TSTP Solution File: SET027-3 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SET027-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:08:52 EDT 2022
% Result : Unsatisfiable 5.69s 5.97s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(ordered_pairs_are_small1,axiom,
little_set(ordered_pair(X,Y)),
input ).
fof(ordered_pairs_are_small1_0,plain,
! [X,Y] :
( little_set(ordered_pair(X,Y))
| $false ),
inference(orientation,[status(thm)],[ordered_pairs_are_small1]) ).
cnf(apply_to_two_arguments,axiom,
apply_to_two_arguments(Xf,X,Y) = apply(Xf,ordered_pair(X,Y)),
input ).
fof(apply_to_two_arguments_0,plain,
! [X,Xf,Y] :
( apply_to_two_arguments(Xf,X,Y) = apply(Xf,ordered_pair(X,Y))
| $false ),
inference(orientation,[status(thm)],[apply_to_two_arguments]) ).
cnf(restrict,axiom,
restrict(X,Y) = intersection(X,cross_product(Y,universal_set)),
input ).
fof(restrict_0,plain,
! [X,Y] :
( restrict(X,Y) = intersection(X,cross_product(Y,universal_set))
| $false ),
inference(orientation,[status(thm)],[restrict]) ).
cnf(choice1,axiom,
function(f25),
input ).
fof(choice1_0,plain,
( function(f25)
| $false ),
inference(orientation,[status(thm)],[choice1]) ).
cnf(infinity2,axiom,
member(empty_set,infinity),
input ).
fof(infinity2_0,plain,
( member(empty_set,infinity)
| $false ),
inference(orientation,[status(thm)],[infinity2]) ).
cnf(infinity1,axiom,
little_set(infinity),
input ).
fof(infinity1_0,plain,
( little_set(infinity)
| $false ),
inference(orientation,[status(thm)],[infinity1]) ).
cnf(empty_set,axiom,
~ member(Z,empty_set),
input ).
fof(empty_set_0,plain,
! [Z] :
( ~ member(Z,empty_set)
| $false ),
inference(orientation,[status(thm)],[empty_set]) ).
cnf(successor,axiom,
successor(X) = union(X,singleton_set(X)),
input ).
fof(successor_0,plain,
! [X] :
( successor(X) = union(X,singleton_set(X))
| $false ),
inference(orientation,[status(thm)],[successor]) ).
cnf(union,axiom,
union(X,Y) = complement(intersection(complement(X),complement(Y))),
input ).
fof(union_0,plain,
! [X,Y] :
( union(X,Y) = complement(intersection(complement(X),complement(Y)))
| $false ),
inference(orientation,[status(thm)],[union]) ).
cnf(ordered_pair,axiom,
ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
input ).
fof(ordered_pair_0,plain,
! [X,Y] :
( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y))
| $false ),
inference(orientation,[status(thm)],[ordered_pair]) ).
cnf(singleton_set,axiom,
singleton_set(X) = non_ordered_pair(X,X),
input ).
fof(singleton_set_0,plain,
! [X] :
( singleton_set(X) = non_ordered_pair(X,X)
| $false ),
inference(orientation,[status(thm)],[singleton_set]) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X,Y)),
input ).
fof(non_ordered_pair4_0,plain,
! [X,Y] :
( little_set(non_ordered_pair(X,Y))
| $false ),
inference(orientation,[status(thm)],[non_ordered_pair4]) ).
fof(def_lhs_atom1,axiom,
! [Y,X] :
( lhs_atom1(Y,X)
<=> little_set(non_ordered_pair(X,Y)) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [X,Y] :
( lhs_atom1(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[non_ordered_pair4_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [X] :
( lhs_atom2(X)
<=> singleton_set(X) = non_ordered_pair(X,X) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [X] :
( lhs_atom2(X)
| $false ),
inference(fold_definition,[status(thm)],[singleton_set_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [Y,X] :
( lhs_atom3(Y,X)
<=> ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [X,Y] :
( lhs_atom3(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[ordered_pair_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [Y,X] :
( lhs_atom4(Y,X)
<=> union(X,Y) = complement(intersection(complement(X),complement(Y))) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [X,Y] :
( lhs_atom4(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[union_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [X] :
( lhs_atom5(X)
<=> successor(X) = union(X,singleton_set(X)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [X] :
( lhs_atom5(X)
| $false ),
inference(fold_definition,[status(thm)],[successor_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [Z] :
( lhs_atom6(Z)
<=> ~ member(Z,empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [Z] :
( lhs_atom6(Z)
| $false ),
inference(fold_definition,[status(thm)],[empty_set_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> little_set(infinity) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[infinity1_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> member(empty_set,infinity) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[infinity2_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> function(f25) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[choice1_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [Y,X] :
( lhs_atom10(Y,X)
<=> restrict(X,Y) = intersection(X,cross_product(Y,universal_set)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [X,Y] :
( lhs_atom10(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[restrict_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [Y,Xf,X] :
( lhs_atom11(Y,Xf,X)
<=> apply_to_two_arguments(Xf,X,Y) = apply(Xf,ordered_pair(X,Y)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [X,Xf,Y] :
( lhs_atom11(Y,Xf,X)
| $false ),
inference(fold_definition,[status(thm)],[apply_to_two_arguments_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [Y,X] :
( lhs_atom12(Y,X)
<=> little_set(ordered_pair(X,Y)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [X,Y] :
( lhs_atom12(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[ordered_pairs_are_small1_0,def_lhs_atom12]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X4,X2] :
( lhs_atom11(X1,X4,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_1,axiom,
! [X1,X2] :
( lhs_atom12(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_2,axiom,
! [X1,X2] :
( lhs_atom10(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_3,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_4,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_5,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_6,axiom,
! [X3] :
( lhs_atom6(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_7,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_8,axiom,
! [X2] :
( lhs_atom2(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_9,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_10,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_11,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_12,plain,
! [X1,X4,X2] : lhs_atom11(X1,X4,X2),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_13,plain,
! [X1,X2] : lhs_atom12(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_14,plain,
! [X1,X2] : lhs_atom10(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_15,plain,
! [X1,X2] : lhs_atom4(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_16,plain,
! [X1,X2] : lhs_atom3(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_17,plain,
! [X1,X2] : lhs_atom1(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_18,plain,
! [X3] : lhs_atom6(X3),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_19,plain,
! [X2] : lhs_atom5(X2),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_20,plain,
! [X2] : lhs_atom2(X2),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_21,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_23,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_24,plain,
! [X5,X6,X7] : lhs_atom11(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_12]) ).
fof(c_0_25,plain,
! [X3,X4] : lhs_atom12(X3,X4),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_26,plain,
! [X3,X4] : lhs_atom10(X3,X4),
inference(variable_rename,[status(thm)],[c_0_14]) ).
fof(c_0_27,plain,
! [X3,X4] : lhs_atom4(X3,X4),
inference(variable_rename,[status(thm)],[c_0_15]) ).
fof(c_0_28,plain,
! [X3,X4] : lhs_atom3(X3,X4),
inference(variable_rename,[status(thm)],[c_0_16]) ).
fof(c_0_29,plain,
! [X3,X4] : lhs_atom1(X3,X4),
inference(variable_rename,[status(thm)],[c_0_17]) ).
fof(c_0_30,plain,
! [X4] : lhs_atom6(X4),
inference(variable_rename,[status(thm)],[c_0_18]) ).
fof(c_0_31,plain,
! [X3] : lhs_atom5(X3),
inference(variable_rename,[status(thm)],[c_0_19]) ).
fof(c_0_32,plain,
! [X3] : lhs_atom2(X3),
inference(variable_rename,[status(thm)],[c_0_20]) ).
fof(c_0_33,plain,
lhs_atom9,
c_0_21 ).
fof(c_0_34,plain,
lhs_atom8,
c_0_22 ).
fof(c_0_35,plain,
lhs_atom7,
c_0_23 ).
cnf(c_0_36,plain,
lhs_atom11(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
lhs_atom12(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
lhs_atom10(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,plain,
lhs_atom3(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
lhs_atom1(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,plain,
lhs_atom6(X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
lhs_atom5(X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
lhs_atom2(X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
lhs_atom11(X1,X2,X3),
c_0_36,
[final] ).
cnf(c_0_49,plain,
lhs_atom12(X1,X2),
c_0_37,
[final] ).
cnf(c_0_50,plain,
lhs_atom10(X1,X2),
c_0_38,
[final] ).
cnf(c_0_51,plain,
lhs_atom4(X1,X2),
c_0_39,
[final] ).
cnf(c_0_52,plain,
lhs_atom3(X1,X2),
c_0_40,
[final] ).
cnf(c_0_53,plain,
lhs_atom1(X1,X2),
c_0_41,
[final] ).
cnf(c_0_54,plain,
lhs_atom6(X1),
c_0_42,
[final] ).
cnf(c_0_55,plain,
lhs_atom5(X1),
c_0_43,
[final] ).
cnf(c_0_56,plain,
lhs_atom2(X1),
c_0_44,
[final] ).
cnf(c_0_57,plain,
lhs_atom9,
c_0_45,
[final] ).
cnf(c_0_58,plain,
lhs_atom8,
c_0_46,
[final] ).
cnf(c_0_59,plain,
lhs_atom7,
c_0_47,
[final] ).
