TPTP Problem File: ITP006^3.p
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%------------------------------------------------------------------------------
% File : ITP006^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p, bushy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p [Gau19]
% : HL402501^3.p [TPAP]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.25 v7.5.0
% Syntax : Number of formulae : 44 ( 7 unt; 17 typ; 0 def)
% Number of atoms : 91 ( 12 equ; 39 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 266 ( 39 ~; 22 |; 25 &; 103 @)
% ( 39 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 3 con; 0-4 aty)
% Number of variables : 94 ( 0 ^; 74 !; 5 ?; 94 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS,type,
c_2EquantHeuristics_2EGUESS__EXISTS:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27b > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27b > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27b > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__FORALL,type,
c_2EquantHeuristics_2EGUESS__FORALL:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27b > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27b > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27b > $o ) > $o ) ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Ebool_2ETRUTH,axiom,
c_2Ebool_2ET ).
thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET
=> V0t )
<=> V0t )
& ( ( V0t
=> c_2Ebool_2ET )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
=> V0t )
<=> c_2Ebool_2ET )
& ( ( V0t
=> c_2Ebool_2EF )
<=> ( (~) @ V0t ) ) ) ).
thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t: $o] :
( ( (~) @ ( (~) @ V0t ) )
<=> V0t )
& ( ( (~) @ c_2Ebool_2ET )
<=> c_2Ebool_2EF )
& ( ( (~) @ c_2Ebool_2EF )
<=> c_2Ebool_2ET ) ) ).
thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( V0x = V1y )
<=> ( V1y = V0x ) ) ).
thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t: $o] :
( ( ( c_2Ebool_2ET = V0t )
<=> V0t )
& ( ( V0t = c_2Ebool_2ET )
<=> V0t )
& ( ( c_2Ebool_2EF = V0t )
<=> ( (~) @ V0t ) )
& ( ( V0t = c_2Ebool_2EF )
<=> ( (~) @ V0t ) ) ) ).
thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1: $o,V1t2: $o,V2t3: $o] :
( ( V0t1
=> ( V1t2
=> V2t3 ) )
<=> ( ( V0t1
& V1t2 )
=> V2t3 ) ) ).
thf(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x: $o,V1x_27: $o,V2y: $o,V3y_27: $o] :
( ( ( V0x = V1x_27 )
& ( V1x_27
=> ( V2y = V3y_27 ) ) )
=> ( ( V0x
=> V2y )
<=> ( V1x_27
=> V3y_27 ) ) ) ).
thf(thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
! [A_27a: $tType,A_27b: $tType,V0i: A_27a > A_27b,V1P: A_27b > $o] :
( ( ( c_2EquantHeuristics_2EGUESS__EXISTS @ A_27a @ A_27b @ V0i @ V1P )
<=> ! [V2v: A_27b] :
( ( V1P @ V2v )
=> ? [V3fv: A_27a] : ( V1P @ ( V0i @ V3fv ) ) ) )
& ( ( c_2EquantHeuristics_2EGUESS__FORALL @ A_27a @ A_27b @ V0i @ V1P )
<=> ! [V4v: A_27b] :
( ( (~) @ ( V1P @ V4v ) )
=> ? [V5fv: A_27a] : ( (~) @ ( V1P @ ( V0i @ V5fv ) ) ) ) )
& ! [V6i: A_27a > A_27b,V7P: A_27b > $o] :
( ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ A_27a @ A_27b @ V6i @ V7P )
<=> ! [V8fv: A_27a] : ( V7P @ ( V6i @ V8fv ) ) )
& ! [V9i: A_27a > A_27b,V10P: A_27b > $o] :
( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ A_27a @ A_27b @ V9i @ V10P )
<=> ! [V11fv: A_27a] : ( (~) @ ( V10P @ ( V9i @ V11fv ) ) ) )
& ! [V12i: A_27a > A_27b,V13P: A_27b > $o] :
( ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ A_27a @ A_27b @ V12i @ V13P )
<=> ! [V14v: A_27b] :
( ( V13P @ V14v )
=> ? [V15fv: A_27a] :
( V14v
= ( V12i @ V15fv ) ) ) )
& ! [V16i: A_27a > A_27b,V17P: A_27b > $o] :
( ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ A_27a @ A_27b @ V16i @ V17P )
<=> ! [V18v: A_27b] :
( ( (~) @ ( V17P @ V18v ) )
=> ? [V19fv: A_27a] :
( V18v
= ( V16i @ V19fv ) ) ) ) ) ).
thf(thm_2Esat_2ENOT__NOT,axiom,
! [V0t: $o] :
( ( (~) @ ( (~) @ V0t ) )
<=> V0t ) ).
thf(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A: $o] :
( V0A
=> ( ( (~) @ V0A )
=> c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( V1A
| V0B ) )
=> c_2Ebool_2EF )
<=> ( ( V1A
=> c_2Ebool_2EF )
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( ( (~) @ V1A )
| V0B ) )
=> c_2Ebool_2EF )
<=> ( V1A
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EAND__INV2,axiom,
! [V0A: $o] :
( ( ( (~) @ V0A )
=> c_2Ebool_2EF )
=> ( ( V0A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2Edc__eq,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q = V0r ) )
<=> ( ( V2p
| V1q
| V0r )
& ( V2p
| ( (~) @ V0r )
| ( (~) @ V1q ) )
& ( V1q
| ( (~) @ V0r )
| ( (~) @ V2p ) )
& ( V0r
| ( (~) @ V1q )
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__disj,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
| V0r ) )
<=> ( ( V2p
| ( (~) @ V1q ) )
& ( V2p
| ( (~) @ V0r ) )
& ( V1q
| V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__imp,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
=> V0r ) )
<=> ( ( V2p
| V1q )
& ( V2p
| ( (~) @ V0r ) )
& ( ( (~) @ V1q )
| V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__neg,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
<=> ( (~) @ V0q ) )
<=> ( ( V1p
| V0q )
& ( ( (~) @ V0q )
| ( (~) @ V1p ) ) ) ) ).
thf(thm_2Esat_2Epth__ni1,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
=> V0q ) )
=> V1p ) ).
thf(thm_2Esat_2Epth__ni2,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
=> V0q ) )
=> ( (~) @ V0q ) ) ).
thf(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [A_27a: $tType,A_27b: $tType,V0i: A_27b > A_27a,V1P: A_27a > $o,V2Q: A_27a > $o] :
( ! [V3x: A_27a] :
( ( V2Q @ V3x )
=> ( V1P @ V3x ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ A_27b @ A_27a @ V0i @ V1P )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ A_27b @ A_27a @ V0i @ V2Q ) ) ) ).
%------------------------------------------------------------------------------