TPTP Problem File: ITP007+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP007+2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW.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_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW.p [Gau19]
% : HL403001+2.p [TPAP]
% Status : Theorem
% Rating : 1.00 v8.1.0, 0.97 v7.5.0
% Syntax : Number of formulae : 86 ( 11 unt; 0 def)
% Number of atoms : 501 ( 37 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 468 ( 53 ~; 45 |; 57 &)
% ( 79 <=>; 234 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 8 con; 0-6 aty)
% Number of variables : 199 ( 194 !; 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_2Emin_2E_40,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)) ) ).
fof(ne_ty_2Eoption_2Eoption,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Eoption_2Eoption(A0)) ) ).
fof(mem_c_2Eoption_2ESOME,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))) ) ).
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_2Ebool_2ECOND,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ) ).
fof(mem_c_2Eoption_2EOPTION__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)))) ) ) ).
fof(mem_c_2EpatternMatches_2EPMATCH__ROW,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2EpatternMatches_2EPMATCH__ROW(A_27a,A_27b,A_27c),arr(arr(A_27b,A_27c),arr(arr(A_27b,bool),arr(arr(A_27b,A_27a),arr(A_27c,ty_2Eoption_2Eoption(A_27a)))))) ) ) ) ).
fof(mem_c_2Eoption_2ENONE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)) ) ).
fof(mem_c_2EpatternMatches_2EPMATCH__ROW__COND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2EpatternMatches_2EPMATCH__ROW__COND(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,arr(A_27a,bool))))) ) ) ).
fof(mem_c_2Eoption_2Esome,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2Esome(A_27a),arr(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a))) ) ).
fof(mem_c_2Eoption_2Eoption__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Eoption_2Eoption__CASE(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),arr(A_27b,arr(arr(A_27a,A_27b),A_27b)))) ) ) ).
fof(mem_c_2EpatternMatches_2EPMATCH__FLATTEN__FUN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN(A_27a,A_27b,A_27c),arr(arr(A_27b,A_27c),arr(arr(A_27b,bool),arr(arr(A_27b,arr(A_27b,ty_2Eoption_2Eoption(A_27a))),arr(A_27c,ty_2Eoption_2Eoption(A_27a)))))) ) ) ) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF) ).
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_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_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,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_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(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( p(V0t)
<=> $true )
| ( p(V0t)
<=> $false ) ) ) ).
fof(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
fof(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ( ( p(V0t1)
=> p(V1t2) )
=> ( ( p(V1t2)
=> p(V0t1) )
=> ( p(V0t1)
<=> p(V1t2) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EFALSITY,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( $false
=> p(V0t) ) ) ).
fof(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( p(V0t)
| ~ p(V0t) ) ) ).
fof(conj_thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> p(V0t) )
<=> p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__F,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( p(V0t)
=> $false )
=> ~ p(V0t) ) ) ).
fof(conj_thm_2Ebool_2EF__IMP,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ~ p(V0t)
=> ( p(V0t)
=> $false ) ) ) ).
fof(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
& p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
& $true )
<=> p(V0t) )
& ( ( $false
& p(V0t) )
<=> $false )
& ( ( p(V0t)
& $false )
<=> $false )
& ( ( p(V0t)
& p(V0t) )
<=> p(V0t) ) ) ) ).
fof(conj_thm_2Ebool_2EOR__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
| p(V0t) )
<=> $true )
& ( ( p(V0t)
| $true )
<=> $true )
& ( ( $false
| p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
| $false )
<=> p(V0t) )
& ( ( p(V0t)
| p(V0t) )
<=> p(V0t) ) ) ) ).
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_2EREFL__CLAUSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $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_2EFUN__EQ__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1g] :
( mem(V1g,arr(A_27a,A_27b))
=> ( V0f = V1g
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ap(V0f,V2x) = ap(V1g,V2x) ) ) ) ) ) ) ).
