TPTP Problem File: SYN741^7.p
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% File : SYN741^7 : TPTP v8.2.0. 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 : ContradictoryAxioms
% Rating : 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 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 ( 33 unt; 40 typ; 32 def)
% Number of atoms : 543 ( 36 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 551 ( 5 ~; 5 |; 9 &; 522 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 8 con; 0-3 aty)
% Number of variables : 90 ( 49 ^; 34 !; 7 ?; 90 :)
% SPC : TH0_CAX_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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