))) ),
    inference(resolve,[$cnf( there_exists(codomain(compose(g,domain(h)))) )],[refute_0_41,refute_0_2]) ).

cnf(refute_0_43,plain,
    ( ~ there_exists(compose(b,g))
    | there_exists(domain(b)) ),
    inference(subst,[],[composition_implies_domain:[bind(X,$fot(b)),bind(Y,$fot(g))]]) ).

cnf(refute_0_44,plain,
    there_exists(domain(b)),
    inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_31,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( domain(b) != codomain(g)
    | ~ there_exists(domain(b))
    | there_exists(codomain(g)) ),
    introduced(tautology,[equality,[$cnf( there_exists(domain(b)) ),[0],$fot(codomain(g))]]) ).

cnf(refute_0_46,plain,
    ( ~ there_exists(domain(b))
    | there_exists(codomain(g)) ),
    inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_33,refute_0_45]) ).

cnf(refute_0_47,plain,
    there_exists(codomain(g)),
    inference(resolve,[$cnf( there_exists(domain(b)) )],[refute_0_44,refute_0_46]) ).

cnf(refute_0_48,plain,
    there_exists(compose(g,domain(h))),
    inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_47,refute_0_42]) ).

cnf(refute_0_49,plain,
    domain(g) = codomain(domain(h)),
    inference(resolve,[$cnf( there_exists(compose(g,domain(h))) )],[refute_0_48,refute_0_1]) ).

cnf(refute_0_50,plain,
    ( ~ there_exists(codomain(h))
    | there_exists(h) ),
    inference(subst,[],[codomain_has_elements:[bind(X,$fot(h))]]) ).

cnf(refute_0_51,plain,
    ( ~ there_exists(compose(b,h))
    | domain(b) = codomain(h) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(b)),bind(Y,$fot(h))]]) ).

cnf(refute_0_52,plain,
    ( compose(b,h) != compose(b,g)
    | ~ there_exists(compose(b,g))
    | there_exists(compose(b,h)) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(b,h)) ),[0],$fot(compose(b,g))]]) ).

cnf(refute_0_53,plain,
    ( ~ there_exists(compose(b,g))
    | there_exists(compose(b,h)) ),
    inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_52]) ).

cnf(refute_0_54,plain,
    ( ~ there_exists(compose(b,g))
    | domain(b) = codomain(h) ),
    inference(resolve,[$cnf( there_exists(compose(b,h)) )],[refute_0_53,refute_0_51]) ).

cnf(refute_0_55,plain,
    ( domain(b) != codomain(g)
    | domain(b) != codomain(h)
    | codomain(g) = codomain(h) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(b),codomain(h)) ),[0],$fot(codomain(g))]]) ).

cnf(refute_0_56,plain,
    ( domain(b) != codomain(h)
    | codomain(g) = codomain(h) ),
    inference(resolve,[$cnf( $equal(domain(b),codomain(g)) )],[refute_0_33,refute_0_55]) ).

cnf(refute_0_57,plain,
    ( ~ there_exists(compose(b,g))
    | codomain(g) = codomain(h) ),
    inference(resolve,[$cnf( $equal(domain(b),codomain(h)) )],[refute_0_54,refute_0_56]) ).

cnf(refute_0_58,plain,
    codomain(g) = codomain(h),
    inference(resolve,[$cnf( there_exists(compose(b,g)) )],[refute_0_31,refute_0_57]) ).

cnf(refute_0_59,plain,
    ( codomain(g) != codomain(h)
    | codomain(h) = codomain(g) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(codomain(g))),bind(Y0,$fot(codomain(h)))]]) ).

cnf(refute_0_60,plain,
    codomain(h) = codomain(g),
    inference(resolve,[$cnf( $equal(codomain(g),codomain(h)) )],[refute_0_58,refute_0_59]) ).

cnf(refute_0_61,plain,
    ( codomain(h) != codomain(g)
    | ~ there_exists(codomain(g))
    | there_exists(codomain(h)) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(codomain(h)) ),[0],$fot(codomain(g))]]) ).

cnf(refute_0_62,plain,
    ( ~ there_exists(codomain(g))
    | there_exists(codomain(h)) ),
    inference(resolve,[$cnf( $equal(codomain(h),codomain(g)) )],[refute_0_60,refute_0_61]) ).

