TPTP Problem File: LCL415-1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : LCL415-1 : TPTP v9.0.0. Released v2.5.0.
% Domain : Logic Calculi (Intuitionistic implication)
% Problem : Non-axiom for intuitionistic implication
% Version : [EF+02] axioms.
% English : Show that the candidate formula is not a single axiom for
% intuitionistic implication by finding a model in which the
% required property fails.
% Refs : [EF+02] Ernst et al. (2002), More First-order Test Problems in
% Source : [EF+02]
% Names : intuit-imp [EF+02]
% Status : Satisfiable
% Rating : 0.00 v9.0.0, 0.33 v8.2.0, 0.67 v8.1.0, 0.33 v7.5.0, 0.67 v6.2.0, 0.60 v6.1.0, 0.33 v5.5.0, 0.50 v5.4.0, 0.78 v5.3.0, 0.71 v5.0.0, 0.88 v4.1.0, 0.86 v4.0.1, 0.71 v4.0.0, 0.75 v3.5.0, 0.86 v3.4.0, 0.83 v3.3.0, 0.67 v3.2.0, 0.80 v3.1.0, 0.43 v2.7.0, 0.40 v2.6.0, 0.50 v2.5.0
% Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% Number of literals : 5 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn)
% SPC : CNF_SAT_RFO_NEQ
% Comments :
%--------------------------------------------------------------------------
%----Condensed detachment
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ) ).
%----Candidate
cnf(candidate,axiom,
is_a_theorem(implies(implies(A,B),implies(implies(B,implies(implies(C,A),D)),implies(A,D)))) ).
%----Required property
cnf(prove_required_property,negated_conjecture,
~ is_a_theorem(implies(a,implies(b,a))) ).
%--------------------------------------------------------------------------