TPTP Problem File: SYN741^7.p

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%------------------------------------------------------------------------------
% File     : SYN741^7 : TPTP v7.4.0. Released v5.5.0.
% Domain   : Syntactic
% Problem  : PSAT - CNF - K=4 C=30 V=4 D=2.3
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Sch99] Schmidt (1999), Decidability by Resolution for Proposit
%          : [HS00a] Hustadt & Schmidt (2000), MSPASS: Modal Reasoning by Tr
%          : [HS00b] Hustadt & Schmidt (2000), Issues of Decidability for De
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-SYM308+1 [Ben12]

% Status   : Theorem
% Rating   : 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0
% Syntax   : Number of formulae    :  108 (   0 unit;  40 type;  32 defn)
%            Number of atoms       :  686 (  36 equality; 143 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  551 (   5   ~;   5   |;   9   &; 522   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  184 ( 184   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  40   :;   0   =)
%            Number of variables   :   90 (   2 sgn;  34   !;   7   ?;  49   ^)
%                                         (  90   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments :
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%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
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thf(v1_type,type,(
    v1: $i > $o )).

thf(v3_type,type,(
    v3: $i > $o )).

thf(v2_type,type,(
    v2: $i > $o )).

thf(v4_type,type,(
    v4: $i > $o )).

thf(persat1,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )).

thf(persat2,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )).

thf(persat3,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) ) ) ) )).

thf(persat4,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat5,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )).

thf(persat6,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )).

thf(persat7,axiom,
    ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )).

thf(persat8,axiom,
    ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat9,axiom,
    ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat10,axiom,
    ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )).

thf(persat11,axiom,
    ( mvalid @ ( mor @ v2 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat12,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) ) ) ) )).

thf(persat13,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) ) ) ) )).

thf(persat14,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) ) ) ) )).

thf(persat15,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )).

thf(persat16,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )).

thf(persat17,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat18,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )).

thf(persat19,axiom,
    ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )).

thf(persat20,axiom,
    ( mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) ) ) ) )).

thf(persat21,axiom,
    ( mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )).

thf(persat22,axiom,
    ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )).

thf(persat23,axiom,
    ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) ) ) ) )).

thf(persat24,axiom,
    ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )).

thf(persat25,axiom,
    ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )).

thf(persat26,axiom,
    ( mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat27,axiom,
    ( mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )).

thf(persat28,axiom,
    ( mvalid @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat29,axiom,
    ( mvalid @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )).

thf(persat30,axiom,
    ( mvalid @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )).

thf(deontic1,axiom,
    ( mvalid @ ( mdia_s4 @ mtrue ) )).

thf(result1,conjecture,
    ( mvalid @ mfalse )).

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