TSTP Solution File: CAT003-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.39s 0.57s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of clauses : 78 ( 24 unt; 0 nHn; 76 RR)
% Number of literals : 168 ( 167 equ; 92 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 : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(endomorphism,hypothesis,
( codomain(compose(a,b)) != domain(X)
| compose(compose(a,b),X) != Y
| codomain(compose(a,b)) != domain(Z)
| compose(compose(a,b),Z) != Y
| X = Z ) ).
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b) ).
cnf(codomain_of_b_equals_domain_of_h,hypothesis,
codomain(b) = domain(h) ).
cnf(codomain_of_b_equals_domain_of_g,hypothesis,
codomain(b) = domain(g) ).
cnf(bh_equals_bg,hypothesis,
compose(b,h) = compose(b,g) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
cnf(refute_0_0,plain,
( codomain(compose(a,b)) != domain(X)
| codomain(compose(a,b)) != domain(Z)
| compose(compose(a,b),X) != compose(compose(a,b),X)
| compose(compose(a,b),Z) != compose(compose(a,b),X)
| X = Z ),
inference(subst,[],[endomorphism:[bind(Y,$fot(compose(compose(a,b),X)))]]) ).
cnf(refute_0_1,plain,
compose(compose(a,b),X) = compose(compose(a,b),X),
introduced(tautology,[refl,[$fot(compose(compose(a,b),X))]]) ).
cnf(refute_0_2,plain,
( codomain(compose(a,b)) != domain(X)
| codomain(compose(a,b)) != domain(Z)
| compose(compose(a,b),Z) != compose(compose(a,b),X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),X),compose(compose(a,b),X)) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( codomain(X_11) != domain(b)
| codomain(compose(X_11,b)) = codomain(b) ),
inference(subst,[],[codomain_domain2:[bind(X,$fot(X_11)),bind(Y,$fot(b))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( codomain(a) != domain(b)
| domain(b) = codomain(a) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(domain(b)))]]) ).
cnf(refute_0_8,plain,
domain(b) = codomain(a),
inference(resolve,[$cnf( $equal(codomain(a),domain(b)) )],[codomain_of_a_equals_domain_of_b,refute_0_7]) ).
cnf(refute_0_9,plain,
( codomain(X_11) != codomain(a)
| domain(b) != codomain(a)
| codomain(X_11) = domain(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(X_11),domain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_10,plain,
( codomain(X_11) != codomain(a)
| codomain(X_11) = domain(b) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( codomain(X_11) != codomain(a)
| codomain(compose(X_11,b)) = codomain(b) ),
inference(resolve,[$cnf( $equal(codomain(X_11),domain(b)) )],[refute_0_10,refute_0_3]) ).
cnf(refute_0_12,plain,
( codomain(a) != codomain(a)
| codomain(compose(a,b)) = codomain(b) ),
inference(subst,[],[refute_0_11:[bind(X_11,$fot(a))]]) ).
cnf(refute_0_13,plain,
codomain(a) = codomain(a),
introduced(tautology,[refl,[$fot(codomain(a))]]) ).
cnf(refute_0_14,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
( codomain(b) != domain(Z)
| codomain(compose(a,b)) != codomain(b)
| codomain(compose(a,b)) = domain(Z) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(compose(a,b)),codomain(b)) ),[1],$fot(domain(Z))]]) ).
cnf(refute_0_16,plain,
( codomain(b) != domain(Z)
| codomain(compose(a,b)) = domain(Z) ),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),codomain(b)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( codomain(b) != domain(Z)
| codomain(compose(a,b)) != domain(X)
| compose(compose(a,b),Z) != compose(compose(a,b),X)
| X = Z ),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),domain(Z)) )],[refute_0_16,refute_0_2]) ).
cnf(refute_0_18,plain,
( codomain(b) != domain(X)
| codomain(compose(a,b)) != codomain(b)
| codomain(compose(a,b)) = domain(X) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(compose(a,b)),codomain(b)) ),[1],$fot(domain(X))]]) ).
cnf(refute_0_19,plain,
( codomain(b) != domain(X)
| codomain(compose(a,b)) = domain(X) ),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),codomain(b)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( codomain(b) != domain(X)
| codomain(b) != domain(Z)
| compose(compose(a,b),Z) != compose(compose(a,b),X)
| X = Z ),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),domain(X)) )],[refute_0_19,refute_0_17]) ).
cnf(refute_0_21,plain,
( codomain(b) != domain(X_195)
| codomain(b) != domain(g)
| compose(compose(a,b),g) != compose(compose(a,b),X_195)
| X_195 = g ),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_195)),bind(Z,$fot(g))]]) ).