% End CNF derivation
cnf(c_0_48_0,axiom,
apply_to_two_arguments(X2,X3,X1) = apply(X2,ordered_pair(X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_48,def_lhs_atom11]) ).
cnf(c_0_49_0,axiom,
little_set(ordered_pair(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_49,def_lhs_atom12]) ).
cnf(c_0_50_0,axiom,
restrict(X2,X1) = intersection(X2,cross_product(X1,universal_set)),
inference(unfold_definition,[status(thm)],[c_0_50,def_lhs_atom10]) ).
cnf(c_0_51_0,axiom,
union(X2,X1) = complement(intersection(complement(X2),complement(X1))),
inference(unfold_definition,[status(thm)],[c_0_51,def_lhs_atom4]) ).
cnf(c_0_52_0,axiom,
ordered_pair(X2,X1) = non_ordered_pair(singleton_set(X2),non_ordered_pair(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_52,def_lhs_atom3]) ).
cnf(c_0_53_0,axiom,
little_set(non_ordered_pair(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_53,def_lhs_atom1]) ).
cnf(c_0_54_0,axiom,
~ member(X1,empty_set),
inference(unfold_definition,[status(thm)],[c_0_54,def_lhs_atom6]) ).
cnf(c_0_55_0,axiom,
successor(X1) = union(X1,singleton_set(X1)),
inference(unfold_definition,[status(thm)],[c_0_55,def_lhs_atom5]) ).
cnf(c_0_56_0,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_56,def_lhs_atom2]) ).
cnf(c_0_57_0,axiom,
function(f25),
inference(unfold_definition,[status(thm)],[c_0_57,def_lhs_atom9]) ).
cnf(c_0_58_0,axiom,
member(empty_set,infinity),
inference(unfold_definition,[status(thm)],[c_0_58,def_lhs_atom8]) ).
cnf(c_0_59_0,axiom,
little_set(infinity),
inference(unfold_definition,[status(thm)],[c_0_59,def_lhs_atom7]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X6,X7,X8,X9,X10] :
( homomorphism(X8,X7,X10,X6,X9)
| ~ closed(X7,X10)
| ~ closed(X6,X9)
| ~ maps(X8,X7,X6)
| apply(X8,apply_to_two_arguments(X10,f32(X8,X7,X10,X6,X9),f33(X8,X7,X10,X6,X9))) != apply_to_two_arguments(X9,apply(X8,f32(X8,X7,X10,X6,X9)),apply(X8,f33(X8,X7,X10,X6,X9))) ),
file('<stdin>',homomorphism7) ).
fof(c_0_1_002,axiom,
! [X6,X7,X8,X9,X10] :
( homomorphism(X8,X7,X10,X6,X9)
| ~ closed(X7,X10)
| ~ closed(X6,X9)
| ~ maps(X8,X7,X6)
| member(f32(X8,X7,X10,X6,X9),X7) ),
file('<stdin>',homomorphism5) ).
fof(c_0_2_003,axiom,
! [X6,X7,X8,X9,X10] :
( homomorphism(X8,X7,X10,X6,X9)
| ~ closed(X7,X10)
| ~ closed(X6,X9)
| ~ maps(X8,X7,X6)
| member(f33(X8,X7,X10,X6,X9),X7) ),
file('<stdin>',homomorphism6) ).
fof(c_0_3_004,axiom,
! [X2,X6,X7,X8,X9,X10,X1] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| ~ member(X1,X7)
| ~ member(X2,X7)
| apply(X8,apply_to_two_arguments(X10,X1,X2)) = apply_to_two_arguments(X9,apply(X8,X1),apply(X8,X2)) ),
file('<stdin>',homomorphism4) ).
fof(c_0_4_005,axiom,
! [X6,X7,X8,X9,X10] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| maps(X8,X7,X6) ),
file('<stdin>',homomorphism3) ).
fof(c_0_5_006,axiom,
! [X6,X7,X8,X9,X10] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| closed(X7,X10) ),
file('<stdin>',homomorphism1) ).
fof(c_0_6_007,axiom,
! [X6,X7,X8,X9,X10] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| closed(X6,X9) ),
file('<stdin>',homomorphism2) ).
fof(c_0_7_008,axiom,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| member(ordered_pair(f29(X5,X12,X11),f31(X5,X12,X11)),X12) ),
file('<stdin>',compose5) ).
fof(c_0_8_009,axiom,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| member(ordered_pair(f31(X5,X12,X11),f30(X5,X12,X11)),X11) ),
file('<stdin>',compose6) ).
fof(c_0_9_010,axiom,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| member(ordered_pair(f10(X5,X1),ordered_pair(f11(X5,X1),f9(X5,X1))),X1) ),
file('<stdin>',rotate_right5) ).
fof(c_0_10_011,axiom,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| member(ordered_pair(f12(X5,X1),ordered_pair(f14(X5,X1),f13(X5,X1))),X1) ),
file('<stdin>',flip_range5) ).
fof(c_0_11_012,axiom,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| member(first(f22(X5,X1,X12)),X1) ),
file('<stdin>',image_and_substitution3) ).
fof(c_0_12_013,axiom,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| member(X5,second(f28(X5,X12,X2))) ),
file('<stdin>',apply4) ).
fof(c_0_13_014,axiom,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| X5 = ordered_pair(f29(X5,X12,X11),f30(X5,X12,X11)) ),
file('<stdin>',compose4) ).
fof(c_0_14_015,axiom,
! [X5,X1,X13,X3,X4] :
( member(X5,rotate_right(X1))
| ~ little_set(X5)
| ~ little_set(X4)
| ~ little_set(X3)
| ~ little_set(X13)
| X5 != ordered_pair(X4,ordered_pair(X3,X13))
| ~ member(ordered_pair(X3,ordered_pair(X13,X4)),X1) ),
file('<stdin>',rotate_right6) ).
fof(c_0_15_016,axiom,
! [X5,X1,X13,X3,X4] :
( member(X5,flip_range_of(X1))
| ~ little_set(X5)
| ~ little_set(X4)
| ~ little_set(X3)
| ~ little_set(X13)
| X5 != ordered_pair(X4,ordered_pair(X3,X13))
| ~ member(ordered_pair(X4,ordered_pair(X13,X3)),X1) ),
file('<stdin>',flip_range6) ).
fof(c_0_16_017,axiom,
! [X5,X2,X11,X12,X1,X13] :
( member(X5,compose(X12,X11))
| ~ little_set(X5)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X13)
| X5 != ordered_pair(X1,X2)
| ~ member(ordered_pair(X1,X13),X12)
| ~ member(ordered_pair(X13,X2),X11) ),
file('<stdin>',compose7) ).
fof(c_0_17_018,axiom,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| X5 = ordered_pair(f9(X5,X1),ordered_pair(f10(X5,X1),f11(X5,X1))) ),
file('<stdin>',rotate_right4) ).
fof(c_0_18_019,axiom,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| X5 = ordered_pair(f12(X5,X1),ordered_pair(f13(X5,X1),f14(X5,X1))) ),
file('<stdin>',flip_range4) ).
fof(c_0_19_020,axiom,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| member(f22(X5,X1,X12),X12) ),
file('<stdin>',image_and_substitution2) ).
fof(c_0_20_021,axiom,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| member(f28(X5,X12,X2),X12) ),
file('<stdin>',apply2) ).
fof(c_0_21_022,axiom,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| second(f22(X5,X1,X12)) = X5 ),
file('<stdin>',image_and_substitution4) ).
fof(c_0_22_023,axiom,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| first(f28(X5,X12,X2)) = X2 ),
file('<stdin>',apply3) ).
fof(c_0_23_024,axiom,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| ordered_pair_predicate(f22(X5,X1,X12)) ),
file('<stdin>',image_and_substitution1) ).
fof(c_0_24_025,axiom,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| ordered_pair_predicate(f28(X5,X12,X2)) ),
file('<stdin>',apply1) ).
fof(c_0_25_026,axiom,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| little_set(f29(X5,X12,X11)) ),
file('<stdin>',compose1) ).
fof(c_0_26_027,axiom,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| little_set(f30(X5,X12,X11)) ),
file('<stdin>',compose2) ).
fof(c_0_27_028,axiom,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| little_set(f31(X5,X12,X11)) ),
file('<stdin>',compose3) ).
fof(c_0_28_029,axiom,
! [X1,X13,X3,X4] :
( ~ single_valued_set(X1)
| ~ little_set(X4)
| ~ little_set(X3)
| ~ little_set(X13)
| ~ member(ordered_pair(X4,X3),X1)
| ~ member(ordered_pair(X4,X13),X1)
| X3 = X13 ),
file('<stdin>',single_valued_set1) ).
fof(c_0_29_030,axiom,
! [X14,X12] :
( closed(X14,X12)
| ~ little_set(X14)
| ~ little_set(X12)
| ~ maps(X12,cross_product(X14,X14),X14) ),
file('<stdin>',closed4) ).
fof(c_0_30_031,axiom,
! [X5,X1] :
( member(X5,converse(X1))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| ~ member(ordered_pair(second(X5),first(X5)),X1) ),
file('<stdin>',converse3) ).
fof(c_0_31_032,axiom,
! [X2,X1] :
( ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2)
| X1 = X2 ),
file('<stdin>',extensionality3) ).
fof(c_0_32_033,axiom,
! [X5,X2,X1] :
( member(X5,cross_product(X1,X2))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| ~ member(first(X5),X1)
| ~ member(second(X5),X2) ),
file('<stdin>',cross_product4) ).
fof(c_0_33_034,axiom,
! [X5,X2,X12,X1] :
( member(X5,image(X1,X12))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X12)
| ~ member(first(X2),X1)
| second(X2) != X5 ),
file('<stdin>',image_and_substitution5) ).
fof(c_0_34_035,axiom,
! [X5,X2,X12,X13] :
( member(X5,apply(X12,X2))
| ~ ordered_pair_predicate(X13)
| ~ member(X13,X12)
| first(X13) != X2
| ~ member(X5,second(X13)) ),
file('<stdin>',apply5) ).
fof(c_0_35_036,axiom,
! [X2,X12,X1] :
( ~ maps(X12,X1,X2)
| subset(range_of(X12),X2) ),
file('<stdin>',maps3) ).
fof(c_0_36_037,axiom,
! [X14,X12] :
( ~ closed(X14,X12)
| maps(X12,cross_product(X14,X14),X14) ),
file('<stdin>',closed3) ).
fof(c_0_37_038,axiom,
! [X2,X12,X1] :
( maps(X12,X1,X2)
| ~ function(X12)
| domain_of(X12) != X1
| ~ subset(range_of(X12),X2) ),
file('<stdin>',maps4) ).
fof(c_0_38_039,axiom,
! [X5,X1] :
( ~ member(X5,first(X1))
| X1 = ordered_pair(f4(X5,X1),f5(X5,X1)) ),
file('<stdin>',first3) ).
fof(c_0_39_040,axiom,
! [X5,X1] :
( ~ member(X5,second(X1))
| X1 = ordered_pair(f6(X5,X1),f7(X5,X1)) ),
file('<stdin>',second3) ).
fof(c_0_40_041,axiom,
! [X5,X1] :
( ~ member(X5,converse(X1))
| member(ordered_pair(second(X5),first(X5)),X1) ),
file('<stdin>',converse2) ).
fof(c_0_41_042,axiom,
! [X2,X12,X1] :
( ~ maps(X12,X1,X2)
| domain_of(X12) = X1 ),
file('<stdin>',maps2) ).
