TSTP Solution File: CAT010-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 00:04:34 EDT 2022
% Result : Unsatisfiable 0.55s 0.74s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 47 ( 19 unt; 0 nHn; 39 RR)
% Number of literals : 82 ( 43 equ; 37 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(domain_has_elements,axiom,
( ~ there_exists(domain(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_codomain,axiom,
compose(codomain(X),X) = X ).
cnf(ab_exists,hypothesis,
there_exists(compose(a,b)) ).
cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
codomain(compose(a,b)) != codomain(a) ).
cnf(refute_0_0,plain,
( ~ there_exists(compose(codomain(X_23),compose(X_23,X_24)))
| domain(codomain(X_23)) = codomain(compose(X_23,X_24)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_23))),bind(Y,$fot(compose(X_23,X_24)))]]) ).
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( $equal(compose(codomain(X_10),compose(X_10,X_11)),compose(compose(codomain(X_10),X_10),X_11)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
compose(codomain(X_23),compose(X_23,X_24)) = compose(X_23,X_24),
inference(subst,[],[refute_0_5:[bind(X_10,$fot(X_23)),bind(X_11,$fot(X_24))]]) ).
cnf(refute_0_7,plain,
( compose(codomain(X_23),compose(X_23,X_24)) != compose(X_23,X_24)
| ~ there_exists(compose(X_23,X_24))
| there_exists(compose(codomain(X_23),compose(X_23,X_24))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_23),compose(X_23,X_24))) ),[0],$fot(compose(X_23,X_24))]]) ).
cnf(refute_0_8,plain,
( ~ there_exists(compose(X_23,X_24))
| there_exists(compose(codomain(X_23),compose(X_23,X_24))) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_23),compose(X_23,X_24)),compose(X_23,X_24)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ there_exists(compose(X_23,X_24))
| domain(codomain(X_23)) = codomain(compose(X_23,X_24)) ),
inference(resolve,[$cnf( there_exists(compose(codomain(X_23),compose(X_23,X_24))) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( ~ there_exists(compose(a,b))
| domain(codomain(a)) = codomain(compose(a,b)) ),
inference(subst,[],[refute_0_9:[bind(X_23,$fot(a)),bind(X_24,$fot(b))]]) ).
cnf(refute_0_11,plain,
domain(codomain(a)) = codomain(compose(a,b)),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ there_exists(compose(codomain(X_6),X_6))
| domain(codomain(X_6)) = codomain(X_6) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_6))),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_13,plain,
compose(codomain(X_6),X_6) = X_6,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_14,plain,
( compose(codomain(X_6),X_6) != X_6
| ~ there_exists(X_6)
| there_exists(compose(codomain(X_6),X_6)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(codomain(X_6),X_6)) ),[0],$fot(X_6)]]) ).
cnf(refute_0_15,plain,
( ~ there_exists(X_6)
| there_exists(compose(codomain(X_6),X_6)) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_6),X_6),X_6) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ there_exists(X_6)
| domain(codomain(X_6)) = codomain(X_6) ),
inference(resolve,[$cnf( there_exists(compose(codomain(X_6),X_6)) )],[refute_0_15,refute_0_12]) ).
cnf(refute_0_17,plain,
( ~ there_exists(a)
| domain(codomain(a)) = codomain(a) ),
inference(subst,[],[refute_0_16:[bind(X_6,$fot(a))]]) ).
cnf(refute_0_18,plain,
( ~ there_exists(domain(a))
| there_exists(a) ),
inference(subst,[],[domain_has_elements:[bind(X,$fot(a))]]) ).
cnf(refute_0_19,plain,
( ~ there_exists(compose(a,b))
| domain(a) = codomain(b) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_20,plain,
domain(a) = codomain(b),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_19]) ).
cnf(refute_0_21,plain,
( domain(a) != codomain(b)
| ~ there_exists(codomain(b))
| there_exists(domain(a)) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(domain(a)) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_22,plain,
( ~ there_exists(codomain(b))
| there_exists(domain(a)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ there_exists(codomain(b))
| there_exists(a) ),
inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( ~ there_exists(compose(a,b))
| there_exists(domain(a)) ),
inference(subst,[],[composition_implies_domain:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_25,plain,
there_exists(domain(a)),
inference(resolve,[$cnf( there_exists(compose(a,b)) )],[ab_exists,refute_0_24]) ).
cnf(refute_0_26,plain,
( domain(a) != codomain(b)
| ~ there_exists(domain(a))
| there_exists(codomain(b)) ),
introduced(tautology,[equality,[$cnf( there_exists(domain(a)) ),[0],$fot(codomain(b))]]) ).
cnf(refute_0_27,plain,
( ~ there_exists(domain(a))
| there_exists(codomain(b)) ),
inference(resolve,[$cnf( $equal(domain(a),codomain(b)) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
there_exists(codomain(b)),
inference(resolve,[$cnf( there_exists(domain(a)) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
there_exists(a),
inference(resolve,[$cnf( there_exists(codomain(b)) )],[refute_0_28,refute_0_23]) ).
cnf(refute_0_30,plain,
domain(codomain(a)) = codomain(a),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_29,refute_0_17]) ).
cnf(refute_0_31,plain,
( domain(codomain(a)) != codomain(a)
| domain(codomain(a)) != codomain(compose(a,b))
| codomain(a) = codomain(compose(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(codomain(a)),codomain(compose(a,b))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_32,plain,
( domain(codomain(a)) != codomain(compose(a,b))
| codomain(a) = codomain(compose(a,b)) ),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
codomain(a) = codomain(compose(a,b)),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(compose(a,b))) )],[refute_0_11,refute_0_32]) ).
cnf(refute_0_34,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_35,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_36,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( codomain(a) != codomain(compose(a,b))
| codomain(compose(a,b)) = codomain(a) ),
inference(subst,[],[refute_0_36:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(codomain(compose(a,b))))]]) ).
cnf(refute_0_38,plain,
codomain(a) != codomain(compose(a,b)),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),codomain(a)) )],[refute_0_37,prove_codomain_of_ab_equals_codomain_of_a]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( $equal(codomain(a),codomain(compose(a,b))) )],[refute_0_33,refute_0_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun May 29 18:10:27 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.55/0.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.74
% 0.55/0.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.55/0.74
%------------------------------------------------------------------------------