TSTP Solution File: CAT016-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT016-4 : 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 00:04:36 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of clauses : 72 ( 39 unt; 0 nHn; 37 RR)
% Number of literals : 118 ( 102 equ; 47 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 104 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(composition_implies_domain,axiom,
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ) ).
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(compose_codomain,axiom,
compose(codomain(X),X) = X ).
cnf(assume_a_exists,hypothesis,
there_exists(a) ).
cnf(prove_domain_of_a_exists,negated_conjecture,
~ there_exists(domain(a)) ).
cnf(refute_0_0,plain,
( ~ there_exists(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42))))
| there_exists(domain(X_42)) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(X_42)),bind(Y,$fot(domain(compose(domain(codomain(codomain(X_42))),X_42))))]]) ).
cnf(refute_0_1,plain,
compose(codomain(X_10),compose(X_10,X_11)) = compose(compose(codomain(X_10),X_10),X_11),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(codomain(X_10))),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_2,plain,
compose(codomain(X_10),X_10) = X_10,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_3,plain,
( compose(codomain(X_10),X_10) != X_10
| compose(codomain(X_10),compose(X_10,X_11)) != compose(compose(codomain(X_10),X_10),X_11)
| compose(codomain(X_10),compose(X_10,X_11)) = compose(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(X_10),compose(X_10,X_11)),compose(compose(codomain(X_10),X_10),X_11)) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_4,plain,
( compose(codomain(X_10),compose(X_10,X_11)) != compose(compose(codomain(X_10),X_10),X_11)
| compose(codomain(X_10),compose(X_10,X_11)) = compose(X_10,X_11) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_10),X_10),X_10) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
compose(codomain(X_10),compose(X_10,X_11)) = compose(X_10,X_11),
inference(resolve,[$cnf( $equal(compose(codomain(X_10),compose(X_10,X_11)),compose(compose(codomain(X_10),X_10),X_11)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
compose(codomain(codomain(X_12)),compose(codomain(X_12),compose(X_12,X_13))) = compose(codomain(X_12),compose(X_12,X_13)),
inference(subst,[],[refute_0_5:[bind(X_10,$fot(codomain(X_12))),bind(X_11,$fot(compose(X_12,X_13)))]]) ).
cnf(refute_0_7,plain,
compose(codomain(X_12),compose(X_12,X_13)) = compose(X_12,X_13),
inference(subst,[],[refute_0_5:[bind(X_10,$fot(X_12)),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_8,plain,
( compose(codomain(X_12),compose(X_12,X_13)) != compose(X_12,X_13)
| compose(codomain(codomain(X_12)),compose(codomain(X_12),compose(X_12,X_13))) != compose(codomain(X_12),compose(X_12,X_13))
| compose(codomain(codomain(X_12)),compose(X_12,X_13)) = compose(codomain(X_12),compose(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(codomain(X_12),compose(X_12,X_13))),compose(codomain(X_12),compose(X_12,X_13))) ),[0,1],$fot(compose(X_12,X_13))]]) ).
cnf(refute_0_9,plain,
( compose(codomain(codomain(X_12)),compose(codomain(X_12),compose(X_12,X_13))) != compose(codomain(X_12),compose(X_12,X_13))
| compose(codomain(codomain(X_12)),compose(X_12,X_13)) = compose(codomain(X_12),compose(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_12),compose(X_12,X_13)),compose(X_12,X_13)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
compose(codomain(codomain(X_12)),compose(X_12,X_13)) = compose(codomain(X_12),compose(X_12,X_13)),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(codomain(X_12),compose(X_12,X_13))),compose(codomain(X_12),compose(X_12,X_13))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( compose(codomain(X_12),compose(X_12,X_13)) != compose(X_12,X_13)
| compose(codomain(codomain(X_12)),compose(X_12,X_13)) != compose(codomain(X_12),compose(X_12,X_13))
| compose(codomain(codomain(X_12)),compose(X_12,X_13)) = compose(X_12,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(X_12,X_13)),compose(codomain(X_12),compose(X_12,X_13))) ),[1],$fot(compose(X_12,X_13))]]) ).
cnf(refute_0_12,plain,
( compose(codomain(codomain(X_12)),compose(X_12,X_13)) != compose(codomain(X_12),compose(X_12,X_13))
| compose(codomain(codomain(X_12)),compose(X_12,X_13)) = compose(X_12,X_13) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_12),compose(X_12,X_13)),compose(X_12,X_13)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
compose(codomain(codomain(X_12)),compose(X_12,X_13)) = compose(X_12,X_13),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(X_12,X_13)),compose(codomain(X_12),compose(X_12,X_13))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))),
inference(subst,[],[refute_0_13:[bind(X_13,$fot(domain(compose(domain(codomain(codomain(X_12))),X_12))))]]) ).