fof(c_0_42_043,axiom,
! [X2,X12,X1] :
( ~ maps(X12,X1,X2)
| function(X12) ),
file('<stdin>',maps1) ).
fof(c_0_43_044,axiom,
! [X5,X2,X1] :
( member(X5,intersection(X1,X2))
| ~ member(X5,X1)
| ~ member(X5,X2) ),
file('<stdin>',intersection3) ).
fof(c_0_44_045,axiom,
! [X5,X2,X1] :
( ~ member(X5,cross_product(X1,X2))
| member(first(X5),X1) ),
file('<stdin>',cross_product2) ).
fof(c_0_45_046,axiom,
! [X5,X2,X1] :
( ~ member(X5,cross_product(X1,X2))
| member(second(X5),X2) ),
file('<stdin>',cross_product3) ).
fof(c_0_46_047,axiom,
! [X2,X1] :
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('<stdin>',extensionality2) ).
fof(c_0_47_048,axiom,
! [X5,X1,X3,X4] :
( member(X5,first(X1))
| ~ little_set(X4)
| ~ little_set(X3)
| X1 != ordered_pair(X4,X3)
| ~ member(X5,X4) ),
file('<stdin>',first5) ).
fof(c_0_48_049,axiom,
! [X5,X1,X3,X4] :
( member(X5,second(X1))
| ~ little_set(X4)
| ~ little_set(X3)
| X1 != ordered_pair(X4,X3)
| ~ member(X5,X3) ),
file('<stdin>',second5) ).
fof(c_0_49_050,axiom,
! [X5,X2,X1] :
( ~ member(X5,intersection(X1,X2))
| member(X5,X1) ),
file('<stdin>',intersection1) ).
fof(c_0_50_051,axiom,
! [X5,X2,X1] :
( ~ member(X5,intersection(X1,X2))
| member(X5,X2) ),
file('<stdin>',intersection2) ).
fof(c_0_51_052,axiom,
! [X2,X1] :
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('<stdin>',subset3) ).
fof(c_0_52_053,axiom,
! [X2,X1,X3,X4] :
( ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X3)
| ordered_pair(X1,X2) != ordered_pair(X4,X3)
| X2 = X3 ),
file('<stdin>',second_components_are_equal) ).
fof(c_0_53_054,axiom,
! [X5,X1] :
( ~ member(X5,first(X1))
| member(X5,f4(X5,X1)) ),
file('<stdin>',first4) ).
fof(c_0_54_055,axiom,
! [X5,X1] :
( ~ member(X5,second(X1))
| member(X5,f7(X5,X1)) ),
file('<stdin>',second4) ).
fof(c_0_55_056,axiom,
! [X5,X1] :
( ~ member(X5,domain_of(X1))
| member(f8(X5,X1),X1) ),
file('<stdin>',domain2) ).
fof(c_0_56_057,axiom,
! [X5,X1] :
( ~ member(X5,sigma(X1))
| member(f16(X5,X1),X1) ),
file('<stdin>',sigma1) ).
fof(c_0_57_058,axiom,
! [X5,X1] :
( ~ member(X5,sigma(X1))
| member(X5,f16(X5,X1)) ),
file('<stdin>',sigma2) ).
fof(c_0_58_059,axiom,
! [X5,X1] :
( ~ member(X5,range_of(X1))
| member(f27(X5,X1),X1) ),
file('<stdin>',range_of2) ).
fof(c_0_59_060,axiom,
! [X1] :
( single_valued_set(X1)
| member(ordered_pair(f19(X1),f20(X1)),X1) ),
file('<stdin>',single_valued_set5) ).
fof(c_0_60,axiom,
! [X1] :
( single_valued_set(X1)
| member(ordered_pair(f19(X1),f21(X1)),X1) ),
file('<stdin>',single_valued_set6) ).
fof(c_0_61,axiom,
! [X5] :
( member(X5,estin)
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| ~ member(first(X5),second(X5)) ),
file('<stdin>',element_relation3) ).
fof(c_0_62,axiom,
! [X2,X1,X4] :
( ~ disjoint(X1,X2)
| ~ member(X4,X1)
| ~ member(X4,X2) ),
file('<stdin>',disjoint1) ).
fof(c_0_63,axiom,
! [X2,X1,X4] :
( ~ member(X4,non_ordered_pair(X1,X2))
| X4 = X1
| X4 = X2 ),
file('<stdin>',non_ordered_pair1) ).
fof(c_0_64,axiom,
! [X5,X2,X1] :
( ~ member(X5,cross_product(X1,X2))
| ordered_pair_predicate(X5) ),
file('<stdin>',cross_product1) ).
fof(c_0_65,axiom,
! [X5,X15,X1] :
( member(X5,domain_of(X1))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X15)
| ~ member(X15,X1)
| X5 != first(X15) ),
file('<stdin>',domain4) ).
fof(c_0_66,axiom,
! [X5,X2,X1] :
( member(X5,sigma(X1))
| ~ member(X2,X1)
| ~ member(X5,X2) ),
file('<stdin>',sigma3) ).
fof(c_0_67,axiom,
! [X5,X15,X1] :
( member(X5,range_of(X1))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X15)
| ~ member(X15,X1)
| X5 != second(X15) ),
file('<stdin>',range_of4) ).
fof(c_0_68,axiom,
! [X5,X1] :
( ~ member(X5,domain_of(X1))
| X5 = first(f8(X5,X1)) ),
file('<stdin>',domain3) ).
fof(c_0_69,axiom,
! [X5,X1] :
( ~ member(X5,range_of(X1))
| X5 = second(f27(X5,X1)) ),
file('<stdin>',range_of3) ).
fof(c_0_70,axiom,
! [X5,X1] :
( ~ member(X5,first(X1))
| little_set(f4(X5,X1)) ),
file('<stdin>',first1) ).
fof(c_0_71,axiom,
! [X5,X1] :
( ~ member(X5,first(X1))
| little_set(f5(X5,X1)) ),
file('<stdin>',first2) ).
fof(c_0_72,axiom,
! [X5,X1] :
( ~ member(X5,second(X1))
| little_set(f6(X5,X1)) ),
file('<stdin>',second1) ).
fof(c_0_73,axiom,
! [X5,X1] :
( ~ member(X5,second(X1))
| little_set(f7(X5,X1)) ),
file('<stdin>',second2) ).
fof(c_0_74,axiom,
! [X5,X1] :
( ~ member(X5,domain_of(X1))
| ordered_pair_predicate(f8(X5,X1)) ),
file('<stdin>',domain1) ).
fof(c_0_75,axiom,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| little_set(f9(X5,X1)) ),
file('<stdin>',rotate_right1) ).
fof(c_0_76,axiom,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| little_set(f10(X5,X1)) ),
file('<stdin>',rotate_right2) ).
fof(c_0_77,axiom,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| little_set(f11(X5,X1)) ),
file('<stdin>',rotate_right3) ).
fof(c_0_78,axiom,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| little_set(f12(X5,X1)) ),
file('<stdin>',flip_range1) ).
fof(c_0_79,axiom,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| little_set(f13(X5,X1)) ),
file('<stdin>',flip_range2) ).
fof(c_0_80,axiom,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| little_set(f14(X5,X1)) ),
file('<stdin>',flip_range3) ).
fof(c_0_81,axiom,
! [X5,X1] :
( ~ member(X5,range_of(X1))
| ordered_pair_predicate(f27(X5,X1)) ),
file('<stdin>',range_of1) ).
fof(c_0_82,axiom,
! [X2,X1,X3,X4] :
( ~ little_set(X1)
| ~ little_set(X4)
| ordered_pair(X1,X2) != ordered_pair(X4,X3)
| X1 = X4 ),
file('<stdin>',first_components_are_equal) ).
fof(c_0_83,axiom,
! [X5,X2,X1] :
( ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X5,X1) != non_ordered_pair(X5,X2)
| X1 = X2 ),
file('<stdin>',left_cancellation) ).
fof(c_0_84,axiom,
! [X2,X1,X4] :
( ~ subset(X1,X2)
| ~ member(X4,X1)
| member(X4,X2) ),
file('<stdin>',subset1) ).
fof(c_0_85,axiom,
! [X1] :
( ~ little_set(X1)
| X1 = empty_set
| member(ordered_pair(X1,f26(X1)),f25) ),
file('<stdin>',choice3) ).
fof(c_0_86,axiom,
! [X5,X1] :
( ~ member(X5,complement(X1))
| ~ member(X5,X1) ),
file('<stdin>',complement1) ).
fof(c_0_87,axiom,
! [X2,X1] :
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('<stdin>',subset2) ).
fof(c_0_88,axiom,
! [X2,X1] :
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
file('<stdin>',disjoint2) ).
fof(c_0_89,axiom,
! [X2,X1] :
( disjoint(X1,X2)
| member(f23(X1,X2),X2) ),
file('<stdin>',disjoint3) ).
fof(c_0_90,axiom,
! [X2,X1,X4] :
( member(X4,non_ordered_pair(X1,X2))
| ~ little_set(X4)
| X4 != X1 ),
file('<stdin>',non_ordered_pair2) ).
fof(c_0_91,axiom,
! [X2,X1,X4] :
( member(X4,non_ordered_pair(X1,X2))
| ~ little_set(X4)
| X4 != X2 ),
file('<stdin>',non_ordered_pair3) ).
fof(c_0_92,axiom,
! [X5,X1] :
( member(X5,powerset(X1))
| ~ little_set(X5)
| ~ subset(X5,X1) ),
file('<stdin>',powerset2) ).
fof(c_0_93,axiom,
! [X2,X1] :
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
file('<stdin>',two_sets_equal) ).
fof(c_0_94,axiom,
! [X5] :
( ~ member(X5,estin)
| member(first(X5),second(X5)) ),
file('<stdin>',element_relation2) ).
fof(c_0_95,axiom,
! [X5,X1] :
( ~ member(X5,powerset(X1))
| subset(X5,X1) ),
file('<stdin>',powerset1) ).
fof(c_0_96,axiom,
! [X2,X1] :
( ~ little_set(X1)
| ~ little_set(X2)
| first(ordered_pair(X1,X2)) = X1 ),
file('<stdin>',property_of_first) ).
fof(c_0_97,axiom,
! [X2,X1] :
( ~ little_set(X1)
| ~ little_set(X2)
| second(ordered_pair(X1,X2)) = X2 ),
file('<stdin>',property_of_second) ).