cnf(refute_0_63,plain,
    ( ~ there_exists(codomain(g))
    | there_exists(h) ),
    inference(resolve,[$cnf( there_exists(codomain(h)) )],[refute_0_62,refute_0_50]) ).

cnf(refute_0_64,plain,
    there_exists(h),
    inference(resolve,[$cnf( there_exists(codomain(g)) )],[refute_0_47,refute_0_63]) ).

cnf(refute_0_65,plain,
    ( ~ there_exists(compose(X_5,domain(X_5)))
    | domain(X_5) = codomain(domain(X_5)) ),
    inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(X_5)),bind(Y,$fot(domain(X_5)))]]) ).

cnf(refute_0_66,plain,
    compose(X_5,domain(X_5)) = X_5,
    inference(subst,[],[compose_domain:[bind(X,$fot(X_5))]]) ).

cnf(refute_0_67,plain,
    ( compose(X_5,domain(X_5)) != X_5
    | ~ there_exists(X_5)
    | there_exists(compose(X_5,domain(X_5))) ),
    introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_5,domain(X_5))) ),[0],$fot(X_5)]]) ).

cnf(refute_0_68,plain,
    ( ~ there_exists(X_5)
    | there_exists(compose(X_5,domain(X_5))) ),
    inference(resolve,[$cnf( $equal(compose(X_5,domain(X_5)),X_5) )],[refute_0_66,refute_0_67]) ).

cnf(refute_0_69,plain,
    ( ~ there_exists(X_5)
    | domain(X_5) = codomain(domain(X_5)) ),
    inference(resolve,[$cnf( there_exists(compose(X_5,domain(X_5))) )],[refute_0_68,refute_0_65]) ).

cnf(refute_0_70,plain,
    ( ~ there_exists(h)
    | domain(h) = codomain(domain(h)) ),
    inference(subst,[],[refute_0_69:[bind(X_5,$fot(h))]]) ).

cnf(refute_0_71,plain,
    domain(h) = codomain(domain(h)),
    inference(resolve,[$cnf( there_exists(h) )],[refute_0_64,refute_0_70]) ).

cnf(refute_0_72,plain,
    ( domain(h) != codomain(domain(h))
    | codomain(domain(h)) = domain(h) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(domain(h))),bind(Y0,$fot(codomain(domain(h))))]]) ).

cnf(refute_0_73,plain,
    codomain(domain(h)) = domain(h),
    inference(resolve,[$cnf( $equal(domain(h),codomain(domain(h))) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    ( codomain(domain(h)) != domain(h)
    | domain(g) != codomain(domain(h))
    | domain(g) = domain(h) ),
    introduced(tautology,[equality,[$cnf( $equal(domain(g),codomain(domain(h))) ),[1],$fot(domain(h))]]) ).

cnf(refute_0_75,plain,
    ( domain(g) != codomain(domain(h))
    | domain(g) = domain(h) ),
    inference(resolve,[$cnf( $equal(codomain(domain(h)),domain(h)) )],[refute_0_73,refute_0_74]) ).

cnf(refute_0_76,plain,
    domain(g) = domain(h),
    inference(resolve,[$cnf( $equal(domain(g),codomain(domain(h))) )],[refute_0_49,refute_0_75]) ).

cnf(refute_0_77,plain,
    ( domain(g) != domain(h)
    | domain(h) = domain(g) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(domain(g))),bind(Y0,$fot(domain(h)))]]) ).

cnf(refute_0_78,plain,
    domain(h) = domain(g),
    inference(resolve,[$cnf( $equal(domain(g),domain(h)) )],[refute_0_76,refute_0_77]) ).

cnf(refute_0_79,plain,
    ( compose(h,domain(h)) != h
    | domain(h) != domain(g)
    | compose(h,domain(g)) = h ),
    introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(h)),h) ),[0,1],$fot(domain(g))]]) ).

cnf(refute_0_80,plain,
    ( compose(h,domain(h)) != h
    | compose(h,domain(g)) = h ),
    inference(resolve,[$cnf( $equal(domain(h),domain(g)) )],[refute_0_78,refute_0_79]) ).

cnf(refute_0_81,plain,
    compose(h,domain(g)) = h,
    inference(resolve,[$cnf( $equal(compose(h,domain(h)),h) )],[refute_0_0,refute_0_80]) ).

cnf(refute_0_82,plain,
    compose(g,domain(g)) = g,
    inference(subst,[],[compose_domain:[bind(X,$fot(g))]]) ).

