TSTP Solution File: COL016-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 00:36:14 EDT 2022
% Result : Unsatisfiable 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 41 ( 40 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l_definition,axiom,
apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).
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(m,apply(l,combinator)) != apply(combinator,apply(m,apply(l,combinator))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(m,apply(l,combinator))))]]) ).
cnf(refute_0_1,plain,
apply(m,apply(l,X_16)) = apply(apply(l,X_16),apply(l,X_16)),
inference(subst,[],[m_definition:[bind(X,$fot(apply(l,X_16)))]]) ).
cnf(refute_0_2,plain,
apply(apply(l,X_2),X_3) = apply(X_2,apply(X_3,X_3)),
inference(subst,[],[l_definition:[bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_3,plain,
apply(m,X_3) = apply(X_3,X_3),
inference(subst,[],[m_definition:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( apply(m,X_3) != apply(X_3,X_3)
| apply(X_3,X_3) = apply(m,X_3) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(apply(m,X_3))),bind(Y0,$fot(apply(X_3,X_3)))]]) ).
cnf(refute_0_8,plain,
apply(X_3,X_3) = apply(m,X_3),
inference(resolve,[$cnf( $equal(apply(m,X_3),apply(X_3,X_3)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( apply(X_3,X_3) != apply(m,X_3)
| apply(apply(l,X_2),X_3) != apply(X_2,apply(X_3,X_3))
| apply(apply(l,X_2),X_3) = apply(X_2,apply(m,X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(l,X_2),X_3),apply(X_2,apply(X_3,X_3))) ),[1,1],$fot(apply(m,X_3))]]) ).
cnf(refute_0_10,plain,
( apply(apply(l,X_2),X_3) != apply(X_2,apply(X_3,X_3))
| apply(apply(l,X_2),X_3) = apply(X_2,apply(m,X_3)) ),
inference(resolve,[$cnf( $equal(apply(X_3,X_3),apply(m,X_3)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(l,X_2),X_3) = apply(X_2,apply(m,X_3)),
inference(resolve,[$cnf( $equal(apply(apply(l,X_2),X_3),apply(X_2,apply(X_3,X_3))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
apply(apply(l,X_16),apply(l,X_16)) = apply(X_16,apply(m,apply(l,X_16))),
inference(subst,[],[refute_0_11:[bind(X_2,$fot(X_16)),bind(X_3,$fot(apply(l,X_16)))]]) ).
cnf(refute_0_13,plain,
( apply(apply(l,X_16),apply(l,X_16)) != apply(X_16,apply(m,apply(l,X_16)))
| apply(m,apply(l,X_16)) != apply(apply(l,X_16),apply(l,X_16))
| apply(m,apply(l,X_16)) = apply(X_16,apply(m,apply(l,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(m,apply(l,X_16)),apply(apply(l,X_16),apply(l,X_16))) ),[1],$fot(apply(X_16,apply(m,apply(l,X_16))))]]) ).
cnf(refute_0_14,plain,
( apply(m,apply(l,X_16)) != apply(apply(l,X_16),apply(l,X_16))
| apply(m,apply(l,X_16)) = apply(X_16,apply(m,apply(l,X_16))) ),
inference(resolve,[$cnf( $equal(apply(apply(l,X_16),apply(l,X_16)),apply(X_16,apply(m,apply(l,X_16)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(m,apply(l,X_16)) = apply(X_16,apply(m,apply(l,X_16))),
inference(resolve,[$cnf( $equal(apply(m,apply(l,X_16)),apply(apply(l,X_16),apply(l,X_16))) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(m,apply(l,combinator)) = apply(combinator,apply(m,apply(l,combinator))),
inference(subst,[],[refute_0_15:[bind(X_16,$fot(combinator))]]) ).
cnf(refute_0_17,plain,
( apply(m,apply(l,combinator)) != apply(combinator,apply(m,apply(l,combinator)))
| apply(combinator,apply(m,apply(l,combinator))) = apply(m,apply(l,combinator)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(apply(m,apply(l,combinator)))),bind(Y0,$fot(apply(combinator,apply(m,apply(l,combinator)))))]]) ).
cnf(refute_0_18,plain,
apply(combinator,apply(m,apply(l,combinator))) = apply(m,apply(l,combinator)),
inference(resolve,[$cnf( $equal(apply(m,apply(l,combinator)),apply(combinator,apply(m,apply(l,combinator)))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( apply(combinator,apply(m,apply(l,combinator))) != apply(m,apply(l,combinator))
| apply(m,apply(l,combinator)) != apply(m,apply(l,combinator))
| apply(m,apply(l,combinator)) = apply(combinator,apply(m,apply(l,combinator))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(m,apply(l,combinator)),apply(combinator,apply(m,apply(l,combinator)))) ),[1],$fot(apply(m,apply(l,combinator)))]]) ).
cnf(refute_0_20,plain,
( apply(m,apply(l,combinator)) != apply(m,apply(l,combinator))
| apply(m,apply(l,combinator)) = apply(combinator,apply(m,apply(l,combinator))) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(m,apply(l,combinator))),apply(m,apply(l,combinator))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
apply(m,apply(l,combinator)) != apply(m,apply(l,combinator)),
inference(resolve,[$cnf( $equal(apply(m,apply(l,combinator)),apply(combinator,apply(m,apply(l,combinator)))) )],[refute_0_20,refute_0_0]) ).
cnf(refute_0_22,plain,
apply(m,apply(l,combinator)) = apply(m,apply(l,combinator)),
introduced(tautology,[refl,[$fot(apply(m,apply(l,combinator)))]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(apply(m,apply(l,combinator)),apply(m,apply(l,combinator))) )],[refute_0_22,refute_0_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 14:11:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45
% 0.18/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.46
%------------------------------------------------------------------------------