fof(c_0_98,axiom,
! [X12,X1] :
( ~ little_set(X1)
| ~ function(X12)
| little_set(image(X1,X12)) ),
file('<stdin>',image_and_substitution6) ).
fof(c_0_99,axiom,
! [X5,X2,X1] :
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X5)
| X1 != ordered_pair(X2,X5) ),
file('<stdin>',ordered_pair_predicate4) ).
fof(c_0_100,axiom,
! [X5,X1] :
( member(X5,complement(X1))
| ~ little_set(X5)
| member(X5,X1) ),
file('<stdin>',complement2) ).
fof(c_0_101,axiom,
! [X5] :
( member(X5,identity_relation)
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| first(X5) != second(X5) ),
file('<stdin>',identity_relation3) ).
fof(c_0_102,axiom,
! [X2,X1] :
( proper_subset(X1,X2)
| ~ subset(X1,X2)
| X1 = X2 ),
file('<stdin>',proper_subset3) ).
fof(c_0_103,axiom,
! [X1] :
( ~ member(X1,infinity)
| member(successor(X1),infinity) ),
file('<stdin>',infinity3) ).
fof(c_0_104,axiom,
! [X2,X1] :
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
file('<stdin>',proper_subset1) ).
fof(c_0_105,axiom,
! [X5,X1] :
( ~ member(X5,converse(X1))
| ordered_pair_predicate(X5) ),
file('<stdin>',converse1) ).
fof(c_0_106,axiom,
! [X1] :
( ~ ordered_pair_predicate(X1)
| X1 = ordered_pair(f2(X1),f3(X1)) ),
file('<stdin>',ordered_pair_predicate3) ).
fof(c_0_107,axiom,
! [X5,X1] :
( ~ relation(X5)
| ~ member(X1,X5)
| ordered_pair_predicate(X1) ),
file('<stdin>',relation1) ).
fof(c_0_108,axiom,
! [X2,X1] :
( little_set(f1(X1,X2))
| X1 = X2 ),
file('<stdin>',extensionality1) ).
fof(c_0_109,axiom,
! [X1] :
( ~ little_set(X1)
| X1 = empty_set
| member(f26(X1),X1) ),
file('<stdin>',choice2) ).
fof(c_0_110,axiom,
! [X5] :
( ~ member(X5,identity_relation)
| first(X5) = second(X5) ),
file('<stdin>',identity_relation2) ).
fof(c_0_111,axiom,
! [X12] :
( one_to_one_function(X12)
| ~ function(X12)
| ~ function(converse(X12)) ),
file('<stdin>',one_to_one_function3) ).
fof(c_0_112,axiom,
! [X1] :
( ~ little_set(X1)
| member(X1,singleton_set(X1)) ),
file('<stdin>',property_of_singleton_sets) ).
fof(c_0_113,axiom,
! [X2,X1] :
( ~ member(X1,X2)
| little_set(X1) ),
file('<stdin>',a2) ).
fof(c_0_114,axiom,
! [X14,X12] :
( ~ closed(X14,X12)
| little_set(X14) ),
file('<stdin>',closed1) ).
fof(c_0_115,axiom,
! [X14,X12] :
( ~ closed(X14,X12)
| little_set(X12) ),
file('<stdin>',closed2) ).
fof(c_0_116,axiom,
! [X2,X1] :
( ~ proper_subset(X1,X2)
| X1 != X2 ),
file('<stdin>',proper_subset2) ).
fof(c_0_117,axiom,
! [X5] :
( relation(X5)
| member(f18(X5),X5) ),
file('<stdin>',relation2) ).
fof(c_0_118,axiom,
! [X5] :
( ~ member(X5,estin)
| ordered_pair_predicate(X5) ),
file('<stdin>',element_relation1) ).
fof(c_0_119,axiom,
! [X5] :
( ~ member(X5,identity_relation)
| ordered_pair_predicate(X5) ),
file('<stdin>',identity_relation1) ).
fof(c_0_120,axiom,
! [X1] :
( X1 = empty_set
| member(f24(X1),X1) ),
file('<stdin>',regularity1) ).
fof(c_0_121,axiom,
! [X1] :
( X1 = empty_set
| disjoint(f24(X1),X1) ),
file('<stdin>',regularity2) ).
fof(c_0_122,axiom,
! [X5] :
( relation(X5)
| ~ ordered_pair_predicate(f18(X5)) ),
file('<stdin>',relation3) ).
fof(c_0_123,axiom,
! [X5] :
( member(X5,universal_set)
| ~ little_set(X5) ),
file('<stdin>',universal_set) ).
fof(c_0_124,axiom,
! [X12] :
( function(X12)
| ~ relation(X12)
| ~ single_valued_set(X12) ),
file('<stdin>',function3) ).
fof(c_0_125,axiom,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(f2(X1)) ),
file('<stdin>',ordered_pair_predicate1) ).
fof(c_0_126,axiom,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(f3(X1)) ),
file('<stdin>',ordered_pair_predicate2) ).
fof(c_0_127,axiom,
! [X4] :
( ~ little_set(X4)
| little_set(sigma(X4)) ),
file('<stdin>',sigma4) ).
fof(c_0_128,axiom,
! [X4] :
( ~ little_set(X4)
| little_set(powerset(X4)) ),
file('<stdin>',powerset3) ).
fof(c_0_129,axiom,
! [X12] :
( ~ one_to_one_function(X12)
| function(converse(X12)) ),
file('<stdin>',one_to_one_function2) ).
fof(c_0_130,axiom,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
file('<stdin>',first_component_is_small) ).
fof(c_0_131,axiom,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
file('<stdin>',second_component_is_small) ).
fof(c_0_132,axiom,
! [X1] :
( single_valued_set(X1)
| f20(X1) != f21(X1) ),
file('<stdin>',single_valued_set7) ).
fof(c_0_133,axiom,
! [X1] :
( single_valued_set(X1)
| little_set(f19(X1)) ),
file('<stdin>',single_valued_set2) ).
fof(c_0_134,axiom,
! [X1] :
( single_valued_set(X1)
| little_set(f20(X1)) ),
file('<stdin>',single_valued_set3) ).
fof(c_0_135,axiom,
! [X1] :
( single_valued_set(X1)
| little_set(f21(X1)) ),
file('<stdin>',single_valued_set4) ).
fof(c_0_136,axiom,
! [X12] :
( ~ function(X12)
| relation(X12) ),
file('<stdin>',function1) ).
fof(c_0_137,axiom,
! [X12] :
( ~ function(X12)
| single_valued_set(X12) ),
file('<stdin>',function2) ).
fof(c_0_138,axiom,
! [X12] :
( ~ one_to_one_function(X12)
| function(X12) ),
file('<stdin>',one_to_one_function1) ).
fof(c_0_139,axiom,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
file('<stdin>',ordered_pairs_are_small2) ).
fof(c_0_140,plain,
! [X6,X7,X8,X9,X10] :
( homomorphism(X8,X7,X10,X6,X9)
| ~ closed(X7,X10)
| ~ closed(X6,X9)
| ~ maps(X8,X7,X6)
| apply(X8,apply_to_two_arguments(X10,f32(X8,X7,X10,X6,X9),f33(X8,X7,X10,X6,X9))) != apply_to_two_arguments(X9,apply(X8,f32(X8,X7,X10,X6,X9)),apply(X8,f33(X8,X7,X10,X6,X9))) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_141,plain,
! [X6,X7,X8,X9,X10] :
( homomorphism(X8,X7,X10,X6,X9)
| ~ closed(X7,X10)
| ~ closed(X6,X9)
| ~ maps(X8,X7,X6)
| member(f32(X8,X7,X10,X6,X9),X7) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_142,plain,
! [X6,X7,X8,X9,X10] :
( homomorphism(X8,X7,X10,X6,X9)
| ~ closed(X7,X10)
| ~ closed(X6,X9)
| ~ maps(X8,X7,X6)
| member(f33(X8,X7,X10,X6,X9),X7) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_143,plain,
! [X2,X6,X7,X8,X9,X10,X1] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| ~ member(X1,X7)
| ~ member(X2,X7)
| apply(X8,apply_to_two_arguments(X10,X1,X2)) = apply_to_two_arguments(X9,apply(X8,X1),apply(X8,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_144,plain,
! [X6,X7,X8,X9,X10] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| maps(X8,X7,X6) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_145,plain,
! [X6,X7,X8,X9,X10] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| closed(X7,X10) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_146,plain,
! [X6,X7,X8,X9,X10] :
( ~ homomorphism(X8,X7,X10,X6,X9)
| closed(X6,X9) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_147,plain,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| member(ordered_pair(f29(X5,X12,X11),f31(X5,X12,X11)),X12) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_148,plain,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| member(ordered_pair(f31(X5,X12,X11),f30(X5,X12,X11)),X11) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_149,plain,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| member(ordered_pair(f10(X5,X1),ordered_pair(f11(X5,X1),f9(X5,X1))),X1) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_150,plain,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| member(ordered_pair(f12(X5,X1),ordered_pair(f14(X5,X1),f13(X5,X1))),X1) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_151,plain,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| member(first(f22(X5,X1,X12)),X1) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_152,plain,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| member(X5,second(f28(X5,X12,X2))) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_153,plain,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| X5 = ordered_pair(f29(X5,X12,X11),f30(X5,X12,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_154,plain,
! [X5,X1,X13,X3,X4] :
( member(X5,rotate_right(X1))
| ~ little_set(X5)
| ~ little_set(X4)
| ~ little_set(X3)
| ~ little_set(X13)
| X5 != ordered_pair(X4,ordered_pair(X3,X13))
| ~ member(ordered_pair(X3,ordered_pair(X13,X4)),X1) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_155,plain,
! [X5,X1,X13,X3,X4] :
( member(X5,flip_range_of(X1))
| ~ little_set(X5)
| ~ little_set(X4)
| ~ little_set(X3)
| ~ little_set(X13)
| X5 != ordered_pair(X4,ordered_pair(X3,X13))
| ~ member(ordered_pair(X4,ordered_pair(X13,X3)),X1) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_156,plain,
! [X5,X2,X11,X12,X1,X13] :
( member(X5,compose(X12,X11))
| ~ little_set(X5)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X13)
| X5 != ordered_pair(X1,X2)
| ~ member(ordered_pair(X1,X13),X12)
| ~ member(ordered_pair(X13,X2),X11) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_157,plain,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| X5 = ordered_pair(f9(X5,X1),ordered_pair(f10(X5,X1),f11(X5,X1))) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_158,plain,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| X5 = ordered_pair(f12(X5,X1),ordered_pair(f13(X5,X1),f14(X5,X1))) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_159,plain,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| member(f22(X5,X1,X12),X12) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_160,plain,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| member(f28(X5,X12,X2),X12) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_161,plain,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| second(f22(X5,X1,X12)) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_162,plain,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| first(f28(X5,X12,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_163,plain,
! [X5,X12,X1] :
( ~ member(X5,image(X1,X12))
| ordered_pair_predicate(f22(X5,X1,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_164,plain,
! [X5,X2,X12] :
( ~ member(X5,apply(X12,X2))
| ordered_pair_predicate(f28(X5,X12,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_165,plain,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| little_set(f29(X5,X12,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_166,plain,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| little_set(f30(X5,X12,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_167,plain,
! [X5,X11,X12] :
( ~ member(X5,compose(X12,X11))
| little_set(f31(X5,X12,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_168,plain,
! [X1,X13,X3,X4] :
( ~ single_valued_set(X1)
| ~ little_set(X4)
| ~ little_set(X3)
| ~ little_set(X13)
| ~ member(ordered_pair(X4,X3),X1)
| ~ member(ordered_pair(X4,X13),X1)
| X3 = X13 ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_169,plain,
! [X14,X12] :
( closed(X14,X12)
| ~ little_set(X14)
| ~ little_set(X12)
| ~ maps(X12,cross_product(X14,X14),X14) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_170,plain,
