TPTP Problem File: SYN036^7.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SYN036^7 : TPTP v8.2.0. Bugfixed v7.1.0.
% Domain : Syntactic
% Problem : Andrews Challenge Problem
% Version : [Ben12] axioms.
% English :
% Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% : [And86] Andrews (1986), An Introduction to Mathematical Logic
% : [DeC79] DeChampeaux (1979), Sub-problem Finder and Instance Ch
% : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% : [Pel88] Pelletier (1988), Errata
% : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source : [Ben12]
% Names : s4-cumul-GSY036+1 [Ben12]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 75 ( 33 unt; 38 typ; 32 def)
% Number of atoms : 412 ( 36 equ; 0 cnn)
% Maximal formula atoms : 306 ( 11 avg)
% Number of connectives : 515 ( 5 ~; 5 |; 9 &; 486 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 7 con; 0-3 aty)
% Number of variables : 138 ( 97 ^; 34 !; 7 ?; 138 :)
% SPC : TH0_THM_EQU_NAR
% Comments : Goedel translation of SYN036+1
% Bugfixes : Reordered includes to get signature of mnot before use
%------------------------------------------------------------------------------
%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
%------------------------------------------------------------------------------
thf(big_q_type,type,
big_q: mu > $i > $o ).
thf(big_p_type,type,
big_p: mu > $i > $o ).
thf(pel34,conjecture,
( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) )
@ ( mexists_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) )
@ ( mexists_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
@ ( mexists_ind
@ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) )
@ ( mexists_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
@ ( mexists_ind
@ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) )
@ ( mexists_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------