TPTP Problem File: SYO065^4.003.p
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% File : SYO065^4.003 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Intuitionistic logic)
% Problem : ILTP Problem SYJ201+1.003
% Version : [Goe33] axioms.
% English :
% Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% Source : [Ben09]
% Names : SYJ201+1.003 [ROK06]
% Status : Theorem
% Rating : 1.00 v4.0.0
% Syntax : Number of formulae : 56 ( 20 unt; 27 typ; 19 def)
% Number of atoms : 273 ( 19 equ; 0 cnn)
% Maximal formula atoms : 27 ( 9 avg)
% Number of connectives : 257 ( 3 ~; 1 |; 2 &; 249 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 102 ( 102 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 31 ^; 7 !; 2 ?; 40 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This is an ILTP problem embedded in TH0
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include('Axioms/LCL010^0.ax').
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thf(p1_type,type,
p1: $i > $o ).
thf(p2_type,type,
p2: $i > $o ).
thf(p3_type,type,
p3: $i > $o ).
thf(p4_type,type,
p4: $i > $o ).
thf(p5_type,type,
p5: $i > $o ).
thf(p6_type,type,
p6: $i > $o ).
thf(p7_type,type,
p7: $i > $o ).
thf(axiom1,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(axiom2,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p2 ) @ ( iatom @ p3 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(axiom3,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p3 ) @ ( iatom @ p4 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(axiom4,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p4 ) @ ( iatom @ p5 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(axiom5,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p5 ) @ ( iatom @ p6 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(axiom6,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(axiom7,axiom,
ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p7 ) @ ( iatom @ p1 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ) ).
thf(con,conjecture,
ivalid @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) ) ) ) ) ) ).
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