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_2ESELECT__ELIM__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ( ( ? [V2x] :
( mem(V2x,A_27a)
& p(ap(V0P,V2x)) )
& ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V0P,V3x))
=> p(ap(V1Q,V3x)) ) ) )
=> p(ap(V1Q,ap(c_2Emin_2E_40(A_27a),V0P))) ) ) ) ) ).
fof(conj_thm_2Ebool_2ENOT__FORALL__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ( ~ ! [V1x] :
( mem(V1x,A_27a)
=> p(ap(V0P,V1x)) )
<=> ? [V2x] :
( mem(V2x,A_27a)
& ~ p(ap(V0P,V2x)) ) ) ) ) ).
fof(conj_thm_2Ebool_2ENOT__EXISTS__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ( ~ ? [V1x] :
( mem(V1x,A_27a)
& p(ap(V0P,V1x)) )
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ~ p(ap(V0P,V2x)) ) ) ) ) ).
fof(conj_thm_2Ebool_2EDISJ__ASSOC,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ! [V2C] :
( mem(V2C,bool)
=> ( ( p(V0A)
| p(V1B)
| p(V2C) )
<=> ( p(V0A)
| p(V1B)
| p(V2C) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EDISJ__SYM,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( p(V0A)
| p(V1B) )
<=> ( p(V1B)
| p(V0A) ) ) ) ) ).
fof(conj_thm_2Ebool_2EDISJ__COMM,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( p(V0A)
| p(V1B) )
<=> ( p(V1B)
| p(V0A) ) ) ) ) ).
fof(conj_thm_2Ebool_2EDE__MORGAN__THM,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
& p(V1B) )
<=> ( ~ p(V0A)
| ~ p(V1B) ) )
& ( ~ ( p(V0A)
| p(V1B) )
<=> ( ~ p(V0A)
& ~ p(V1B) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EIMP__DISJ__THM,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( p(V0A)
=> p(V1B) )
<=> ( ~ p(V0A)
| p(V1B) ) ) ) ) ).
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_2Ebool_2EAND__CONG,axiom,
! [V0P] :
( mem(V0P,bool)
=> ! [V1P_27] :
( mem(V1P_27,bool)
=> ! [V2Q] :
( mem(V2Q,bool)
=> ! [V3Q_27] :
( mem(V3Q_27,bool)
=> ( ( ( p(V2Q)
=> ( p(V0P)
<=> p(V1P_27) ) )
& ( p(V1P_27)
=> ( p(V2Q)
<=> p(V3Q_27) ) ) )
=> ( ( p(V0P)
& p(V2Q) )
<=> ( p(V1P_27)
& p(V3Q_27) ) ) ) ) ) ) ) ).
fof(conj_thm_2Ebool_2EUNWIND__FORALL__THM2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,bool))
=> ! [V1v] :
( mem(V1v,A_27a)
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ( V2x = V1v
=> p(ap(V0f,V2x)) ) )
<=> p(ap(V0f,V1v)) ) ) ) ) ).
fof(conj_thm_2Eoption_2Eoption__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0opt] :
( mem(V0opt,ty_2Eoption_2Eoption(A_27a))
=> ( V0opt = c_2Eoption_2ENONE(A_27a)
| ? [V1x] :
( mem(V1x,A_27a)
& V0opt = ap(c_2Eoption_2ESOME(A_27a),V1x) ) ) ) ) ).
fof(ax_thm_2Eoption_2Eoption__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0v] :
( mem(V0v,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V0v),V1f) = V0v ) )
& ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3v] :
( mem(V3v,A_27b)
=> ! [V4f] :
( mem(V4f,arr(A_27a,A_27b))
=> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V2x)),V3v),V4f) = ap(V4f,V2x) ) ) ) ) ) ) ).
fof(conj_thm_2Eoption_2ESOME__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ( ap(c_2Eoption_2ESOME(A_27a),V0x) = ap(c_2Eoption_2ESOME(A_27a),V1y)
<=> V0x = V1y ) ) ) ) ).
fof(ax_thm_2Eoption_2EOPTION__MAP__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(c_2Eoption_2ESOME(A_27b),ap(V0f,V1x)) ) )
& ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27b) ) ) ) ) ).
fof(conj_thm_2Eoption_2EIF__EQUALS__OPTION,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,bool)
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27a)
<=> ~ p(V0P) )
& ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x)) = c_2Eoption_2ENONE(A_27a)
<=> p(V0P) )
& ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)) = ap(c_2Eoption_2ESOME(A_27a),V2y)
<=> ( p(V0P)
& V1x = V2y ) )
& ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(c_2Eoption_2ESOME(A_27a),V2y)
<=> ( ~ p(V0P)
& V1x = V2y ) ) ) ) ) ) ) ).
