TSTP Solution File: CAT018-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 00:04:37 EDT 2022
% Result : Unsatisfiable 2.93s 3.13s
% Output : CNFRefutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 18 unt; 0 nHn; 35 RR)
% Number of literals : 74 ( 0 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_composition,axiom,
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ) ).
cnf(associative_property2,axiom,
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) ) ).
cnf(category_theory_axiom3,axiom,
( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) ) ).
cnf(category_theory_axiom6,axiom,
( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) ) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X)) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X),X) ).
cnf(product_on_codomain,axiom,
product(codomain(X),X,X) ).
cnf(identity2,axiom,
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ).
cnf(assume_ab_exists,hypothesis,
defined(a,b) ).
cnf(assume_bc_exists,hypothesis,
defined(b,c) ).
cnf(prove_a_bc_exists,negated_conjecture,
~ defined(a,compose(b,c)) ).
cnf(refute_0_0,plain,
product(codomain(X_112),X_112,X_112),
inference(subst,[],[product_on_codomain:[bind(X,$fot(X_112))]]) ).
cnf(refute_0_1,plain,
( ~ defined(X_110,X_112)
| ~ product(codomain(X_112),X_112,X_112)
| defined(X_110,codomain(X_112)) ),
inference(subst,[],[category_theory_axiom3:[bind(X,$fot(X_110)),bind(Y,$fot(codomain(X_112))),bind(Yz,$fot(X_112)),bind(Z,$fot(X_112))]]) ).
cnf(refute_0_2,plain,
( ~ defined(X_110,X_112)
| defined(X_110,codomain(X_112)) ),
inference(resolve,[$cnf( product(codomain(X_112),X_112,X_112) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ defined(a,b)
| defined(a,codomain(b)) ),
inference(subst,[],[refute_0_2:[bind(X_110,$fot(a)),bind(X_112,$fot(b))]]) ).
cnf(refute_0_4,plain,
defined(a,codomain(b)),
inference(resolve,[$cnf( defined(a,b) )],[assume_ab_exists,refute_0_3]) ).
cnf(refute_0_5,plain,
defined(codomain(X_82),X_82),
inference(subst,[],[mapping_from_codomain_of_x_to_x:[bind(X,$fot(X_82))]]) ).
cnf(refute_0_6,plain,
( ~ defined(codomain(X_82),X_82)
| ~ product(X_79,X_81,codomain(X_82))
| defined(X_81,X_82) ),
inference(subst,[],[associative_property2:[bind(X,$fot(X_79)),bind(Xy,$fot(codomain(X_82))),bind(Y,$fot(X_81)),bind(Z,$fot(X_82))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_79,X_81,codomain(X_82))
| defined(X_81,X_82) ),
inference(resolve,[$cnf( defined(codomain(X_82),X_82) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(codomain(compose(b,c)),codomain(b),codomain(compose(b,c)))
| defined(codomain(b),compose(b,c)) ),
inference(subst,[],[refute_0_7:[bind(X_79,$fot(codomain(compose(b,c)))),bind(X_81,$fot(codomain(b))),bind(X_82,$fot(compose(b,c)))]]) ).
cnf(refute_0_9,plain,
( ~ defined(codomain(compose(b,c)),codomain(b))
| ~ identity_map(codomain(b))
| product(codomain(compose(b,c)),codomain(b),codomain(compose(b,c))) ),
inference(subst,[],[identity2:[bind(X,$fot(codomain(compose(b,c)))),bind(Y,$fot(codomain(b)))]]) ).
cnf(refute_0_10,plain,
defined(codomain(compose(b,c)),compose(b,c)),
inference(subst,[],[mapping_from_codomain_of_x_to_x:[bind(X,$fot(compose(b,c)))]]) ).
cnf(refute_0_11,plain,
( ~ defined(b,c)
| product(b,c,compose(b,c)) ),
inference(subst,[],[closure_of_composition:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_12,plain,
product(b,c,compose(b,c)),
inference(resolve,[$cnf( defined(b,c) )],[assume_bc_exists,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ defined(X_110,compose(b,c))
| ~ product(b,c,compose(b,c))
| defined(X_110,b) ),
inference(subst,[],[category_theory_axiom3:[bind(X,$fot(X_110)),bind(Y,$fot(b)),bind(Yz,$fot(compose(b,c))),bind(Z,$fot(c))]]) ).
cnf(refute_0_14,plain,
( ~ defined(X_110,compose(b,c))
| defined(X_110,b) ),
inference(resolve,[$cnf( product(b,c,compose(b,c)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ defined(codomain(compose(b,c)),compose(b,c))
| defined(codomain(compose(b,c)),b) ),
inference(subst,[],[refute_0_14:[bind(X_110,$fot(codomain(compose(b,c))))]]) ).
cnf(refute_0_16,plain,
defined(codomain(compose(b,c)),b),
inference(resolve,[$cnf( defined(codomain(compose(b,c)),compose(b,c)) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ defined(codomain(compose(b,c)),b)
| defined(codomain(compose(b,c)),codomain(b)) ),
inference(subst,[],[refute_0_2:[bind(X_110,$fot(codomain(compose(b,c)))),bind(X_112,$fot(b))]]) ).
cnf(refute_0_18,plain,
defined(codomain(compose(b,c)),codomain(b)),
inference(resolve,[$cnf( defined(codomain(compose(b,c)),b) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ identity_map(codomain(b))
| product(codomain(compose(b,c)),codomain(b),codomain(compose(b,c))) ),
inference(resolve,[$cnf( defined(codomain(compose(b,c)),codomain(b)) )],[refute_0_18,refute_0_9]) ).
cnf(refute_0_20,plain,
identity_map(codomain(b)),
inference(subst,[],[codomain_is_an_identity_map:[bind(X,$fot(b))]]) ).
cnf(refute_0_21,plain,
product(codomain(compose(b,c)),codomain(b),codomain(compose(b,c))),
inference(resolve,[$cnf( identity_map(codomain(b)) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
defined(codomain(b),compose(b,c)),
inference(resolve,[$cnf( product(codomain(compose(b,c)),codomain(b),codomain(compose(b,c))) )],[refute_0_21,refute_0_8]) ).
cnf(refute_0_23,plain,
( ~ defined(X_170,codomain(b))
| ~ defined(codomain(b),compose(b,c))
| ~ identity_map(codomain(b))
| defined(X_170,compose(b,c)) ),
inference(subst,[],[category_theory_axiom6:[bind(X,$fot(X_170)),bind(Y,$fot(codomain(b))),bind(Z,$fot(compose(b,c)))]]) ).
cnf(refute_0_24,plain,
( ~ defined(X_170,codomain(b))
| ~ identity_map(codomain(b))
| defined(X_170,compose(b,c)) ),
inference(resolve,[$cnf( defined(codomain(b),compose(b,c)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ defined(X_170,codomain(b))
| defined(X_170,compose(b,c)) ),
inference(resolve,[$cnf( identity_map(codomain(b)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ defined(a,codomain(b))
| defined(a,compose(b,c)) ),
inference(subst,[],[refute_0_25:[bind(X_170,$fot(a))]]) ).
cnf(refute_0_27,plain,
defined(a,compose(b,c)),
inference(resolve,[$cnf( defined(a,codomain(b)) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( defined(a,compose(b,c)) )],[refute_0_27,prove_a_bc_exists]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.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 16:44:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.93/3.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/3.13
% 2.93/3.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.93/3.13
%------------------------------------------------------------------------------