TPTP Problem File: AGT030^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : AGT030^1 : TPTP v8.2.0. Released v5.2.0.
% Domain : Agents
% Problem : Five different degrees of belief - agent 1
% Version : [Ben11] axioms.
% English :
% Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
% : [Ben11] Benzmueller (2011), Combining and Automating Classical
% Source : [Ben11]
% Names : Ex_11_3 [Ben11]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 .0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0
% Syntax : Number of formulae : 145 ( 31 unt; 47 typ; 31 def)
% Number of atoms : 667 ( 36 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 760 ( 4 ~; 4 |; 8 &; 736 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 235 ( 235 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 54 usr; 13 con; 0-3 aty)
% Number of variables : 147 ( 112 ^; 29 !; 6 ?; 147 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
%------------------------------------------------------------------------------
%----Include embedding of quantified multimodal logic in simple type theory
include('Axioms/LCL013^0.ax').
%------------------------------------------------------------------------------
thf(r1,type,
r1: $i > $i > $o ).
thf(r2,type,
r2: $i > $i > $o ).
thf(r3,type,
r3: $i > $i > $o ).
thf(r4,type,
r4: $i > $i > $o ).
thf(r5,type,
r5: $i > $i > $o ).
thf(john,type,
john: mu ).
thf(tom,type,
tom: mu ).
thf(peter,type,
peter: mu ).
thf(mike,type,
mike: mu ).
thf(good_in_maths,type,
good_in_maths: mu > $i > $o ).
thf(maths_teacher,type,
maths_teacher: mu > $i > $o ).
thf(mathematician,type,
mathematician: mu > $i > $o ).
thf(maths_student,type,
maths_student: mu > $i > $o ).
thf(good_in_physics,type,
good_in_physics: mu > $i > $o ).
thf(physics_student,type,
physics_student: mu > $i > $o ).
thf(axiom_r1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( maths_teacher @ X ) @ ( mbox @ r4 @ ( good_in_maths @ X ) ) ) ) ) ).
thf(axiom_r2_1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r1 @ ( mathematician @ X ) ) @ ( mbox @ r1 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r2_2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r2 @ ( mathematician @ X ) ) @ ( mbox @ r2 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r2_3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r3 @ ( mathematician @ X ) ) @ ( mbox @ r3 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r2_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r4 @ ( mathematician @ X ) ) @ ( mbox @ r4 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r2_5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r5 @ ( mathematician @ X ) ) @ ( mbox @ r5 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r3_1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ X ) @ ( mdia @ r1 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r3_2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ X ) @ ( mdia @ r2 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r3_3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ X ) @ ( mdia @ r3 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r3_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ X ) @ ( mdia @ r4 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r3_5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ X ) @ ( mdia @ r5 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_r4_1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ X ) @ ( mdia @ r1 @ ( good_in_physics @ X ) ) ) ) ) ) ).
thf(axiom_r4_2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ X ) @ ( mdia @ r2 @ ( good_in_physics @ X ) ) ) ) ) ) ).
thf(axiom_r4_3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ X ) @ ( mdia @ r3 @ ( good_in_physics @ X ) ) ) ) ) ) ).
thf(axiom_r4_4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ X ) @ ( mdia @ r4 @ ( good_in_physics @ X ) ) ) ) ) ) ).
thf(axiom_r4_5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ X ) @ ( mdia @ r5 @ ( good_in_physics @ X ) ) ) ) ) ) ).
thf(axiom_r5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ r2 @ ( mimplies @ ( good_in_physics @ X ) @ ( mdia @ r2 @ ( good_in_maths @ X ) ) ) ) ) ) ).
thf(axiom_a6,axiom,
mvalid @ ( maths_teacher @ john ) ).
thf(axiom_a7,axiom,
mvalid @ ( mbox @ r2 @ ( mathematician @ tom ) ) ).
thf(axiom_a8,axiom,
mvalid @ ( mbox @ r5 @ ( maths_student @ peter ) ) ).
thf(axiom_a9,axiom,
mvalid @ ( mbox @ r5 @ ( physics_student @ mike ) ) ).
thf(axiom_D_for_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mnot @ ( mbox @ r1 @ ( mnot @ Phi ) ) ) ) ) ) ).
thf(axiom_D_for_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mnot @ ( mbox @ r2 @ ( mnot @ Phi ) ) ) ) ) ) ).
thf(axiom_D_for_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mnot @ ( mbox @ r3 @ ( mnot @ Phi ) ) ) ) ) ) ).
thf(axiom_D_for_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mnot @ ( mbox @ r4 @ ( mnot @ Phi ) ) ) ) ) ) ).
thf(axiom_D_for_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mnot @ ( mbox @ r5 @ ( mnot @ Phi ) ) ) ) ) ) ).
thf(axiom_I_for_r2_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ) ).
thf(axiom_I_for_r3_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ) ).
thf(axiom_I_for_r4_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ) ).
thf(axiom_I_for_r45r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ) ).
thf(axiom_I_for_r3_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r2 @ Phi ) ) ) ) ).
thf(axiom_I_for_r4_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r2 @ Phi ) ) ) ) ).
thf(axiom_I_for_r5_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r2 @ Phi ) ) ) ) ).
thf(axiom_I_for_r4_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r3 @ Phi ) ) ) ) ).
thf(axiom_I_for_r5_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r3 @ Phi ) ) ) ) ).
thf(axiom_I_for_r5_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r4 @ Phi ) ) ) ) ).
thf(axiom_4s_for_r1_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r1_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r1_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r1_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r4 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r1_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r5 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r2_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r2_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r2_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r2_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r4 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r2_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r5 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r3_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r3_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r3_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r3_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r4 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r3_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r5 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r4_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r4 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r4_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r4 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r4_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r4 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r4_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r4 @ ( mbox @ r4 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r4_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r4 @ Phi ) @ ( mbox @ r5 @ ( mbox @ r4 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r5_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r5 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r5_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r5 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r5_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r5 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r5_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r4 @ ( mbox @ r5 @ Phi ) ) ) ) ) ).
thf(axiom_4s_for_r5_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r5 @ Phi ) @ ( mbox @ r5 @ ( mbox @ r5 @ Phi ) ) ) ) ) ).
thf(axiom_5_for_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) ) ).
thf(axiom_5_for_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) ) ).
thf(axiom_5_for_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ).
thf(axiom_5_for_r4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r4 @ Phi ) ) @ ( mbox @ r4 @ ( mnot @ ( mbox @ r4 @ Phi ) ) ) ) ) ) ).
thf(axiom_5_for_r5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r5 @ Phi ) ) @ ( mbox @ r5 @ ( mnot @ ( mbox @ r5 @ Phi ) ) ) ) ) ) ).
thf(conj,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X: mu] : ( mdia @ r1 @ ( good_in_maths @ X ) ) ) ) ).
%------------------------------------------------------------------------------