fof(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1x] :
( mem(V1x,ty_2Eoption_2Eoption(A_27b))
=> ( ( ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x) = c_2Eoption_2ENONE(A_27a)
<=> V1x = c_2Eoption_2ENONE(A_27b) )
& ( c_2Eoption_2ENONE(A_27a) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x)
<=> V1x = c_2Eoption_2ENONE(A_27b) ) ) ) ) ) ) ).
fof(ax_thm_2Eoption_2Esome__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ap(c_2Eoption_2Esome(A_27a),V0P) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_3F(A_27a),f49(A_27a,V0P))),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Emin_2E_40(A_27a),f108(A_27a,V0P)))),c_2Eoption_2ENONE(A_27a)) ) ) ).
fof(ax_thm_2EpatternMatches_2EPMATCH__ROW__COND__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0pat] :
( mem(V0pat,arr(A_27a,A_27b))
=> ! [V1guard] :
( mem(V1guard,arr(A_27a,bool))
=> ! [V2inp] :
( mem(V2inp,A_27b)
=> ! [V3v] :
( mem(V3v,A_27a)
=> ( p(ap(ap(ap(ap(c_2EpatternMatches_2EPMATCH__ROW__COND(A_27a,A_27b),V0pat),V1guard),V2inp),V3v))
<=> ( ap(V0pat,V3v) = V2inp
& p(ap(V1guard,V3v)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2EpatternMatches_2EPMATCH__ROW__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0pat] :
( mem(V0pat,arr(A_27b,A_27c))
=> ! [V1guard] :
( mem(V1guard,arr(A_27b,bool))
=> ! [V2rhs] :
( mem(V2rhs,arr(A_27b,A_27a))
=> ! [V3i] :
( mem(V3i,A_27c)
=> ap(ap(ap(ap(c_2EpatternMatches_2EPMATCH__ROW(A_27a,A_27b,A_27c),V0pat),V1guard),V2rhs),V3i) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V2rhs),ap(c_2Eoption_2Esome(A_27b),f822(A_27c,A_27b,V3i,V0pat,V1guard))) ) ) ) ) ) ) ) ).
fof(ax_thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0p] :
( mem(V0p,arr(A_27b,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27b,bool))
=> ! [V2row] :
( mem(V2row,arr(A_27b,arr(A_27b,ty_2Eoption_2Eoption(A_27a))))
=> ! [V3v] :
( mem(V3v,A_27c)
=> ap(ap(ap(ap(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN(A_27a,A_27b,A_27c),V0p),V1g),V2row),V3v) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27b,ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2Esome(A_27b),f850(A_27c,A_27b,V3v,V0p,V1g))),c_2Eoption_2ENONE(A_27a)),f851(A_27a,A_27b,V2row)) ) ) ) ) ) ) ) ).
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__conj,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(V1q)
| ~ p(V0p) )
& ( p(V2r)
| ~ 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_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0p] :
( mem(V0p,arr(A_27a,A_27b))
=> ( ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] :
( mem(V2x2,A_27a)
=> ( ap(V0p,V1x1) = ap(V0p,V2x2)
=> V1x1 = V2x2 ) ) )
=> ! [V3g] :
( mem(V3g,arr(A_27a,bool))
=> ! [V4p_27] :
( mem(V4p_27,arr(A_27c,A_27a))
=> ! [V5g_27] :
( mem(V5g_27,arr(A_27a,arr(A_27c,bool)))
=> ! [V6r_27] :
( mem(V6r_27,arr(A_27a,arr(A_27c,A_27d)))
=> ap(ap(ap(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN(A_27d,A_27a,A_27b),V0p),V3g),f859(A_27d,A_27c,A_27a,V4p_27,V5g_27,V6r_27)) = ap(ap(ap(c_2EpatternMatches_2EPMATCH__ROW(A_27d,A_27c,A_27b),f860(A_27a,A_27b,A_27c,V4p_27,V0p)),f861(A_27a,A_27c,V3g,V5g_27,V4p_27)),f862(A_27d,A_27a,A_27c,V6r_27,V4p_27)) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------