TSTP Solution File: CAT011-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 58.74s 58.92s
% Output : CNFRefutation 58.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 13 unt; 0 nHn; 29 RR)
% Number of literals : 58 ( 36 equ; 26 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(domain_has_elements,axiom,
( ~ there_exists(domain(X))
| there_exists(X) ) ).
cnf(domain_codomain_composition1,axiom,
( ~ there_exists(compose(X,Y))
| domain(X) = codomain(Y) ) ).
cnf(compose_domain,axiom,
compose(X,domain(X)) = X ).
cnf(compose_codomain,axiom,
compose(codomain(X),X) = X ).
cnf(assume_domain_exists,hypothesis,
there_exists(domain(a)) ).
cnf(prove_domain_is_idempotent,negated_conjecture,
domain(domain(a)) != domain(a) ).
cnf(refute_0_0,plain,
( ~ there_exists(compose(domain(a),domain(a)))
| domain(domain(a)) = codomain(domain(a)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(domain(a))),bind(Y,$fot(domain(a)))]]) ).
cnf(refute_0_1,plain,
compose(codomain(domain(a)),domain(a)) = domain(a),
inference(subst,[],[compose_codomain:[bind(X,$fot(domain(a)))]]) ).
cnf(refute_0_2,plain,
( ~ there_exists(domain(a))
| there_exists(a) ),
inference(subst,[],[domain_has_elements:[bind(X,$fot(a))]]) ).
cnf(refute_0_3,plain,
there_exists(a),
inference(resolve,[$cnf( there_exists(domain(a)) )],[assume_domain_exists,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ there_exists(compose(X_68,domain(X_68)))
| domain(X_68) = codomain(domain(X_68)) ),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(X_68)),bind(Y,$fot(domain(X_68)))]]) ).
cnf(refute_0_5,plain,
compose(X_68,domain(X_68)) = X_68,
inference(subst,[],[compose_domain:[bind(X,$fot(X_68))]]) ).
cnf(refute_0_6,plain,
( compose(X_68,domain(X_68)) != X_68
| ~ there_exists(X_68)
| there_exists(compose(X_68,domain(X_68))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(X_68,domain(X_68))) ),[0],$fot(X_68)]]) ).
cnf(refute_0_7,plain,
( ~ there_exists(X_68)
| there_exists(compose(X_68,domain(X_68))) ),
inference(resolve,[$cnf( $equal(compose(X_68,domain(X_68)),X_68) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ there_exists(X_68)
| domain(X_68) = codomain(domain(X_68)) ),
inference(resolve,[$cnf( there_exists(compose(X_68,domain(X_68))) )],[refute_0_7,refute_0_4]) ).
cnf(refute_0_9,plain,
( ~ there_exists(a)
| domain(a) = codomain(domain(a)) ),
inference(subst,[],[refute_0_8:[bind(X_68,$fot(a))]]) ).
cnf(refute_0_10,plain,
domain(a) = codomain(domain(a)),
inference(resolve,[$cnf( there_exists(a) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( domain(a) != codomain(domain(a))
| codomain(domain(a)) = domain(a) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(domain(a))),bind(Y0,$fot(codomain(domain(a))))]]) ).
cnf(refute_0_15,plain,
codomain(domain(a)) = domain(a),
inference(resolve,[$cnf( $equal(domain(a),codomain(domain(a))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( codomain(domain(a)) != domain(a)
| compose(codomain(domain(a)),domain(a)) != domain(a)
| compose(domain(a),domain(a)) = domain(a) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(domain(a)),domain(a)),domain(a)) ),[0,0],$fot(domain(a))]]) ).
cnf(refute_0_17,plain,
( compose(codomain(domain(a)),domain(a)) != domain(a)
| compose(domain(a),domain(a)) = domain(a) ),
inference(resolve,[$cnf( $equal(codomain(domain(a)),domain(a)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
compose(domain(a),domain(a)) = domain(a),
inference(resolve,[$cnf( $equal(compose(codomain(domain(a)),domain(a)),domain(a)) )],[refute_0_1,refute_0_17]) ).
cnf(refute_0_19,plain,
( compose(domain(a),domain(a)) != domain(a)
| ~ there_exists(domain(a))
| there_exists(compose(domain(a),domain(a))) ),
introduced(tautology,[equality,[$cnf( ~ there_exists(compose(domain(a),domain(a))) ),[0],$fot(domain(a))]]) ).
cnf(refute_0_20,plain,
( ~ there_exists(domain(a))
| there_exists(compose(domain(a),domain(a))) ),
inference(resolve,[$cnf( $equal(compose(domain(a),domain(a)),domain(a)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ there_exists(domain(a))
| domain(domain(a)) = codomain(domain(a)) ),
inference(resolve,[$cnf( there_exists(compose(domain(a),domain(a))) )],[refute_0_20,refute_0_0]) ).
cnf(refute_0_22,plain,
( codomain(domain(a)) != domain(a)
| domain(domain(a)) != codomain(domain(a))
| domain(domain(a)) = domain(a) ),
introduced(tautology,[equality,[$cnf( $equal(domain(domain(a)),codomain(domain(a))) ),[1],$fot(domain(a))]]) ).
cnf(refute_0_23,plain,
( domain(domain(a)) != codomain(domain(a))
| domain(domain(a)) = domain(a) ),
inference(resolve,[$cnf( $equal(codomain(domain(a)),domain(a)) )],[refute_0_15,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ there_exists(domain(a))
| domain(domain(a)) = domain(a) ),
inference(resolve,[$cnf( $equal(domain(domain(a)),codomain(domain(a))) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
domain(domain(a)) = domain(a),
inference(resolve,[$cnf( there_exists(domain(a)) )],[assume_domain_exists,refute_0_24]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(domain(domain(a)),domain(a)) )],[refute_0_25,prove_domain_is_idempotent]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 15:24:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 58.74/58.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.74/58.92
% 58.74/58.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.74/58.93
%------------------------------------------------------------------------------