cnf(refute_0_83,plain,
    ( compose(compose(a,b),X) != compose(compose(a,b),X)
    | compose(compose(a,b),Z) != compose(compose(a,b),X)
    | X = Z ),
    inference(subst,[],[monomorphism:[bind(Y,$fot(compose(compose(a,b),X)))]]) ).

cnf(refute_0_84,plain,
    compose(compose(a,b),X) = compose(compose(a,b),X),
    introduced(tautology,[refl,[$fot(compose(compose(a,b),X))]]) ).

cnf(refute_0_85,plain,
    ( compose(compose(a,b),Z) != compose(compose(a,b),X)
    | X = Z ),
    inference(resolve,[$cnf( $equal(compose(compose(a,b),X),compose(compose(a,b),X)) )],[refute_0_84,refute_0_83]) ).

cnf(refute_0_86,plain,
    compose(compose(a,b),Z) = compose(a,compose(b,Z)),
    inference(subst,[],[refute_0_12:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_87,plain,
    ( compose(a,compose(b,Z)) != compose(compose(a,b),X)
    | compose(compose(a,b),Z) != compose(a,compose(b,Z))
    | compose(compose(a,b),Z) = compose(compose(a,b),X) ),
    introduced(tautology,[equality,[$cnf( $equal(compose(compose(a,b),Z),compose(a,compose(b,Z))) ),[1],$fot(compose(compose(a,b),X))]]) ).

cnf(refute_0_88,plain,
    ( compose(a,compose(b,Z)) != compose(compose(a,b),X)
    | compose(compose(a,b),Z) = compose(compose(a,b),X) ),
    inference(resolve,[$cnf( $equal(compose(compose(a,b),Z),compose(a,compose(b,Z))) )],[refute_0_86,refute_0_87]) ).

cnf(refute_0_89,plain,
    compose(compose(a,b),X) = compose(a,compose(b,X)),
    inference(subst,[],[refute_0_12:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X))]]) ).

cnf(refute_0_90,plain,
    ( compose(a,compose(b,Z)) != compose(a,compose(b,X))
    | compose(compose(a,b),X) != compose(a,compose(b,X))
    | compose(a,compose(b,Z)) = compose(compose(a,b),X) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,Z)),compose(compose(a,b),X)) ),[1],$fot(compose(a,compose(b,X)))]]) ).

cnf(refute_0_91,plain,
    ( compose(a,compose(b,Z)) != compose(a,compose(b,X))
    | compose(a,compose(b,Z)) = compose(compose(a,b),X) ),
    inference(resolve,[$cnf( $equal(compose(compose(a,b),X),compose(a,compose(b,X))) )],[refute_0_89,refute_0_90]) ).

cnf(refute_0_92,plain,
    ( compose(a,compose(b,Z)) != compose(a,compose(b,X))
    | compose(compose(a,b),Z) = compose(compose(a,b),X) ),
    inference(resolve,[$cnf( $equal(compose(a,compose(b,Z)),compose(compose(a,b),X)) )],[refute_0_91,refute_0_88]) ).

cnf(refute_0_93,plain,
    ( compose(a,compose(b,Z)) != compose(a,compose(b,X))
    | X = Z ),
    inference(resolve,[$cnf( $equal(compose(compose(a,b),Z),compose(compose(a,b),X)) )],[refute_0_92,refute_0_85]) ).

cnf(refute_0_94,plain,
    ( compose(a,compose(b,compose(h,X_9))) != compose(a,compose(b,X_193))
    | X_193 = compose(h,X_9) ),
    inference(subst,[],[refute_0_93:[bind(X,$fot(X_193)),bind(Z,$fot(compose(h,X_9)))]]) ).

cnf(refute_0_95,plain,
    ( compose(a,compose(b,compose(g,X_9))) != compose(a,compose(b,X_193))
    | compose(b,compose(h,X_9)) != compose(b,compose(g,X_9))
    | compose(a,compose(b,compose(h,X_9))) = compose(a,compose(b,X_193)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,compose(h,X_9))),compose(a,compose(b,X_193))) ),[0,1],$fot(compose(b,compose(g,X_9)))]]) ).

