TPTP Problem File: LCL881^1.p
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- Solve Problem
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% File : LCL881^1 : TPTP v8.2.0. Released v5.2.0.
% Domain : Logic Calculi (Doxastic multimodal logic)
% Problem : Axiom 5s is dependent
% Version : [Ben11] axioms.
% English :
% Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
% : [Ben11] Benzmueller (2011), Combining and Automating Classical
% Source : [Ben11]
% Names : Ex_7_6 [Ben11]
% Status : Theorem
% Rating : 0.90 v8.2.0, 0.92 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0
% Syntax : Number of formulae : 85 ( 31 unt; 35 typ; 31 def)
% Number of atoms : 347 ( 36 equ; 0 cnn)
% Maximal formula atoms : 99 ( 6 avg)
% Number of connectives : 413 ( 4 ~; 4 |; 16 &; 381 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 201 ( 201 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 7 con; 0-3 aty)
% Number of variables : 111 ( 76 ^; 29 !; 6 ?; 111 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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%----Include embedding of quantified multimodal logic in simple type theory
include('Axioms/LCL013^0.ax').
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thf(r1,type,
r1: $i > $i > $o ).
thf(r2,type,
r2: $i > $i > $o ).
thf(r3,type,
r3: $i > $i > $o ).
thf(axiom_D_for_r1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mdia @ r1 @ Phi ) ) ) ) ).
thf(axiom_D_for_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mdia @ r2 @ Phi ) ) ) ) ).
thf(axiom_D_for_r3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mdia @ r3 @ 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_r3_r2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r2 @ 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_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_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_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(conj,conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ) ).
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