TPTP Problem File: PHI008^4.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : PHI008^4 : TPTP v9.0.0. Released v6.4.0.
% Domain : Philosophy
% Problem : Modal Collapse of Goedel's ontological argument in Scott's variant
% Version : [Ben16] axioms : Biased.
% English :
% Refs : [Ben16] Benzmueller (2016), Email to Geoff Sutcliffe
% Source : [Ben16]
% Names : Sledgehammer_MC_S5U_direct_satallax.p [Ben16]
% Status : Theorem
% Rating : 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0
% Syntax : Number of formulae : 18 ( 4 unt; 6 typ; 0 def)
% Number of atoms : 24 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 72 ( 5 ~; 1 |; 2 &; 54 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 2-3 aty)
% Number of variables : 40 ( 11 ^; 27 !; 2 ?; 40 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This problem file has been generated by Sledgehammer (satallax
% translation) in default setting.
%------------------------------------------------------------------------------
%----Could-be-implicit typings (2)
thf(ty_n_t__QML____S5U__O__092__060mu__062,type,
qML_mu: $tType ).
thf(ty_n_t__QML____S5U__Oi,type,
qML_i: $tType ).
%----Explicit typings (4)
thf(sy_c_Scott__S5U_OG,type,
scott_G: qML_mu > qML_i > $o ).
thf(sy_c_Scott__S5U_ONE_001t__QML____S5U__O__092__060mu__062,type,
scott_NE_QML_mu: qML_mu > qML_i > $o ).
thf(sy_c_Scott__S5U_OP,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(sy_c_Scott__S5U_Oess_001t__QML____S5U__O__092__060mu__062,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
%----Relevant facts (11)
thf(fact_0_G__def,axiom,
( scott_G
= ( ^ [X: qML_mu,W: qML_i] :
! [Y: qML_mu > qML_i > $o] :
( ( scott_P @ Y @ W )
=> ( Y @ X @ W ) ) ) ) ).
% G_def
thf(fact_1_A4,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ W2 )
=> ! [X_1: qML_i] : ( scott_P @ X2 @ X_1 ) ) ).
% A4
thf(fact_2_T3,axiom,
! [W2: qML_i,V: qML_i] :
? [X3: qML_mu] : ( scott_G @ X3 @ V ) ).
% T3
thf(fact_3_A3,axiom,
! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).
% A3
thf(fact_4_ess__def,axiom,
( scott_ess_QML_mu
= ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
( ( Phi @ X @ W )
& ! [Y: qML_mu > qML_i > $o] :
( ( Y @ X @ W )
=> ! [V2: qML_i,Z: qML_mu] :
( ( Phi @ Z @ V2 )
=> ( Y @ Z @ V2 ) ) ) ) ) ) ).
% ess_def
thf(fact_5_A2,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
( ( ( scott_P @ X2 @ W2 )
& ! [V3: qML_i,Xb: qML_mu] :
( ( X2 @ Xb @ V3 )
=> ( Xa @ Xb @ V3 ) ) )
=> ( scott_P @ Xa @ W2 ) ) ).
% A2
thf(fact_6_A1b,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X2 @ W2 )
=> ( scott_P
@ ^ [Y: qML_mu,Z: qML_i] :
~ ( X2 @ Y @ Z )
@ W2 ) ) ).
% A1b
thf(fact_7_A5,axiom,
! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).
% A5
thf(fact_8_A1a,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Y: qML_mu,Z: qML_i] :
~ ( X2 @ Y @ Z )
@ W2 )
=> ~ ( scott_P @ X2 @ W2 ) ) ).
% A1a
thf(fact_9_T2,axiom,
! [W2: qML_i,X2: qML_mu] :
( ( scott_G @ X2 @ W2 )
=> ( scott_ess_QML_mu @ scott_G @ X2 @ W2 ) ) ).
% T2
thf(fact_10_NE__def,axiom,
( scott_NE_QML_mu
= ( ^ [X: qML_mu,W: qML_i] :
! [Y: qML_mu > qML_i > $o] :
( ( scott_ess_QML_mu @ Y @ X @ W )
=> ! [V2: qML_i] :
? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).
% NE_def
%----Conjectures (1)
thf(conj_0,conjecture,
! [W3: qML_i,X3: qML_i > $o] :
( ~ ( X3 @ W3 )
| ! [V3: qML_i] : ( X3 @ V3 ) ) ).
%------------------------------------------------------------------------------