TPTP Problem File: ITP006+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP006+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory 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+2.p [TPAP]
% Status : Theorem
% Rating : 0.58 v8.1.0, 0.61 v7.5.0
% Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% Number of atoms : 291 ( 10 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 279 ( 40 ~; 22 |; 30 &)
% ( 47 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-2 aty)
% Number of variables : 112 ( 107 !; 5 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001+2.ax').
%------------------------------------------------------------------------------
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET) ).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__GAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS__GAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS__POINT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2Ebool_2E_3F,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ) ).
fof(ax_ex_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_3F(A),Q))
<=> ? [X] :
( mem(X,A)
& p(ap(Q,X)) ) ) ) ) ).
fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF) ).
fof(mem_c_2Ebool_2E_5C_2F,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) ).
fof(ax_or_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ) ).
fof(mem_c_2Ebool_2E_2F_5C,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ).
fof(ax_and_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ) ).
fof(mem_c_2Emin_2E_3D,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ) ).
fof(ax_eq_p,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)) ).
fof(ax_neg_p,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ) ).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ).
fof(ax_imp_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) ).
fof(ax_all_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ) ).
fof(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
fof(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
=> $true )
<=> $true )
& ( ( $false
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> $false )
<=> ~ p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) )
& ( ~ $true
<=> $false )
& ( ~ $false
<=> $true ) ) ).
fof(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ( V0x = V1y
<=> V1y = V0x ) ) ) ) ).
fof(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
<=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
<=> $true )
<=> p(V0t) )
& ( ( $false
<=> p(V0t) )
<=> ~ p(V0t) )
& ( ( p(V0t)
<=> $false )
<=> ~ p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ! [V2t3] :
( mem(V2t3,bool)
=> ( ( p(V0t1)
=> ( p(V1t2)
=> p(V2t3) ) )
<=> ( ( p(V0t1)
& p(V1t2) )
=> p(V2t3) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__CONG,axiom,
! [V0x] :
( mem(V0x,bool)
=> ! [V1x_27] :
( mem(V1x_27,bool)
=> ! [V2y] :
( mem(V2y,bool)
=> ! [V3y_27] :
( mem(V3y_27,bool)
=> ( ( ( p(V0x)
<=> p(V1x_27) )
& ( p(V1x_27)
=> ( p(V2y)
<=> p(V3y_27) ) ) )
=> ( ( p(V0x)
=> p(V2y) )
<=> ( p(V1x_27)
=> p(V3y_27) ) ) ) ) ) ) ) ).
fof(conj_thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0i] :
( mem(V0i,arr(A_27a,A_27b))
=> ! [V1P] :
( mem(V1P,arr(A_27b,bool))
=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P))
<=> ! [V2v] :
( mem(V2v,A_27b)
=> ( p(ap(V1P,V2v))
=> ? [V3fv] :
( mem(V3fv,A_27a)
& p(ap(V1P,ap(V0i,V3fv))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))
<=> ! [V4v] :
( mem(V4v,A_27b)
=> ( ~ p(ap(V1P,V4v))
=> ? [V5fv] :
( mem(V5fv,A_27a)
& ~ p(ap(V1P,ap(V0i,V5fv))) ) ) ) )
& ! [V6i] :
( mem(V6i,arr(A_27a,A_27b))
=> ! [V7P] :
( mem(V7P,arr(A_27b,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V6i),V7P))
<=> ! [V8fv] :
( mem(V8fv,A_27a)
=> p(ap(V7P,ap(V6i,V8fv))) ) ) ) )
& ! [V9i] :
( mem(V9i,arr(A_27a,A_27b))
=> ! [V10P] :
( mem(V10P,arr(A_27b,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V9i),V10P))
<=> ! [V11fv] :
( mem(V11fv,A_27a)
=> ~ p(ap(V10P,ap(V9i,V11fv))) ) ) ) )
& ! [V12i] :
( mem(V12i,arr(A_27a,A_27b))
=> ! [V13P] :
( mem(V13P,arr(A_27b,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V12i),V13P))
<=> ! [V14v] :
( mem(V14v,A_27b)
=> ( p(ap(V13P,V14v))
=> ? [V15fv] :
( mem(V15fv,A_27a)
& V14v = ap(V12i,V15fv) ) ) ) ) ) )
& ! [V16i] :
( mem(V16i,arr(A_27a,A_27b))
=> ! [V17P] :
( mem(V17P,arr(A_27b,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V16i),V17P))
<=> ! [V18v] :
( mem(V18v,A_27b)
=> ( ~ p(ap(V17P,V18v))
=> ? [V19fv] :
( mem(V19fv,A_27a)
& V18v = ap(V16i,V19fv) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) ) ).
fof(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( p(V0A)
=> ( ~ p(V0A)
=> $false ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( ~ p(V0A)
| p(V1B) )
=> $false )
<=> ( p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ) ).
fof(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ) ).
fof(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q)
| p(V2r) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V1q)
| ~ p(V2r)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__disj,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
| p(V2r) ) )
<=> ( ( p(V0p)
| ~ p(V1q) )
& ( p(V0p)
| ~ p(V2r) )
& ( p(V1q)
| p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__imp,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q) )
& ( p(V0p)
| ~ p(V2r) )
& ( ~ p(V1q)
| p(V2r)
| ~ p(V0p) ) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( p(V0p)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ).
fof(conj_thm_2Esat_2Epth__ni1,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ~ ( p(V0p)
=> p(V1q) )
=> p(V0p) ) ) ) ).
fof(conj_thm_2Esat_2Epth__ni2,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ~ ( p(V0p)
=> p(V1q) )
=> ~ p(V1q) ) ) ) ).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0i] :
( mem(V0i,arr(A_27b,A_27a))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2Q] :
( mem(V2Q,arr(A_27a,bool))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V2Q,V3x))
=> p(ap(V1P,V3x)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V1P))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V2Q)) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------