cnf(refute_0_15,plain,
compose(X_9,compose(domain(X_9),X_11)) = compose(compose(X_9,domain(X_9)),X_11),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_9)),bind(Y,$fot(domain(X_9))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_16,plain,
compose(X_9,domain(X_9)) = X_9,
inference(subst,[],[compose_domain:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_17,plain,
( compose(X_9,compose(domain(X_9),X_11)) != compose(compose(X_9,domain(X_9)),X_11)
| compose(X_9,domain(X_9)) != X_9
| compose(X_9,compose(domain(X_9),X_11)) = compose(X_9,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_11)),compose(compose(X_9,domain(X_9)),X_11)) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_18,plain,
( compose(X_9,compose(domain(X_9),X_11)) != compose(compose(X_9,domain(X_9)),X_11)
| compose(X_9,compose(domain(X_9),X_11)) = compose(X_9,X_11) ),
inference(resolve,[$cnf( $equal(compose(X_9,domain(X_9)),X_9) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
compose(X_9,compose(domain(X_9),X_11)) = compose(X_9,X_11),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_11)),compose(compose(X_9,domain(X_9)),X_11)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
compose(X_9,compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30))))) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))),
inference(subst,[],[refute_0_19:[bind(X_11,$fot(compose(X_30,domain(compose(domain(X_9),X_30)))))]]) ).
cnf(refute_0_21,plain,
compose(compose(X_9,X_10),domain(compose(X_9,X_10))) = compose(X_9,X_10),
inference(subst,[],[compose_domain:[bind(X,$fot(compose(X_9,X_10)))]]) ).
cnf(refute_0_22,plain,
compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(compose(X_9,X_10),domain(compose(X_9,X_10))),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(domain(compose(X_9,X_10))))]]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) != compose(compose(X_9,X_10),domain(compose(X_9,X_10)))
| compose(compose(X_9,X_10),domain(compose(X_9,X_10))) = compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(compose(X_9,compose(X_10,domain(compose(X_9,X_10)))))),bind(Y0,$fot(compose(compose(X_9,X_10),domain(compose(X_9,X_10)))))]]) ).
cnf(refute_0_27,plain,
compose(compose(X_9,X_10),domain(compose(X_9,X_10))) = compose(X_9,compose(X_10,domain(compose(X_9,X_10)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(X_10,domain(compose(X_9,X_10)))),compose(compose(X_9,X_10),domain(compose(X_9,X_10)))) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( compose(compose(X_9,X_10),domain(compose(X_9,X_10))) != compose(X_9,X_10)
| compose(compose(X_9,X_10),domain(compose(X_9,X_10))) != compose(X_9,compose(X_10,domain(compose(X_9,X_10))))
| compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(X_9,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(X_9,X_10),domain(compose(X_9,X_10))),compose(X_9,X_10)) ),[0],$fot(compose(X_9,compose(X_10,domain(compose(X_9,X_10)))))]]) ).
cnf(refute_0_29,plain,
( compose(compose(X_9,X_10),domain(compose(X_9,X_10))) != compose(X_9,X_10)
| compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(X_9,X_10) ),
inference(resolve,[$cnf( $equal(compose(compose(X_9,X_10),domain(compose(X_9,X_10))),compose(X_9,compose(X_10,domain(compose(X_9,X_10))))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
compose(X_9,compose(X_10,domain(compose(X_9,X_10)))) = compose(X_9,X_10),
inference(resolve,[$cnf( $equal(compose(compose(X_9,X_10),domain(compose(X_9,X_10))),compose(X_9,X_10)) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30)))) = compose(domain(X_9),X_30),
inference(subst,[],[refute_0_30:[bind(X_10,$fot(X_30)),bind(X_9,$fot(domain(X_9)))]]) ).
cnf(refute_0_32,plain,
( compose(X_9,compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30))))) != compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))
| compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30)))) != compose(domain(X_9),X_30)
| compose(X_9,compose(domain(X_9),X_30)) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30))))),compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))) ),[0,1],$fot(compose(domain(X_9),X_30))]]) ).
cnf(refute_0_33,plain,
( compose(X_9,compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30))))) != compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))
| compose(X_9,compose(domain(X_9),X_30)) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))) ),
inference(resolve,[$cnf( $equal(compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30)))),compose(domain(X_9),X_30)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
compose(X_9,compose(domain(X_9),X_30)) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),compose(X_30,domain(compose(domain(X_9),X_30))))),compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))) )],[refute_0_20,refute_0_33]) ).
cnf(refute_0_35,plain,
compose(X_9,compose(domain(X_9),X_30)) = compose(X_9,X_30),
inference(subst,[],[refute_0_19:[bind(X_11,$fot(X_30))]]) ).
cnf(refute_0_36,plain,
( compose(X_9,compose(domain(X_9),X_30)) != compose(X_9,X_30)
| compose(X_9,compose(domain(X_9),X_30)) != compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))
| compose(X_9,X_30) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_30)),compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))) ),[0],$fot(compose(X_9,X_30))]]) ).
cnf(refute_0_37,plain,
( compose(X_9,compose(domain(X_9),X_30)) != compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))
| compose(X_9,X_30) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))) ),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_30)),compose(X_9,X_30)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
compose(X_9,X_30) = compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30)))),
inference(resolve,[$cnf( $equal(compose(X_9,compose(domain(X_9),X_30)),compose(X_9,compose(X_30,domain(compose(domain(X_9),X_30))))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
compose(codomain(codomain(X_12)),X_12) = compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))),
inference(subst,[],[refute_0_38:[bind(X_30,$fot(X_12)),bind(X_9,$fot(codomain(codomain(X_12))))]]) ).