cnf(refute_0_96,plain,
    ( compose(a,compose(b,compose(g,X_9))) != compose(a,compose(b,X_193))
    | compose(a,compose(b,compose(h,X_9))) = compose(a,compose(b,X_193)) ),
    inference(resolve,[$cnf( $equal(compose(b,compose(h,X_9)),compose(b,compose(g,X_9))) )],[refute_0_16,refute_0_95]) ).

cnf(refute_0_97,plain,
    ( compose(a,compose(b,compose(g,X_9))) != compose(a,compose(b,X_193))
    | X_193 = compose(h,X_9) ),
    inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(h,X_9))),compose(a,compose(b,X_193))) )],[refute_0_96,refute_0_94]) ).

cnf(refute_0_98,plain,
    ( compose(a,compose(b,compose(g,X_9))) != compose(a,compose(b,compose(g,X_9)))
    | compose(g,X_9) = compose(h,X_9) ),
    inference(subst,[],[refute_0_97:[bind(X_193,$fot(compose(g,X_9)))]]) ).

cnf(refute_0_99,plain,
    compose(a,compose(b,compose(g,X_9))) = compose(a,compose(b,compose(g,X_9))),
    introduced(tautology,[refl,[$fot(compose(a,compose(b,compose(g,X_9))))]]) ).

cnf(refute_0_100,plain,
    compose(g,X_9) = compose(h,X_9),
    inference(resolve,[$cnf( $equal(compose(a,compose(b,compose(g,X_9))),compose(a,compose(b,compose(g,X_9)))) )],[refute_0_99,refute_0_98]) ).

cnf(refute_0_101,plain,
    ( compose(g,X_9) != compose(h,X_9)
    | compose(h,X_9) = compose(g,X_9) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(compose(g,X_9))),bind(Y0,$fot(compose(h,X_9)))]]) ).

cnf(refute_0_102,plain,
    compose(h,X_9) = compose(g,X_9),
    inference(resolve,[$cnf( $equal(compose(g,X_9),compose(h,X_9)) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    compose(h,domain(g)) = compose(g,domain(g)),
    inference(subst,[],[refute_0_102:[bind(X_9,$fot(domain(g)))]]) ).

cnf(refute_0_104,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_105,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_10,refute_0_104]) ).

cnf(refute_0_106,plain,
    ( compose(g,domain(g)) != g
    | compose(h,domain(g)) != compose(g,domain(g))
    | compose(h,domain(g)) = g ),
    inference(subst,[],[refute_0_105:[bind(X0,$fot(compose(h,domain(g)))),bind(Y0,$fot(compose(g,domain(g)))),bind(Z0,$fot(g))]]) ).

cnf(refute_0_107,plain,
    ( compose(g,domain(g)) != g
    | compose(h,domain(g)) = g ),
    inference(resolve,[$cnf( $equal(compose(h,domain(g)),compose(g,domain(g))) )],[refute_0_103,refute_0_106]) ).

cnf(refute_0_108,plain,
    compose(h,domain(g)) = g,
    inference(resolve,[$cnf( $equal(compose(g,domain(g)),g) )],[refute_0_82,refute_0_107]) ).

cnf(refute_0_109,plain,
    ( compose(h,domain(g)) != g
    | compose(h,domain(g)) != h
    | g = h ),
    introduced(tautology,[equality,[$cnf( $equal(compose(h,domain(g)),h) ),[0],$fot(g)]]) ).

cnf(refute_0_110,plain,
    ( compose(h,domain(g)) != h
    | g = h ),
    inference(resolve,[$cnf( $equal(compose(h,domain(g)),g) )],[refute_0_108,refute_0_109]) ).

cnf(refute_0_111,plain,
    g = h,
    inference(resolve,[$cnf( $equal(compose(h,domain(g)),h) )],[refute_0_81,refute_0_110]) ).

cnf(refute_0_112,plain,
    ( g != h
    | h = g ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(g)),bind(Y0,$fot(h))]]) ).

cnf(refute_0_113,plain,
    g != h,
    inference(resolve,[$cnf( $equal(h,g) )],[refute_0_112,prove_h_equals_g]) ).

cnf(refute_0_114,plain,
    $false,
    inference(resolve,[$cnf( $equal(g,h) )],[refute_0_111,refute_0_113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : CAT001-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11  % Command  : metis --show proof --show saturation %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Sun May 29 15:55:41 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.10/0.30  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.24/2.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.24/2.41  
% 2.24/2.41  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.26/2.42  
%------------------------------------------------------------------------------