TSTP Solution File: COL025-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL025-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 0.19s 0.44s
% Output : CNFRefutation 0.19s
% 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 : 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 : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(w_definition,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(X_13,X_13) != apply(combinator,apply(X_13,X_13)),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(X_13,X_13)))]]) ).
cnf(refute_0_1,plain,
apply(apply(w,apply(b,X_9)),Y) = apply(apply(apply(b,X_9),Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(apply(b,X_9)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(b,X_9),Y),Y) = apply(X_9,apply(Y,Y)),
inference(subst,[],[b_definition:[bind(X,$fot(X_9)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(b,X_9),Y),Y) != apply(X_9,apply(Y,Y))
| apply(apply(w,apply(b,X_9)),Y) != apply(apply(apply(b,X_9),Y),Y)
| apply(apply(w,apply(b,X_9)),Y) = apply(X_9,apply(Y,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(b,X_9)),Y),apply(apply(apply(b,X_9),Y),Y)) ),[1],$fot(apply(X_9,apply(Y,Y)))]]) ).
cnf(refute_0_4,plain,
( apply(apply(w,apply(b,X_9)),Y) != apply(apply(apply(b,X_9),Y),Y)
| apply(apply(w,apply(b,X_9)),Y) = apply(X_9,apply(Y,Y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_9),Y),Y),apply(X_9,apply(Y,Y))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(apply(w,apply(b,X_9)),Y) = apply(X_9,apply(Y,Y)),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(b,X_9)),Y),apply(apply(apply(b,X_9),Y),Y)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
apply(apply(w,apply(b,combinator)),X_13) = apply(combinator,apply(X_13,X_13)),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_13)),bind(X_9,$fot(combinator))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( apply(apply(w,apply(b,combinator)),X_13) != apply(combinator,apply(X_13,X_13))
| apply(combinator,apply(X_13,X_13)) = apply(apply(w,apply(b,combinator)),X_13) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(apply(w,apply(b,combinator)),X_13))),bind(Y0,$fot(apply(combinator,apply(X_13,X_13))))]]) ).
cnf(refute_0_11,plain,
apply(combinator,apply(X_13,X_13)) = apply(apply(w,apply(b,combinator)),X_13),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(b,combinator)),X_13),apply(combinator,apply(X_13,X_13))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( apply(X_13,X_13) != apply(apply(w,apply(b,combinator)),X_13)
| apply(combinator,apply(X_13,X_13)) != apply(apply(w,apply(b,combinator)),X_13)
| apply(X_13,X_13) = apply(combinator,apply(X_13,X_13)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_13,X_13),apply(combinator,apply(X_13,X_13))) ),[1],$fot(apply(apply(w,apply(b,combinator)),X_13))]]) ).
cnf(refute_0_13,plain,
( apply(X_13,X_13) != apply(apply(w,apply(b,combinator)),X_13)
| apply(X_13,X_13) = apply(combinator,apply(X_13,X_13)) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(X_13,X_13)),apply(apply(w,apply(b,combinator)),X_13)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(X_13,X_13) != apply(apply(w,apply(b,combinator)),X_13),
inference(resolve,[$cnf( $equal(apply(X_13,X_13),apply(combinator,apply(X_13,X_13))) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator))) != apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator))),
inference(subst,[],[refute_0_14:[bind(X_13,$fot(apply(w,apply(b,combinator))))]]) ).
cnf(refute_0_16,plain,
apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator))) = apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator))),
introduced(tautology,[refl,[$fot(apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator))))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator))),apply(apply(w,apply(b,combinator)),apply(w,apply(b,combinator)))) )],[refute_0_16,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL025-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n024.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 : Tue May 31 15:15:51 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.44
%------------------------------------------------------------------------------