%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 00:36:13 EDT 2022
% Result : Unsatisfiable 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 10 unt; 0 nHn; 11 RR)
% Number of literals : 22 ( 21 equ; 11 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(u_definition,axiom,
apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(apply(X_1,X_1),combinator) != apply(combinator,apply(apply(X_1,X_1),combinator)),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(X_1,X_1),combinator)))]]) ).
cnf(refute_0_1,plain,
apply(apply(u,X_1),combinator) = apply(combinator,apply(apply(X_1,X_1),combinator)),
inference(subst,[],[u_definition:[bind(X,$fot(X_1)),bind(Y,$fot(combinator))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( apply(apply(u,X_1),combinator) != apply(combinator,apply(apply(X_1,X_1),combinator))
| apply(combinator,apply(apply(X_1,X_1),combinator)) = apply(apply(u,X_1),combinator) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(u,X_1),combinator))),bind(Y0,$fot(apply(combinator,apply(apply(X_1,X_1),combinator))))]]) ).
cnf(refute_0_6,plain,
apply(combinator,apply(apply(X_1,X_1),combinator)) = apply(apply(u,X_1),combinator),
inference(resolve,[$cnf( $equal(apply(apply(u,X_1),combinator),apply(combinator,apply(apply(X_1,X_1),combinator))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( apply(apply(X_1,X_1),combinator) != apply(apply(u,X_1),combinator)
| apply(combinator,apply(apply(X_1,X_1),combinator)) != apply(apply(u,X_1),combinator)
| apply(apply(X_1,X_1),combinator) = apply(combinator,apply(apply(X_1,X_1),combinator)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X_1,X_1),combinator),apply(combinator,apply(apply(X_1,X_1),combinator))) ),[1],$fot(apply(apply(u,X_1),combinator))]]) ).
cnf(refute_0_8,plain,
( apply(apply(X_1,X_1),combinator) != apply(apply(u,X_1),combinator)
| apply(apply(X_1,X_1),combinator) = apply(combinator,apply(apply(X_1,X_1),combinator)) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(apply(X_1,X_1),combinator)),apply(apply(u,X_1),combinator)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(X_1,X_1),combinator) != apply(apply(u,X_1),combinator),
inference(resolve,[$cnf( $equal(apply(apply(X_1,X_1),combinator),apply(combinator,apply(apply(X_1,X_1),combinator))) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
apply(apply(u,u),combinator) != apply(apply(u,u),combinator),
inference(subst,[],[refute_0_9:[bind(X_1,$fot(u))]]) ).
cnf(refute_0_11,plain,
apply(apply(u,u),combinator) = apply(apply(u,u),combinator),
introduced(tautology,[refl,[$fot(apply(apply(u,u),combinator))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(u,u),combinator),apply(apply(u,u),combinator)) )],[refute_0_11,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.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 09:19:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------