cnf(refute_0_22,plain,
( codomain(X_113) != domain(b)
| codomain(b) != domain(X_115)
| compose(X_113,compose(b,X_115)) = compose(compose(X_113,b),X_115) ),
inference(subst,[],[star_property:[bind(X,$fot(X_113)),bind(Y,$fot(b)),bind(Z,$fot(X_115))]]) ).
cnf(refute_0_23,plain,
( codomain(X_113) != codomain(a)
| domain(b) != codomain(a)
| codomain(X_113) = domain(b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(X_113),domain(b)) ),[1],$fot(codomain(a))]]) ).
cnf(refute_0_24,plain,
( codomain(X_113) != codomain(a)
| codomain(X_113) = domain(b) ),
inference(resolve,[$cnf( $equal(domain(b),codomain(a)) )],[refute_0_8,refute_0_23]) ).
cnf(refute_0_25,plain,
( codomain(X_113) != codomain(a)
| codomain(b) != domain(X_115)
| compose(X_113,compose(b,X_115)) = compose(compose(X_113,b),X_115) ),
inference(resolve,[$cnf( $equal(codomain(X_113),domain(b)) )],[refute_0_24,refute_0_22]) ).
cnf(refute_0_26,plain,
( codomain(a) != codomain(a)
| codomain(b) != domain(X_115)
| compose(a,compose(b,X_115)) = compose(compose(a,b),X_115) ),
inference(subst,[],[refute_0_25:[bind(X_113,$fot(a))]]) ).
cnf(refute_0_27,plain,
( codomain(b) != domain(X_115)
| compose(a,compose(b,X_115)) = compose(compose(a,b),X_115) ),
inference(resolve,[$cnf( $equal(codomain(a),codomain(a)) )],[refute_0_13,refute_0_26]) ).
cnf(refute_0_28,plain,
( codomain(b) != domain(g)
| compose(a,compose(b,g)) = compose(compose(a,b),g) ),
inference(subst,[],[refute_0_27:[bind(X_115,$fot(g))]]) ).
cnf(refute_0_29,plain,
( codomain(b) != domain(g)
| domain(g) = codomain(b) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(codomain(b))),bind(Y0,$fot(domain(g)))]]) ).
cnf(refute_0_30,plain,
domain(g) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(b),domain(g)) )],[codomain_of_b_equals_domain_of_g,refute_0_29]) ).
cnf(refute_0_31,plain,
( codomain(b) != codomain(b)
| domain(g) != codomain(b)
| codomain(b) = domain(g) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(b),domain(g)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_32,plain,
( codomain(b) != codomain(b)
| codomain(b) = domain(g) ),
inference(resolve,[$cnf( $equal(domain(g),codomain(b)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,g)) = compose(compose(a,b),g) ),
inference(resolve,[$cnf( $equal(codomain(b),domain(g)) )],[refute_0_32,refute_0_28]) ).
cnf(refute_0_34,plain,
codomain(b) = codomain(b),
introduced(tautology,[refl,[$fot(codomain(b))]]) ).
cnf(refute_0_35,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( compose(a,compose(b,g)) != compose(compose(a,b),g)
| compose(compose(a,b),g) = compose(a,compose(b,g)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(compose(a,compose(b,g)))),bind(Y0,$fot(compose(compose(a,b),g)))]]) ).
cnf(refute_0_37,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(compose(a,b),g)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( compose(a,compose(b,g)) != compose(compose(a,b),X_195)
| compose(compose(a,b),g) != compose(a,compose(b,g))
| compose(compose(a,b),g) = compose(compose(a,b),X_195) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(a,b),g),compose(a,compose(b,g))) ),[1],$fot(compose(compose(a,b),X_195))]]) ).
cnf(refute_0_39,plain,
( compose(a,compose(b,g)) != compose(compose(a,b),X_195)
| compose(compose(a,b),g) = compose(compose(a,b),X_195) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),g),compose(a,compose(b,g))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( codomain(b) != domain(X_195)
| codomain(b) != domain(g)
| compose(a,compose(b,g)) != compose(compose(a,b),X_195)
| X_195 = g ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),g),compose(compose(a,b),X_195)) )],[refute_0_39,refute_0_21]) ).
cnf(refute_0_41,plain,
( codomain(b) != codomain(b)
| codomain(b) != domain(X_195)
| compose(a,compose(b,g)) != compose(compose(a,b),X_195)
| X_195 = g ),
inference(resolve,[$cnf( $equal(codomain(b),domain(g)) )],[refute_0_32,refute_0_40]) ).
cnf(refute_0_42,plain,
( codomain(b) != domain(X_195)
| compose(a,compose(b,g)) != compose(compose(a,b),X_195)
| X_195 = g ),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_34,refute_0_41]) ).