! [X5,X1] :
( member(X5,converse(X1))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| ~ member(ordered_pair(second(X5),first(X5)),X1) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_171,plain,
! [X2,X1] :
( ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_172,plain,
! [X5,X2,X1] :
( member(X5,cross_product(X1,X2))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| ~ member(first(X5),X1)
| ~ member(second(X5),X2) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_173,plain,
! [X5,X2,X12,X1] :
( member(X5,image(X1,X12))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X12)
| ~ member(first(X2),X1)
| second(X2) != X5 ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_174,plain,
! [X5,X2,X12,X13] :
( member(X5,apply(X12,X2))
| ~ ordered_pair_predicate(X13)
| ~ member(X13,X12)
| first(X13) != X2
| ~ member(X5,second(X13)) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_175,plain,
! [X2,X12,X1] :
( ~ maps(X12,X1,X2)
| subset(range_of(X12),X2) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_176,plain,
! [X14,X12] :
( ~ closed(X14,X12)
| maps(X12,cross_product(X14,X14),X14) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_177,plain,
! [X2,X12,X1] :
( maps(X12,X1,X2)
| ~ function(X12)
| domain_of(X12) != X1
| ~ subset(range_of(X12),X2) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_178,plain,
! [X5,X1] :
( ~ member(X5,first(X1))
| X1 = ordered_pair(f4(X5,X1),f5(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_179,plain,
! [X5,X1] :
( ~ member(X5,second(X1))
| X1 = ordered_pair(f6(X5,X1),f7(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_180,plain,
! [X5,X1] :
( ~ member(X5,converse(X1))
| member(ordered_pair(second(X5),first(X5)),X1) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_181,plain,
! [X2,X12,X1] :
( ~ maps(X12,X1,X2)
| domain_of(X12) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_182,plain,
! [X2,X12,X1] :
( ~ maps(X12,X1,X2)
| function(X12) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_183,plain,
! [X5,X2,X1] :
( member(X5,intersection(X1,X2))
| ~ member(X5,X1)
| ~ member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_184,plain,
! [X5,X2,X1] :
( ~ member(X5,cross_product(X1,X2))
| member(first(X5),X1) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_185,plain,
! [X5,X2,X1] :
( ~ member(X5,cross_product(X1,X2))
| member(second(X5),X2) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_186,axiom,
! [X2,X1] :
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
c_0_46 ).
fof(c_0_187,plain,
! [X5,X1,X3,X4] :
( member(X5,first(X1))
| ~ little_set(X4)
| ~ little_set(X3)
| X1 != ordered_pair(X4,X3)
| ~ member(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_188,plain,
! [X5,X1,X3,X4] :
( member(X5,second(X1))
| ~ little_set(X4)
| ~ little_set(X3)
| X1 != ordered_pair(X4,X3)
| ~ member(X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_189,plain,
! [X5,X2,X1] :
( ~ member(X5,intersection(X1,X2))
| member(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_190,plain,
! [X5,X2,X1] :
( ~ member(X5,intersection(X1,X2))
| member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_191,plain,
! [X2,X1] :
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_192,plain,
! [X2,X1,X3,X4] :
( ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X3)
| ordered_pair(X1,X2) != ordered_pair(X4,X3)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_193,plain,
! [X5,X1] :
( ~ member(X5,first(X1))
| member(X5,f4(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_194,plain,
! [X5,X1] :
( ~ member(X5,second(X1))
| member(X5,f7(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_195,plain,
! [X5,X1] :
( ~ member(X5,domain_of(X1))
| member(f8(X5,X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_196,plain,
! [X5,X1] :
( ~ member(X5,sigma(X1))
| member(f16(X5,X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_197,plain,
! [X5,X1] :
( ~ member(X5,sigma(X1))
| member(X5,f16(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_198,plain,
! [X5,X1] :
( ~ member(X5,range_of(X1))
| member(f27(X5,X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_199,axiom,
! [X1] :
( single_valued_set(X1)
| member(ordered_pair(f19(X1),f20(X1)),X1) ),
c_0_59 ).
fof(c_0_200,axiom,
! [X1] :
( single_valued_set(X1)
| member(ordered_pair(f19(X1),f21(X1)),X1) ),
c_0_60 ).
fof(c_0_201,plain,
! [X5] :
( member(X5,estin)
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| ~ member(first(X5),second(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_202,plain,
! [X2,X1,X4] :
( ~ disjoint(X1,X2)
| ~ member(X4,X1)
| ~ member(X4,X2) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_203,plain,
! [X2,X1,X4] :
( ~ member(X4,non_ordered_pair(X1,X2))
| X4 = X1
| X4 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_204,plain,
! [X5,X2,X1] :
( ~ member(X5,cross_product(X1,X2))
| ordered_pair_predicate(X5) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_205,plain,
! [X5,X15,X1] :
( member(X5,domain_of(X1))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X15)
| ~ member(X15,X1)
| X5 != first(X15) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_206,plain,
! [X5,X2,X1] :
( member(X5,sigma(X1))
| ~ member(X2,X1)
| ~ member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_207,plain,
! [X5,X15,X1] :
( member(X5,range_of(X1))
| ~ little_set(X5)
| ~ ordered_pair_predicate(X15)
| ~ member(X15,X1)
| X5 != second(X15) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_208,plain,
! [X5,X1] :
( ~ member(X5,domain_of(X1))
| X5 = first(f8(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_209,plain,
! [X5,X1] :
( ~ member(X5,range_of(X1))
| X5 = second(f27(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_210,plain,
! [X5,X1] :
( ~ member(X5,first(X1))
| little_set(f4(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_211,plain,
! [X5,X1] :
( ~ member(X5,first(X1))
| little_set(f5(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_212,plain,
! [X5,X1] :
( ~ member(X5,second(X1))
| little_set(f6(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_213,plain,
! [X5,X1] :
( ~ member(X5,second(X1))
| little_set(f7(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_214,plain,
! [X5,X1] :
( ~ member(X5,domain_of(X1))
| ordered_pair_predicate(f8(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_215,plain,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| little_set(f9(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_216,plain,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| little_set(f10(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_217,plain,
! [X5,X1] :
( ~ member(X5,rotate_right(X1))
| little_set(f11(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_218,plain,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| little_set(f12(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_219,plain,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| little_set(f13(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_220,plain,
! [X5,X1] :
( ~ member(X5,flip_range_of(X1))
| little_set(f14(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_221,plain,
! [X5,X1] :
( ~ member(X5,range_of(X1))
| ordered_pair_predicate(f27(X5,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_222,plain,
! [X2,X1,X3,X4] :
( ~ little_set(X1)
| ~ little_set(X4)
| ordered_pair(X1,X2) != ordered_pair(X4,X3)
| X1 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_223,plain,
! [X5,X2,X1] :
( ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X5,X1) != non_ordered_pair(X5,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_224,plain,
! [X2,X1,X4] :
( ~ subset(X1,X2)
| ~ member(X4,X1)
| member(X4,X2) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_225,plain,
! [X1] :
( ~ little_set(X1)
| X1 = empty_set
| member(ordered_pair(X1,f26(X1)),f25) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_226,plain,
! [X5,X1] :
( ~ member(X5,complement(X1))
| ~ member(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_227,axiom,
! [X2,X1] :
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
c_0_87 ).
fof(c_0_228,axiom,
! [X2,X1] :
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
c_0_88 ).
fof(c_0_229,axiom,
! [X2,X1] :
( disjoint(X1,X2)
| member(f23(X1,X2),X2) ),
c_0_89 ).
fof(c_0_230,plain,
! [X2,X1,X4] :
( member(X4,non_ordered_pair(X1,X2))
| ~ little_set(X4)
| X4 != X1 ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_231,plain,
! [X2,X1,X4] :
( member(X4,non_ordered_pair(X1,X2))
| ~ little_set(X4)
| X4 != X2 ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_232,plain,
! [X5,X1] :
( member(X5,powerset(X1))
| ~ little_set(X5)
| ~ subset(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_233,plain,
! [X2,X1] :
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_234,plain,
! [X5] :
( ~ member(X5,estin)
| member(first(X5),second(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_235,plain,
! [X5,X1] :
( ~ member(X5,powerset(X1))
| subset(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_236,plain,
! [X2,X1] :
( ~ little_set(X1)
| ~ little_set(X2)
| first(ordered_pair(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_237,plain,
! [X2,X1] :
( ~ little_set(X1)
| ~ little_set(X2)
| second(ordered_pair(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_238,plain,
! [X12,X1] :
( ~ little_set(X1)
| ~ function(X12)
| little_set(image(X1,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_239,plain,
! [X5,X2,X1] :
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X5)
| X1 != ordered_pair(X2,X5) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_240,plain,
! [X5,X1] :
( member(X5,complement(X1))
| ~ little_set(X5)
| member(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_241,plain,
! [X5] :
( member(X5,identity_relation)
| ~ little_set(X5)
| ~ ordered_pair_predicate(X5)
| first(X5) != second(X5) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_242,plain,
! [X2,X1] :
( proper_subset(X1,X2)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_243,plain,
! [X1] :
( ~ member(X1,infinity)
| member(successor(X1),infinity) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_244,plain,
! [X2,X1] :
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_245,plain,
! [X5,X1] :
( ~ member(X5,converse(X1))
| ordered_pair_predicate(X5) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_246,plain,
! [X1] :
( ~ ordered_pair_predicate(X1)
| X1 = ordered_pair(f2(X1),f3(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_247,plain,
! [X5,X1] :
( ~ relation(X5)
| ~ member(X1,X5)
| ordered_pair_predicate(X1) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_248,axiom,
! [X2,X1] :
( little_set(f1(X1,X2))
| X1 = X2 ),
c_0_108 ).