cnf(refute_0_40,plain,
( compose(codomain(codomain(X_12)),X_12) != compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))))
| compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) = compose(codomain(codomain(X_12)),X_12) ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(compose(codomain(codomain(X_12)),X_12))),bind(Y0,$fot(compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))))))]]) ).
cnf(refute_0_41,plain,
compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) = compose(codomain(codomain(X_12)),X_12),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),X_12),compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) != compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))
| compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) != compose(codomain(codomain(X_12)),X_12)
| compose(codomain(codomain(X_12)),X_12) = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) ),[0],$fot(compose(codomain(codomain(X_12)),X_12))]]) ).
cnf(refute_0_43,plain,
( compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) != compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))
| compose(codomain(codomain(X_12)),X_12) = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))),compose(codomain(codomain(X_12)),X_12)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
compose(codomain(codomain(X_12)),X_12) = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) )],[refute_0_14,refute_0_43]) ).
cnf(refute_0_45,plain,
compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)) = compose(codomain(X_13),X_13),
inference(subst,[],[refute_0_5:[bind(X_10,$fot(codomain(X_13))),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_46,plain,
compose(codomain(X_13),X_13) = X_13,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_47,plain,
( compose(codomain(X_13),X_13) != X_13
| compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = compose(codomain(X_13),X_13) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)),compose(codomain(X_13),X_13)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_48,plain,
( compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = compose(codomain(X_13),X_13) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_13),X_13),X_13) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
compose(codomain(codomain(X_13)),X_13) = compose(codomain(X_13),X_13),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_13)),compose(codomain(X_13),X_13)),compose(codomain(X_13),X_13)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( compose(codomain(X_13),X_13) != X_13
| compose(codomain(codomain(X_13)),X_13) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_13)),X_13),compose(codomain(X_13),X_13)) ),[1],$fot(X_13)]]) ).
cnf(refute_0_51,plain,
( compose(codomain(codomain(X_13)),X_13) != compose(codomain(X_13),X_13)
| compose(codomain(codomain(X_13)),X_13) = X_13 ),
inference(resolve,[$cnf( $equal(compose(codomain(X_13),X_13),X_13) )],[refute_0_46,refute_0_50]) ).
cnf(refute_0_52,plain,
compose(codomain(codomain(X_13)),X_13) = X_13,
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_13)),X_13),compose(codomain(X_13),X_13)) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
compose(codomain(codomain(X_12)),X_12) = X_12,
inference(subst,[],[refute_0_52:[bind(X_13,$fot(X_12))]]) ).
cnf(refute_0_54,plain,
( compose(codomain(codomain(X_12)),X_12) != X_12
| compose(codomain(codomain(X_12)),X_12) != compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))
| X_12 = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(codomain(X_12)),X_12),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) ),[0],$fot(X_12)]]) ).
cnf(refute_0_55,plain,
( compose(codomain(codomain(X_12)),X_12) != compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))
| X_12 = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))) ),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),X_12),X_12) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
X_12 = compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12))),
inference(resolve,[$cnf( $equal(compose(codomain(codomain(X_12)),X_12),compose(X_12,domain(compose(domain(codomain(codomain(X_12))),X_12)))) )],[refute_0_44,refute_0_55]) ).
cnf(refute_0_57,plain,
X_42 = compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42))),
inference(subst,[],[refute_0_56:[bind(X_12,$fot(X_42))]]) ).
cnf(refute_0_58,plain,
( X_42 != compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))
| compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42))) = X_42 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(X_42)),bind(Y0,$fot(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))))]]) ).
cnf(refute_0_59,plain,
compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42))) = X_42,
inference(resolve,[$cnf( $equal(X_42,compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42))) != X_42
| ~ there_exists(X_42)
| there_exists(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))) ),[0],$fot(X_42)]]) ).
cnf(refute_0_61,plain,
( ~ there_exists(X_42)
| there_exists(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))) ),
inference(resolve,[$cnf( $equal(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42))),X_42) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ there_exists(X_42)
| there_exists(domain(X_42)) ),
inference(resolve,[$cnf( there_exists(compose(X_42,domain(compose(domain(codomain(codomain(X_42))),X_42)))) )],[refute_0_61,refute_0_0]) ).
cnf(refute_0_63,plain,
( ~ there_exists(a)
| there_exists(domain(a)) ),
inference(subst,[],[refute_0_62:[bind(X_42,$fot(a))]]) ).
cnf(refute_0_64,plain,
there_exists(domain(a)),
inference(resolve,[$cnf( there_exists(a) )],[assume_a_exists,refute_0_63]) ).
cnf(refute_0_65,plain,
$false,
inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_64,prove_domain_of_a_exists]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 23:31:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.42
%------------------------------------------------------------------------------