TPTP Problem File: COL075-2.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : COL075-2 : TPTP v8.2.0. Released v1.2.0.
% Domain : Combinatory Logic
% Problem : Lemma 1 for showing the unsatisfiable variant of TRC
% Version : [Jec95] (equality) axioms : Reduced > Incomplete.
% English : Searching for a diagonal combinator F with the property
% f X Y = X X.
% Refs : [Jec95] Jech (1995), Otter Experiments in a System of Combinat
% Source : [Jec95]
% Names : - [Jec95]
% Status : Unsatisfiable
% Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.21 v7.4.0, 0.26 v7.3.0, 0.21 v7.1.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.18 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.18 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.0.0
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% Number of literals : 3 ( 3 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% 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 ).
%----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)) ).
%----Subsitution axioms
cnf(prove_diagonal_combinator,negated_conjecture,
apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)) ).
%--------------------------------------------------------------------------