fof(c_0_249,plain,
! [X1] :
( ~ little_set(X1)
| X1 = empty_set
| member(f26(X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_250,plain,
! [X5] :
( ~ member(X5,identity_relation)
| first(X5) = second(X5) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_251,plain,
! [X12] :
( one_to_one_function(X12)
| ~ function(X12)
| ~ function(converse(X12)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_252,plain,
! [X1] :
( ~ little_set(X1)
| member(X1,singleton_set(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_253,plain,
! [X2,X1] :
( ~ member(X1,X2)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_254,plain,
! [X14,X12] :
( ~ closed(X14,X12)
| little_set(X14) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_255,plain,
! [X14,X12] :
( ~ closed(X14,X12)
| little_set(X12) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_256,plain,
! [X2,X1] :
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_257,axiom,
! [X5] :
( relation(X5)
| member(f18(X5),X5) ),
c_0_117 ).
fof(c_0_258,plain,
! [X5] :
( ~ member(X5,estin)
| ordered_pair_predicate(X5) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_259,plain,
! [X5] :
( ~ member(X5,identity_relation)
| ordered_pair_predicate(X5) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_260,axiom,
! [X1] :
( X1 = empty_set
| member(f24(X1),X1) ),
c_0_120 ).
fof(c_0_261,axiom,
! [X1] :
( X1 = empty_set
| disjoint(f24(X1),X1) ),
c_0_121 ).
fof(c_0_262,plain,
! [X5] :
( relation(X5)
| ~ ordered_pair_predicate(f18(X5)) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_263,plain,
! [X5] :
( member(X5,universal_set)
| ~ little_set(X5) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_264,plain,
! [X12] :
( function(X12)
| ~ relation(X12)
| ~ single_valued_set(X12) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_265,plain,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(f2(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_266,plain,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(f3(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_267,plain,
! [X4] :
( ~ little_set(X4)
| little_set(sigma(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_268,plain,
! [X4] :
( ~ little_set(X4)
| little_set(powerset(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_269,plain,
! [X12] :
( ~ one_to_one_function(X12)
| function(converse(X12)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_270,plain,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_271,plain,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_272,axiom,
! [X1] :
( single_valued_set(X1)
| f20(X1) != f21(X1) ),
c_0_132 ).
fof(c_0_273,axiom,
! [X1] :
( single_valued_set(X1)
| little_set(f19(X1)) ),
c_0_133 ).
fof(c_0_274,axiom,
! [X1] :
( single_valued_set(X1)
| little_set(f20(X1)) ),
c_0_134 ).
fof(c_0_275,axiom,
! [X1] :
( single_valued_set(X1)
| little_set(f21(X1)) ),
c_0_135 ).
fof(c_0_276,plain,
! [X12] :
( ~ function(X12)
| relation(X12) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_277,plain,
! [X12] :
( ~ function(X12)
| single_valued_set(X12) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_278,plain,
! [X12] :
( ~ one_to_one_function(X12)
| function(X12) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_279,plain,
! [X1] :
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_280,plain,
! [X11,X12,X13,X14,X15] :
( homomorphism(X13,X12,X15,X11,X14)
| ~ closed(X12,X15)
| ~ closed(X11,X14)
| ~ maps(X13,X12,X11)
| apply(X13,apply_to_two_arguments(X15,f32(X13,X12,X15,X11,X14),f33(X13,X12,X15,X11,X14))) != apply_to_two_arguments(X14,apply(X13,f32(X13,X12,X15,X11,X14)),apply(X13,f33(X13,X12,X15,X11,X14))) ),
inference(variable_rename,[status(thm)],[c_0_140]) ).
fof(c_0_281,plain,
! [X11,X12,X13,X14,X15] :
( homomorphism(X13,X12,X15,X11,X14)
| ~ closed(X12,X15)
| ~ closed(X11,X14)
| ~ maps(X13,X12,X11)
| member(f32(X13,X12,X15,X11,X14),X12) ),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_282,plain,
! [X11,X12,X13,X14,X15] :
( homomorphism(X13,X12,X15,X11,X14)
| ~ closed(X12,X15)
| ~ closed(X11,X14)
| ~ maps(X13,X12,X11)
| member(f33(X13,X12,X15,X11,X14),X12) ),
inference(variable_rename,[status(thm)],[c_0_142]) ).
fof(c_0_283,plain,
! [X11,X12,X13,X14,X15,X16,X17] :
( ~ homomorphism(X14,X13,X16,X12,X15)
| ~ member(X17,X13)
| ~ member(X11,X13)
| apply(X14,apply_to_two_arguments(X16,X17,X11)) = apply_to_two_arguments(X15,apply(X14,X17),apply(X14,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_143])])]) ).
fof(c_0_284,plain,
! [X11,X12,X13,X14,X15] :
( ~ homomorphism(X13,X12,X15,X11,X14)
| maps(X13,X12,X11) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_144])])]) ).
fof(c_0_285,plain,
! [X11,X12,X13,X14,X15] :
( ~ homomorphism(X13,X12,X15,X11,X14)
| closed(X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_286,plain,
! [X11,X12,X13,X14,X15] :
( ~ homomorphism(X13,X12,X15,X11,X14)
| closed(X11,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_146])])]) ).
fof(c_0_287,plain,
! [X13,X14,X15] :
( ~ member(X13,compose(X15,X14))
| member(ordered_pair(f29(X13,X15,X14),f31(X13,X15,X14)),X15) ),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_288,plain,
! [X13,X14,X15] :
( ~ member(X13,compose(X15,X14))
| member(ordered_pair(f31(X13,X15,X14),f30(X13,X15,X14)),X14) ),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_289,plain,
! [X6,X7] :
( ~ member(X6,rotate_right(X7))
| member(ordered_pair(f10(X6,X7),ordered_pair(f11(X6,X7),f9(X6,X7))),X7) ),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_290,plain,
! [X6,X7] :
( ~ member(X6,flip_range_of(X7))
| member(ordered_pair(f12(X6,X7),ordered_pair(f14(X6,X7),f13(X6,X7))),X7) ),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_291,plain,
! [X13,X14,X15] :
( ~ member(X13,image(X15,X14))
| member(first(f22(X13,X15,X14)),X15) ),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_292,plain,
! [X13,X14,X15] :
( ~ member(X13,apply(X15,X14))
| member(X13,second(f28(X13,X15,X14))) ),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_293,plain,
! [X13,X14,X15] :
( ~ member(X13,compose(X15,X14))
| X13 = ordered_pair(f29(X13,X15,X14),f30(X13,X15,X14)) ),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_294,plain,
! [X14,X15,X16,X17,X18] :
( member(X14,rotate_right(X15))
| ~ little_set(X14)
| ~ little_set(X18)
| ~ little_set(X17)
| ~ little_set(X16)
| X14 != ordered_pair(X18,ordered_pair(X17,X16))
| ~ member(ordered_pair(X17,ordered_pair(X16,X18)),X15) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_154])])]) ).
fof(c_0_295,plain,
! [X14,X15,X16,X17,X18] :
( member(X14,flip_range_of(X15))
| ~ little_set(X14)
| ~ little_set(X18)
| ~ little_set(X17)
| ~ little_set(X16)
| X14 != ordered_pair(X18,ordered_pair(X17,X16))
| ~ member(ordered_pair(X18,ordered_pair(X16,X17)),X15) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_155])])]) ).
fof(c_0_296,plain,
! [X14,X15,X16,X17,X18,X19] :
( member(X14,compose(X17,X16))
| ~ little_set(X14)
| ~ little_set(X18)
| ~ little_set(X15)
| ~ little_set(X19)
| X14 != ordered_pair(X18,X15)
| ~ member(ordered_pair(X18,X19),X17)
| ~ member(ordered_pair(X19,X15),X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_156])])]) ).
fof(c_0_297,plain,
! [X6,X7] :
( ~ member(X6,rotate_right(X7))
| X6 = ordered_pair(f9(X6,X7),ordered_pair(f10(X6,X7),f11(X6,X7))) ),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_298,plain,
! [X6,X7] :
( ~ member(X6,flip_range_of(X7))
| X6 = ordered_pair(f12(X6,X7),ordered_pair(f13(X6,X7),f14(X6,X7))) ),
inference(variable_rename,[status(thm)],[c_0_158]) ).
fof(c_0_299,plain,
! [X13,X14,X15] :
( ~ member(X13,image(X15,X14))
| member(f22(X13,X15,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_300,plain,
! [X13,X14,X15] :
( ~ member(X13,apply(X15,X14))
| member(f28(X13,X15,X14),X15) ),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_301,plain,
! [X13,X14,X15] :
( ~ member(X13,image(X15,X14))
| second(f22(X13,X15,X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_302,plain,
! [X13,X14,X15] :
( ~ member(X13,apply(X15,X14))
| first(f28(X13,X15,X14)) = X14 ),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_303,plain,
! [X13,X14,X15] :
( ~ member(X13,image(X15,X14))
| ordered_pair_predicate(f22(X13,X15,X14)) ),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_304,plain,
! [X13,X14,X15] :
( ~ member(X13,apply(X15,X14))
| ordered_pair_predicate(f28(X13,X15,X14)) ),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_305,plain,
! [X13,X14,X15] :
( ~ member(X13,compose(X15,X14))
| little_set(f29(X13,X15,X14)) ),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_306,plain,
! [X13,X14,X15] :
( ~ member(X13,compose(X15,X14))
| little_set(f30(X13,X15,X14)) ),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_307,plain,
! [X13,X14,X15] :
( ~ member(X13,compose(X15,X14))
| little_set(f31(X13,X15,X14)) ),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_308,plain,
! [X14,X15,X16,X17] :
( ~ single_valued_set(X14)
| ~ little_set(X17)
| ~ little_set(X16)
| ~ little_set(X15)
| ~ member(ordered_pair(X17,X16),X14)
| ~ member(ordered_pair(X17,X15),X14)
| X16 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_168])])]) ).
