TSTP Solution File: COL024-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL024-1 : 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 00:36:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 13 RR)
% Number of literals : 31 ( 30 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(m_definition,axiom,
apply(m,X) = apply(X,X) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(X_23,apply(apply(b,combinator),X_23)) != apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(X_23,apply(apply(b,combinator),X_23))))]]) ).
cnf(refute_0_1,plain,
apply(m,apply(apply(b,X_13),X_14)) = apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14)),
inference(subst,[],[m_definition:[bind(X,$fot(apply(apply(b,X_13),X_14)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14)) = apply(X_13,apply(X_14,apply(apply(b,X_13),X_14))),
inference(subst,[],[b_definition:[bind(X,$fot(X_13)),bind(Y,$fot(X_14)),bind(Z,$fot(apply(apply(b,X_13),X_14)))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14)) != apply(X_13,apply(X_14,apply(apply(b,X_13),X_14)))
| apply(m,apply(apply(b,X_13),X_14)) != apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14))
| apply(m,apply(apply(b,X_13),X_14)) = apply(X_13,apply(X_14,apply(apply(b,X_13),X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(m,apply(apply(b,X_13),X_14)),apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14))) ),[1],$fot(apply(X_13,apply(X_14,apply(apply(b,X_13),X_14))))]]) ).
cnf(refute_0_4,plain,
( apply(m,apply(apply(b,X_13),X_14)) != apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14))
| apply(m,apply(apply(b,X_13),X_14)) = apply(X_13,apply(X_14,apply(apply(b,X_13),X_14))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14)),apply(X_13,apply(X_14,apply(apply(b,X_13),X_14)))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(m,apply(apply(b,X_13),X_14)) = apply(X_13,apply(X_14,apply(apply(b,X_13),X_14))),
inference(resolve,[$cnf( $equal(apply(m,apply(apply(b,X_13),X_14)),apply(apply(apply(b,X_13),X_14),apply(apply(b,X_13),X_14))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
apply(m,apply(apply(b,combinator),X_23)) = apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))),
inference(subst,[],[refute_0_5:[bind(X_13,$fot(combinator)),bind(X_14,$fot(X_23))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( apply(m,apply(apply(b,combinator),X_23)) != apply(combinator,apply(X_23,apply(apply(b,combinator),X_23)))
| apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))) = apply(m,apply(apply(b,combinator),X_23)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(m,apply(apply(b,combinator),X_23)))),bind(Y0,$fot(apply(combinator,apply(X_23,apply(apply(b,combinator),X_23)))))]]) ).
cnf(refute_0_11,plain,
apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))) = apply(m,apply(apply(b,combinator),X_23)),
inference(resolve,[$cnf( $equal(apply(m,apply(apply(b,combinator),X_23)),apply(combinator,apply(X_23,apply(apply(b,combinator),X_23)))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( apply(X_23,apply(apply(b,combinator),X_23)) != apply(m,apply(apply(b,combinator),X_23))
| apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))) != apply(m,apply(apply(b,combinator),X_23))
| apply(X_23,apply(apply(b,combinator),X_23)) = apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_23,apply(apply(b,combinator),X_23)),apply(combinator,apply(X_23,apply(apply(b,combinator),X_23)))) ),[1],$fot(apply(m,apply(apply(b,combinator),X_23)))]]) ).
cnf(refute_0_13,plain,
( apply(X_23,apply(apply(b,combinator),X_23)) != apply(m,apply(apply(b,combinator),X_23))
| apply(X_23,apply(apply(b,combinator),X_23)) = apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(X_23,apply(apply(b,combinator),X_23))),apply(m,apply(apply(b,combinator),X_23))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(X_23,apply(apply(b,combinator),X_23)) != apply(m,apply(apply(b,combinator),X_23)),
inference(resolve,[$cnf( $equal(apply(X_23,apply(apply(b,combinator),X_23)),apply(combinator,apply(X_23,apply(apply(b,combinator),X_23)))) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
apply(m,apply(apply(b,combinator),m)) != apply(m,apply(apply(b,combinator),m)),
inference(subst,[],[refute_0_14:[bind(X_23,$fot(m))]]) ).
cnf(refute_0_16,plain,
apply(m,apply(apply(b,combinator),m)) = apply(m,apply(apply(b,combinator),m)),
introduced(tautology,[refl,[$fot(apply(m,apply(apply(b,combinator),m)))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(apply(m,apply(apply(b,combinator),m)),apply(m,apply(apply(b,combinator),m))) )],[refute_0_16,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COL024-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 06:51:50 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.55
% 0.20/0.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.55
%------------------------------------------------------------------------------