cnf(refute_0_43,plain,
( codomain(b) != domain(h)
| compose(a,compose(b,g)) != compose(compose(a,b),h)
| h = g ),
inference(subst,[],[refute_0_42:[bind(X_195,$fot(h))]]) ).
cnf(refute_0_44,plain,
( codomain(b) != domain(h)
| compose(a,compose(b,h)) = compose(compose(a,b),h) ),
inference(subst,[],[refute_0_27:[bind(X_115,$fot(h))]]) ).
cnf(refute_0_45,plain,
( codomain(b) != domain(h)
| domain(h) = codomain(b) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(codomain(b))),bind(Y0,$fot(domain(h)))]]) ).
cnf(refute_0_46,plain,
domain(h) = codomain(b),
inference(resolve,[$cnf( $equal(codomain(b),domain(h)) )],[codomain_of_b_equals_domain_of_h,refute_0_45]) ).
cnf(refute_0_47,plain,
( codomain(b) != codomain(b)
| domain(h) != codomain(b)
| codomain(b) = domain(h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(codomain(b),domain(h)) ),[1],$fot(codomain(b))]]) ).
cnf(refute_0_48,plain,
( codomain(b) != codomain(b)
| codomain(b) = domain(h) ),
inference(resolve,[$cnf( $equal(domain(h),codomain(b)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,h)) = compose(compose(a,b),h) ),
inference(resolve,[$cnf( $equal(codomain(b),domain(h)) )],[refute_0_48,refute_0_44]) ).
cnf(refute_0_50,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_34,refute_0_49]) ).
cnf(refute_0_51,plain,
compose(a,compose(b,h)) = compose(a,compose(b,h)),
introduced(tautology,[refl,[$fot(compose(a,compose(b,h)))]]) ).
cnf(refute_0_52,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,h))
| compose(b,h) != compose(b,g)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,h))) ),[1,1],$fot(compose(b,g))]]) ).
cnf(refute_0_53,plain,
( compose(b,h) != compose(b,g)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,h))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[bh_equals_bg,refute_0_53]) ).
cnf(refute_0_55,plain,
( compose(a,compose(b,h)) != compose(a,compose(b,g))
| compose(a,compose(b,h)) != compose(compose(a,b),h)
| compose(a,compose(b,g)) = compose(compose(a,b),h) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(b,h)),compose(compose(a,b),h)) ),[0],$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_56,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),h)
| compose(a,compose(b,g)) = compose(compose(a,b),h) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
compose(a,compose(b,g)) = compose(compose(a,b),h),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(compose(a,b),h)) )],[refute_0_50,refute_0_56]) ).
cnf(refute_0_58,plain,
( compose(a,compose(b,g)) != compose(compose(a,b),h)
| compose(compose(a,b),h) = compose(a,compose(b,g)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(compose(a,compose(b,g)))),bind(Y0,$fot(compose(compose(a,b),h)))]]) ).
cnf(refute_0_59,plain,
compose(compose(a,b),h) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(compose(a,b),h)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( compose(a,compose(b,g)) != compose(a,compose(b,g))
| compose(compose(a,b),h) != compose(a,compose(b,g))
| compose(a,compose(b,g)) = compose(compose(a,b),h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,g)),compose(compose(a,b),h)) ),[1],$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_61,plain,
( compose(a,compose(b,g)) != compose(a,compose(b,g))
| compose(a,compose(b,g)) = compose(compose(a,b),h) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(a,compose(b,g))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( codomain(b) != domain(h)
| compose(a,compose(b,g)) != compose(a,compose(b,g))
| h = g ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(compose(a,b),h)) )],[refute_0_61,refute_0_43]) ).
cnf(refute_0_63,plain,
compose(a,compose(b,g)) = compose(a,compose(b,g)),
introduced(tautology,[refl,[$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_64,plain,
( codomain(b) != domain(h)
| h = g ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(a,compose(b,g))) )],[refute_0_63,refute_0_62]) ).
cnf(refute_0_65,plain,
( codomain(b) != codomain(b)
| h = g ),
inference(resolve,[$cnf( $equal(codomain(b),domain(h)) )],[refute_0_48,refute_0_64]) ).
cnf(refute_0_66,plain,
h = g,
inference(resolve,[$cnf( $equal(codomain(b),codomain(b)) )],[refute_0_34,refute_0_65]) ).
cnf(refute_0_67,plain,
( h != g
| g = h ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(h)),bind(Y0,$fot(g))]]) ).
cnf(refute_0_68,plain,
h != g,
inference(resolve,[$cnf( $equal(g,h) )],[refute_0_67,prove_g_equals_h]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( $equal(h,g) )],[refute_0_66,refute_0_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun May 29 17:26:03 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.57
% 0.39/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.41/0.58
%------------------------------------------------------------------------------