fof(c_0_309,plain,
! [X15,X16] :
( closed(X15,X16)
| ~ little_set(X15)
| ~ little_set(X16)
| ~ maps(X16,cross_product(X15,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_310,plain,
! [X6,X7] :
( member(X6,converse(X7))
| ~ little_set(X6)
| ~ ordered_pair_predicate(X6)
| ~ member(ordered_pair(second(X6),first(X6)),X7) ),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_311,plain,
! [X3,X4] :
( ~ member(f1(X4,X3),X4)
| ~ member(f1(X4,X3),X3)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_312,plain,
! [X6,X7,X8] :
( member(X6,cross_product(X8,X7))
| ~ little_set(X6)
| ~ ordered_pair_predicate(X6)
| ~ member(first(X6),X8)
| ~ member(second(X6),X7) ),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_313,plain,
! [X13,X14,X15,X16] :
( member(X13,image(X16,X15))
| ~ little_set(X13)
| ~ ordered_pair_predicate(X14)
| ~ member(X14,X15)
| ~ member(first(X14),X16)
| second(X14) != X13 ),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_314,plain,
! [X14,X15,X16,X17] :
( member(X14,apply(X16,X15))
| ~ ordered_pair_predicate(X17)
| ~ member(X17,X16)
| first(X17) != X15
| ~ member(X14,second(X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_174])])]) ).
fof(c_0_315,plain,
! [X13,X14,X15] :
( ~ maps(X14,X15,X13)
| subset(range_of(X14),X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_175])])]) ).
fof(c_0_316,plain,
! [X15,X16] :
( ~ closed(X15,X16)
| maps(X16,cross_product(X15,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_317,plain,
! [X13,X14,X15] :
( maps(X14,X15,X13)
| ~ function(X14)
| domain_of(X14) != X15
| ~ subset(range_of(X14),X13) ),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_318,plain,
! [X6,X7] :
( ~ member(X6,first(X7))
| X7 = ordered_pair(f4(X6,X7),f5(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_319,plain,
! [X6,X7] :
( ~ member(X6,second(X7))
| X7 = ordered_pair(f6(X6,X7),f7(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_320,plain,
! [X6,X7] :
( ~ member(X6,converse(X7))
| member(ordered_pair(second(X6),first(X6)),X7) ),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_321,plain,
! [X13,X14,X15] :
( ~ maps(X14,X15,X13)
| domain_of(X14) = X15 ),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_322,plain,
! [X13,X14,X15] :
( ~ maps(X14,X15,X13)
| function(X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_182])])]) ).
fof(c_0_323,plain,
! [X6,X7,X8] :
( member(X6,intersection(X8,X7))
| ~ member(X6,X8)
| ~ member(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_324,plain,
! [X6,X7,X8] :
( ~ member(X6,cross_product(X8,X7))
| member(first(X6),X8) ),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_325,plain,
! [X6,X7,X8] :
( ~ member(X6,cross_product(X8,X7))
| member(second(X6),X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_185])])]) ).
fof(c_0_326,plain,
! [X3,X4] :
( member(f1(X4,X3),X4)
| member(f1(X4,X3),X3)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_327,plain,
! [X6,X7,X8,X9] :
( member(X6,first(X7))
| ~ little_set(X9)
| ~ little_set(X8)
| X7 != ordered_pair(X9,X8)
| ~ member(X6,X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_187])])]) ).
fof(c_0_328,plain,
! [X6,X7,X8,X9] :
( member(X6,second(X7))
| ~ little_set(X9)
| ~ little_set(X8)
| X7 != ordered_pair(X9,X8)
| ~ member(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_188])])]) ).
fof(c_0_329,plain,
! [X6,X7,X8] :
( ~ member(X6,intersection(X8,X7))
| member(X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_330,plain,
! [X6,X7,X8] :
( ~ member(X6,intersection(X8,X7))
| member(X6,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_190])])]) ).
fof(c_0_331,plain,
! [X3,X4] :
( subset(X4,X3)
| ~ member(f17(X4,X3),X3) ),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_332,plain,
! [X5,X6,X7,X8] :
( ~ little_set(X6)
| ~ little_set(X5)
| ~ little_set(X8)
| ~ little_set(X7)
| ordered_pair(X6,X5) != ordered_pair(X8,X7)
| X5 = X7 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_192])])]) ).
fof(c_0_333,plain,
! [X6,X7] :
( ~ member(X6,first(X7))
| member(X6,f4(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_334,plain,
! [X6,X7] :
( ~ member(X6,second(X7))
| member(X6,f7(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_335,plain,
! [X6,X7] :
( ~ member(X6,domain_of(X7))
| member(f8(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_336,plain,
! [X6,X7] :
( ~ member(X6,sigma(X7))
| member(f16(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_337,plain,
! [X6,X7] :
( ~ member(X6,sigma(X7))
| member(X6,f16(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_338,plain,
! [X6,X7] :
( ~ member(X6,range_of(X7))
| member(f27(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_339,plain,
! [X2] :
( single_valued_set(X2)
| member(ordered_pair(f19(X2),f20(X2)),X2) ),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_340,plain,
! [X2] :
( single_valued_set(X2)
| member(ordered_pair(f19(X2),f21(X2)),X2) ),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_341,plain,
! [X6] :
( member(X6,estin)
| ~ little_set(X6)
| ~ ordered_pair_predicate(X6)
| ~ member(first(X6),second(X6)) ),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_342,plain,
! [X5,X6,X7] :
( ~ disjoint(X6,X5)
| ~ member(X7,X6)
| ~ member(X7,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_202])])]) ).
fof(c_0_343,plain,
! [X5,X6,X7] :
( ~ member(X7,non_ordered_pair(X6,X5))
| X7 = X6
| X7 = X5 ),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_344,plain,
! [X6,X7,X8] :
( ~ member(X6,cross_product(X8,X7))
| ordered_pair_predicate(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_204])])]) ).
fof(c_0_345,plain,
! [X16,X17,X18] :
( member(X16,domain_of(X18))
| ~ little_set(X16)
| ~ ordered_pair_predicate(X17)
| ~ member(X17,X18)
| X16 != first(X17) ),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_346,plain,
! [X6,X7,X8] :
( member(X6,sigma(X8))
| ~ member(X7,X8)
| ~ member(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_347,plain,
! [X16,X17,X18] :
( member(X16,range_of(X18))
| ~ little_set(X16)
| ~ ordered_pair_predicate(X17)
| ~ member(X17,X18)
| X16 != second(X17) ),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_348,plain,
! [X6,X7] :
( ~ member(X6,domain_of(X7))
| X6 = first(f8(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_349,plain,
! [X6,X7] :
( ~ member(X6,range_of(X7))
| X6 = second(f27(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_350,plain,
! [X6,X7] :
( ~ member(X6,first(X7))
| little_set(f4(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_351,plain,
! [X6,X7] :
( ~ member(X6,first(X7))
| little_set(f5(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_352,plain,
! [X6,X7] :
( ~ member(X6,second(X7))
| little_set(f6(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_353,plain,
! [X6,X7] :
( ~ member(X6,second(X7))
| little_set(f7(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_354,plain,
! [X6,X7] :
( ~ member(X6,domain_of(X7))
| ordered_pair_predicate(f8(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_355,plain,
! [X6,X7] :
( ~ member(X6,rotate_right(X7))
| little_set(f9(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_356,plain,
! [X6,X7] :
( ~ member(X6,rotate_right(X7))
| little_set(f10(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_357,plain,
! [X6,X7] :
( ~ member(X6,rotate_right(X7))
| little_set(f11(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_358,plain,
! [X6,X7] :
( ~ member(X6,flip_range_of(X7))
| little_set(f12(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_359,plain,
! [X6,X7] :
( ~ member(X6,flip_range_of(X7))
| little_set(f13(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_360,plain,
! [X6,X7] :
( ~ member(X6,flip_range_of(X7))
| little_set(f14(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_361,plain,
! [X6,X7] :
( ~ member(X6,range_of(X7))
| ordered_pair_predicate(f27(X6,X7)) ),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_362,plain,
! [X5,X6,X7,X8] :
( ~ little_set(X6)
| ~ little_set(X8)
| ordered_pair(X6,X5) != ordered_pair(X8,X7)
| X6 = X8 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_222])])]) ).
fof(c_0_363,plain,
! [X6,X7,X8] :
( ~ little_set(X8)
| ~ little_set(X7)
| non_ordered_pair(X6,X8) != non_ordered_pair(X6,X7)
| X8 = X7 ),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_364,plain,
! [X5,X6,X7] :
( ~ subset(X6,X5)
| ~ member(X7,X6)
| member(X7,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_224])])]) ).
