TPTP Problem File: COL076-2.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : COL076-2 : TPTP v8.2.0. Released v1.2.0.
% Domain : Combinatory Logic
% Problem : Lemma 2 for showing the unsatisfiable variant of TRC
% Version : [Jec95] (equality) axioms :
% Reduced & Augmented > Incomplete.
% English : Searching for the self-referential combinator with the
% property s = eq <k s,k p2>.
% Refs : [Jec95] Jech (1995), Otter Experiments in a System of Combinat
% Source : [Jec95]
% Names : - [Jec95]
% Status : Unsatisfiable
% Rating : 0.67 v8.2.0, 0.81 v8.1.0, 0.63 v7.5.0, 0.82 v7.3.0, 0.77 v7.2.0, 0.75 v7.1.0, 0.64 v7.0.0, 0.69 v6.4.0, 0.71 v6.3.0, 0.70 v6.1.0, 0.73 v6.0.0, 0.57 v5.5.0, 0.62 v5.4.0, 0.78 v5.3.0, 0.80 v5.2.0, 0.62 v5.1.0, 0.67 v5.0.0, 0.70 v4.1.0, 0.67 v4.0.1, 0.88 v4.0.0, 0.71 v3.7.0, 0.43 v3.4.0, 0.33 v3.3.0, 0.44 v3.2.0, 0.56 v3.1.0, 0.60 v2.7.0, 0.75 v2.6.0, 0.67 v2.5.0, 0.75 v2.4.0, 1.00 v2.0.0
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 2 RR)
% Number of literals : 10 ( 10 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 4 sgn)
% SPC : CNF_UNS_RFO_PEQ_NUE
% Comments :
%--------------------------------------------------------------------------
%----Don't include axioms of Type-respecting combinators
%include('Axioms/COL001-0.ax').
%--------------------------------------------------------------------------
%----Replace k function by k combinator
%input_clause(k_definition,axiom,
% [++equal(apply(k(X),Y),X)]).
cnf(k_definition,axiom,
apply(apply(k,X),Y) = X ).
cnf(projection1,axiom,
apply(projection1,pair(X,Y)) = X ).
cnf(projection2,axiom,
apply(projection2,pair(X,Y)) = Y ).
cnf(pairing,axiom,
pair(apply(projection1,X),apply(projection2,X)) = X ).
cnf(pairwise_application,axiom,
apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)) ).
%----Replace k function by k combinator
%input_clause(abstraction,axiom,
% [++equal(apply(apply(apply(abstraction,X),Y),Z),apply(apply(X,k(Z)),
%apply(Y,Z)))]).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)) ).
cnf(extensionality2,axiom,
( X = Y
| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ).
%----Subsitution axioms
%----This is the extra lemma
cnf(diagonal_combinator,axiom,
apply(apply(f,X),Y) = apply(X,X) ).
cnf(prove_self_referential,negated_conjecture,
Y != apply(eq,pair(apply(k,Y),apply(k,projection2))) ).
%--------------------------------------------------------------------------