## TPTP Problem File: SYO525+1.024.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO525+1.024 : TPTP v8.1.0. Released v5.2.0.
% Domain   : Syntactic
% Problem  : Linear can be exponential
% Version  : Especial.
% English  :

% Refs     : [Bez10] Bezem (2010), Email to Geoff Sutcliffe
% Source   : [Bez10]
% Names    :

% Status   : Theorem
% Rating   : 0.00 v7.5.0, 0.33 v7.3.0, 1.00 v5.2.0
% Syntax   : Number of formulae    :   30 (   2 unt;   0 def)
%            Number of atoms       :   58 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   28 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  14 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   1 prp; 0-27 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :  354 ( 354   !;   0   ?)
% SPC      : FOF_THM_EPR_NEQ

%------------------------------------------------------------------------------
fof(start,axiom,
bin_count(n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ).

fof(qed24,axiom,
! [A,B,C] :
( bin_count(A,B,C,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> goal ) ).

fof(p27,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,n0)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,n1) ) ).

fof(p26,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,n0,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,n1,n0) ) ).

fof(p25,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,n0,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,n1,n0,n0) ) ).

fof(p24,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,n0,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,n1,n0,n0,n0) ) ).

fof(p23,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,n0,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,n1,n0,n0,n0,n0) ) ).

fof(p22,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,n0,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,n1,n0,n0,n0,n0,n0) ) ).

fof(p21,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,n0,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,n1,n0,n0,n0,n0,n0,n0) ) ).

fof(p20,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,n0,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,n1,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p19,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,n0,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,n1,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p18,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p17,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p16,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p15,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,N,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p14,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,M,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p13,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,L,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,L,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p12,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( bin_count(A,B,C,D,E,F,G,H,I,J,K,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,K,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p11,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( bin_count(A,B,C,D,E,F,G,H,I,J,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,J,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p10,axiom,
! [A,B,C,D,E,F,G,H,I] :
( bin_count(A,B,C,D,E,F,G,H,I,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,I,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p9,axiom,
! [A,B,C,D,E,F,G,H] :
( bin_count(A,B,C,D,E,F,G,H,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,H,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p8,axiom,
! [A,B,C,D,E,F,G] :
( bin_count(A,B,C,D,E,F,G,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,G,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p7,axiom,
! [A,B,C,D,E,F] :
( bin_count(A,B,C,D,E,F,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,F,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p6,axiom,
! [A,B,C,D,E] :
( bin_count(A,B,C,D,E,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,E,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p5,axiom,
! [A,B,C,D] :
( bin_count(A,B,C,D,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,D,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p4,axiom,
! [A,B,C] :
( bin_count(A,B,C,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,C,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p3,axiom,
! [A,B] :
( bin_count(A,B,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,B,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p2,axiom,
! [A] :
( bin_count(A,n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(A,n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(p1,axiom,
( bin_count(n0,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1,n1)
=> bin_count(n1,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0,n0) ) ).

fof(goal_to_be_proved,conjecture,
goal ).

%------------------------------------------------------------------------------
```