TSTP Solution File: COL027-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL027-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 38.38s 38.56s
% Output : CNFRefutation 38.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 18 unt; 0 nHn; 16 RR)
% Number of literals : 42 ( 41 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 62 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(h_definition,axiom,
apply(apply(apply(h,X),Y),Z) = apply(apply(apply(X,Y),Z),Y) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(apply(X_103,X_104),X_103) != apply(combinator,apply(apply(X_103,X_104),X_103)),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(X_103,X_104),X_103)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(b,X),apply(Z,X_12)),Z) = apply(X,apply(apply(Z,X_12),Z)),
inference(subst,[],[b_definition:[bind(Y,$fot(apply(Z,X_12)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(h,apply(b,X_4)),Y),Z) = apply(apply(apply(apply(b,X_4),Y),Z),Y),
inference(subst,[],[h_definition:[bind(X,$fot(apply(b,X_4)))]]) ).
cnf(refute_0_3,plain,
apply(apply(apply(b,X_4),Y),Z) = apply(X_4,apply(Y,Z)),
inference(subst,[],[b_definition:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_4,plain,
( apply(apply(apply(b,X_4),Y),Z) != apply(X_4,apply(Y,Z))
| apply(apply(apply(h,apply(b,X_4)),Y),Z) != apply(apply(apply(apply(b,X_4),Y),Z),Y)
| apply(apply(apply(h,apply(b,X_4)),Y),Z) = apply(apply(X_4,apply(Y,Z)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(h,apply(b,X_4)),Y),Z),apply(apply(apply(apply(b,X_4),Y),Z),Y)) ),[1,0],$fot(apply(X_4,apply(Y,Z)))]]) ).
cnf(refute_0_5,plain,
( apply(apply(apply(h,apply(b,X_4)),Y),Z) != apply(apply(apply(apply(b,X_4),Y),Z),Y)
| apply(apply(apply(h,apply(b,X_4)),Y),Z) = apply(apply(X_4,apply(Y,Z)),Y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_4),Y),Z),apply(X_4,apply(Y,Z))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
apply(apply(apply(h,apply(b,X_4)),Y),Z) = apply(apply(X_4,apply(Y,Z)),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(h,apply(b,X_4)),Y),Z),apply(apply(apply(apply(b,X_4),Y),Z),Y)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12) = apply(apply(apply(b,X),apply(Z,X_12)),Z),
inference(subst,[],[refute_0_6:[bind(Y,$fot(Z)),bind(Z,$fot(X_12)),bind(X_4,$fot(apply(b,X)))]]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12) != apply(apply(apply(b,X),apply(Z,X_12)),Z)
| apply(apply(apply(b,X),apply(Z,X_12)),Z) = apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12))),bind(Y0,$fot(apply(apply(apply(b,X),apply(Z,X_12)),Z)))]]) ).
cnf(refute_0_12,plain,
apply(apply(apply(b,X),apply(Z,X_12)),Z) = apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12),
inference(resolve,[$cnf( $equal(apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12),apply(apply(apply(b,X),apply(Z,X_12)),Z)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(b,X),apply(Z,X_12)),Z) != apply(X,apply(apply(Z,X_12),Z))
| apply(apply(apply(b,X),apply(Z,X_12)),Z) != apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12)
| apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12) = apply(X,apply(apply(Z,X_12),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),apply(Z,X_12)),Z),apply(X,apply(apply(Z,X_12),Z))) ),[0],$fot(apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12))]]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(b,X),apply(Z,X_12)),Z) != apply(X,apply(apply(Z,X_12),Z))
| apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12) = apply(X,apply(apply(Z,X_12),Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(Z,X_12)),Z),apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(apply(apply(h,apply(b,apply(b,X))),Z),X_12) = apply(X,apply(apply(Z,X_12),Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(Z,X_12)),Z),apply(X,apply(apply(Z,X_12),Z))) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104) = apply(combinator,apply(apply(X_103,X_104),X_103)),
inference(subst,[],[refute_0_15:[bind(X,$fot(combinator)),bind(Z,$fot(X_103)),bind(X_12,$fot(X_104))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104) != apply(combinator,apply(apply(X_103,X_104),X_103))
| apply(combinator,apply(apply(X_103,X_104),X_103)) = apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104))),bind(Y0,$fot(apply(combinator,apply(apply(X_103,X_104),X_103))))]]) ).
cnf(refute_0_18,plain,
apply(combinator,apply(apply(X_103,X_104),X_103)) = apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104),
inference(resolve,[$cnf( $equal(apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104),apply(combinator,apply(apply(X_103,X_104),X_103))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( apply(apply(X_103,X_104),X_103) != apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104)
| apply(combinator,apply(apply(X_103,X_104),X_103)) != apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104)
| apply(apply(X_103,X_104),X_103) = apply(combinator,apply(apply(X_103,X_104),X_103)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X_103,X_104),X_103),apply(combinator,apply(apply(X_103,X_104),X_103))) ),[1],$fot(apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104))]]) ).
cnf(refute_0_20,plain,
( apply(apply(X_103,X_104),X_103) != apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104)
| apply(apply(X_103,X_104),X_103) = apply(combinator,apply(apply(X_103,X_104),X_103)) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(apply(X_103,X_104),X_103)),apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
apply(apply(X_103,X_104),X_103) != apply(apply(apply(h,apply(b,apply(b,combinator))),X_103),X_104),
inference(resolve,[$cnf( $equal(apply(apply(X_103,X_104),X_103),apply(combinator,apply(apply(X_103,X_104),X_103))) )],[refute_0_20,refute_0_0]) ).
cnf(refute_0_22,plain,
apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator)))) != apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator)))),
inference(subst,[],[refute_0_21:[bind(X_103,$fot(apply(h,apply(b,apply(b,combinator))))),bind(X_104,$fot(apply(h,apply(b,apply(b,combinator)))))]]) ).
cnf(refute_0_23,plain,
apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator)))) = apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator)))),
introduced(tautology,[refl,[$fot(apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator)))))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator)))),apply(apply(apply(h,apply(b,apply(b,combinator))),apply(h,apply(b,apply(b,combinator)))),apply(h,apply(b,apply(b,combinator))))) )],[refute_0_23,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL027-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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 15:57:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 38.38/38.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.38/38.56
% 38.38/38.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.38/38.56
%------------------------------------------------------------------------------