fof(c_0_365,plain,
! [X2] :
( ~ little_set(X2)
| X2 = empty_set
| member(ordered_pair(X2,f26(X2)),f25) ),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_366,plain,
! [X6,X7] :
( ~ member(X6,complement(X7))
| ~ member(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_367,plain,
! [X3,X4] :
( subset(X4,X3)
| member(f17(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_368,plain,
! [X3,X4] :
( disjoint(X4,X3)
| member(f23(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_369,plain,
! [X3,X4] :
( disjoint(X4,X3)
| member(f23(X4,X3),X3) ),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_370,plain,
! [X5,X6,X7] :
( member(X7,non_ordered_pair(X6,X5))
| ~ little_set(X7)
| X7 != X6 ),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_371,plain,
! [X5,X6,X7] :
( member(X7,non_ordered_pair(X6,X5))
| ~ little_set(X7)
| X7 != X5 ),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_372,plain,
! [X6,X7] :
( member(X6,powerset(X7))
| ~ little_set(X6)
| ~ subset(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_373,plain,
! [X3,X4] :
( ~ subset(X4,X3)
| ~ subset(X3,X4)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_374,plain,
! [X6] :
( ~ member(X6,estin)
| member(first(X6),second(X6)) ),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_375,plain,
! [X6,X7] :
( ~ member(X6,powerset(X7))
| subset(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_376,plain,
! [X3,X4] :
( ~ little_set(X4)
| ~ little_set(X3)
| first(ordered_pair(X4,X3)) = X4 ),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_377,plain,
! [X3,X4] :
( ~ little_set(X4)
| ~ little_set(X3)
| second(ordered_pair(X4,X3)) = X3 ),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_378,plain,
! [X13,X14] :
( ~ little_set(X14)
| ~ function(X13)
| little_set(image(X14,X13)) ),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_379,plain,
! [X6,X7,X8] :
( ordered_pair_predicate(X8)
| ~ little_set(X7)
| ~ little_set(X6)
| X8 != ordered_pair(X7,X6) ),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_380,plain,
! [X6,X7] :
( member(X6,complement(X7))
| ~ little_set(X6)
| member(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_381,plain,
! [X6] :
( member(X6,identity_relation)
| ~ little_set(X6)
| ~ ordered_pair_predicate(X6)
| first(X6) != second(X6) ),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_382,plain,
! [X3,X4] :
( proper_subset(X4,X3)
| ~ subset(X4,X3)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_383,plain,
! [X2] :
( ~ member(X2,infinity)
| member(successor(X2),infinity) ),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_384,plain,
! [X3,X4] :
( ~ proper_subset(X4,X3)
| subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_385,plain,
! [X6,X7] :
( ~ member(X6,converse(X7))
| ordered_pair_predicate(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_245])])]) ).
fof(c_0_386,plain,
! [X2] :
( ~ ordered_pair_predicate(X2)
| X2 = ordered_pair(f2(X2),f3(X2)) ),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_387,plain,
! [X6,X7] :
( ~ relation(X6)
| ~ member(X7,X6)
| ordered_pair_predicate(X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_247])])]) ).
fof(c_0_388,plain,
! [X3,X4] :
( little_set(f1(X4,X3))
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_389,plain,
! [X2] :
( ~ little_set(X2)
| X2 = empty_set
| member(f26(X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_390,plain,
! [X6] :
( ~ member(X6,identity_relation)
| first(X6) = second(X6) ),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_391,plain,
! [X13] :
( one_to_one_function(X13)
| ~ function(X13)
| ~ function(converse(X13)) ),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_392,plain,
! [X2] :
( ~ little_set(X2)
| member(X2,singleton_set(X2)) ),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_393,plain,
! [X3,X4] :
( ~ member(X4,X3)
| little_set(X4) ),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_394,plain,
! [X15,X16] :
( ~ closed(X15,X16)
| little_set(X15) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_254])])]) ).
fof(c_0_395,plain,
! [X15,X16] :
( ~ closed(X15,X16)
| little_set(X16) ),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_396,plain,
! [X3,X4] :
( ~ proper_subset(X4,X3)
| X4 != X3 ),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_397,plain,
! [X6] :
( relation(X6)
| member(f18(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_398,plain,
! [X6] :
( ~ member(X6,estin)
| ordered_pair_predicate(X6) ),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_399,plain,
! [X6] :
( ~ member(X6,identity_relation)
| ordered_pair_predicate(X6) ),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_400,plain,
! [X2] :
( X2 = empty_set
| member(f24(X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_401,plain,
! [X2] :
( X2 = empty_set
| disjoint(f24(X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_402,plain,
! [X6] :
( relation(X6)
| ~ ordered_pair_predicate(f18(X6)) ),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_403,plain,
! [X6] :
( member(X6,universal_set)
| ~ little_set(X6) ),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_404,plain,
! [X13] :
( function(X13)
| ~ relation(X13)
| ~ single_valued_set(X13) ),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_405,plain,
! [X2] :
( ~ ordered_pair_predicate(X2)
| little_set(f2(X2)) ),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_406,plain,
! [X2] :
( ~ ordered_pair_predicate(X2)
| little_set(f3(X2)) ),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_407,plain,
! [X5] :
( ~ little_set(X5)
| little_set(sigma(X5)) ),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_408,plain,
! [X5] :
( ~ little_set(X5)
| little_set(powerset(X5)) ),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_409,plain,
! [X13] :
( ~ one_to_one_function(X13)
| function(converse(X13)) ),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_410,plain,
! [X2] :
( ~ ordered_pair_predicate(X2)
| little_set(first(X2)) ),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_411,plain,
! [X2] :
( ~ ordered_pair_predicate(X2)
| little_set(second(X2)) ),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_412,plain,
! [X2] :
( single_valued_set(X2)
| f20(X2) != f21(X2) ),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_413,plain,
! [X2] :
( single_valued_set(X2)
| little_set(f19(X2)) ),
inference(variable_rename,[status(thm)],[c_0_273]) ).
fof(c_0_414,plain,
! [X2] :
( single_valued_set(X2)
| little_set(f20(X2)) ),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_415,plain,
! [X2] :
( single_valued_set(X2)
| little_set(f21(X2)) ),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_416,plain,
! [X13] :
( ~ function(X13)
| relation(X13) ),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_417,plain,
! [X13] :
( ~ function(X13)
| single_valued_set(X13) ),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_418,plain,
! [X13] :
( ~ one_to_one_function(X13)
| function(X13) ),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_419,plain,
! [X2] :
( ~ ordered_pair_predicate(X2)
| little_set(X2) ),
inference(variable_rename,[status(thm)],[c_0_279]) ).
cnf(c_0_420,plain,
( homomorphism(X1,X3,X2,X4,X5)
| apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| ~ maps(X1,X3,X4)
| ~ closed(X4,X5)
| ~ closed(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_421,plain,
( member(f32(X1,X2,X3,X4,X5),X2)
| homomorphism(X1,X2,X3,X4,X5)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_422,plain,
( member(f33(X1,X2,X3,X4,X5),X2)
| homomorphism(X1,X2,X3,X4,X5)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_423,plain,
( apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
| ~ member(X4,X6)
| ~ member(X3,X6)
| ~ homomorphism(X1,X6,X2,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_424,plain,
( maps(X1,X2,X3)
| ~ homomorphism(X1,X2,X4,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_425,plain,
( closed(X1,X2)
| ~ homomorphism(X3,X1,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_426,plain,
( closed(X1,X2)
| ~ homomorphism(X3,X4,X5,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_427,plain,
( member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2)
| ~ member(X1,compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_428,plain,
( member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3)
| ~ member(X1,compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_429,plain,
( member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2)
| ~ member(X1,rotate_right(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_430,plain,
( member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2)
| ~ member(X1,flip_range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_431,plain,
( member(first(f22(X1,X2,X3)),X2)
| ~ member(X1,image(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_432,plain,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_433,plain,
( X1 = ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_434,plain,
( member(X5,rotate_right(X4))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X5) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_435,plain,
( member(X5,flip_range_of(X4))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ little_set(X2)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X5) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_436,plain,
( member(X6,compose(X5,X3))
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X4,X1),X5)
| X6 != ordered_pair(X4,X2)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_437,plain,
( X1 = ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2)))
| ~ member(X1,rotate_right(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_438,plain,
( X1 = ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2)))
| ~ member(X1,flip_range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_439,plain,
( member(f22(X1,X2,X3),X3)
| ~ member(X1,image(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_440,plain,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_441,plain,
( second(f22(X1,X2,X3)) = X1
| ~ member(X1,image(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_442,plain,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_443,plain,
( ordered_pair_predicate(f22(X1,X2,X3))
| ~ member(X1,image(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_444,plain,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_445,plain,
( little_set(f29(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_446,plain,
( little_set(f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_447,plain,
( little_set(f31(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_448,plain,
( X1 = X2
| ~ member(ordered_pair(X3,X2),X4)
| ~ member(ordered_pair(X3,X1),X4)
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_449,plain,
( closed(X2,X1)
| ~ maps(X1,cross_product(X2,X2),X2)
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_450,plain,
( member(X1,converse(X2))
| ~ member(ordered_pair(second(X1),first(X1)),X2)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_451,plain,
( X1 = X2
| ~ member(f1(X1,X2),X2)
| ~ member(f1(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_452,plain,
( member(X1,cross_product(X3,X2))
| ~ member(second(X1),X2)
| ~ member(first(X1),X3)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_453,plain,
( member(X2,image(X3,X4))
| second(X1) != X2
| ~ member(first(X1),X3)
| ~ member(X1,X4)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X2) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_454,plain,
( member(X1,apply(X4,X3))
| ~ member(X1,second(X2))
| first(X2) != X3
| ~ member(X2,X4)
| ~ ordered_pair_predicate(X2) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_455,plain,
( subset(range_of(X1),X2)
| ~ maps(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_456,plain,
( maps(X1,cross_product(X2,X2),X2)
| ~ closed(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_457,plain,
( maps(X1,X3,X2)
| ~ subset(range_of(X1),X2)
| domain_of(X1) != X3
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_458,plain,
( X1 = ordered_pair(f4(X2,X1),f5(X2,X1))
| ~ member(X2,first(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_459,plain,
( X1 = ordered_pair(f6(X2,X1),f7(X2,X1))
| ~ member(X2,second(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_460,plain,
( member(ordered_pair(second(X1),first(X1)),X2)
| ~ member(X1,converse(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_461,plain,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_462,plain,
( function(X1)
| ~ maps(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_463,plain,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_464,plain,
( member(first(X1),X2)
| ~ member(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_465,plain,
( member(second(X1),X2)
| ~ member(X1,cross_product(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_466,plain,
( X1 = X2
| member(f1(X1,X2),X2)
| member(f1(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_467,plain,
( member(X1,first(X3))
| ~ member(X1,X2)
| X3 != ordered_pair(X2,X4)
| ~ little_set(X4)
| ~ little_set(X2) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_468,plain,
( member(X1,second(X3))
| ~ member(X1,X2)
| X3 != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_469,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_470,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_471,plain,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_472,plain,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X1)
| ~ little_set(X3) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_473,plain,
( member(X1,f4(X1,X2))
| ~ member(X1,first(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_474,plain,
( member(X1,f7(X1,X2))
| ~ member(X1,second(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_475,plain,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_476,plain,
( member(f16(X1,X2),X2)
| ~ member(X1,sigma(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_477,plain,
( member(X1,f16(X1,X2))
| ~ member(X1,sigma(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_478,plain,
( member(f27(X1,X2),X2)
| ~ member(X1,range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_479,plain,
( member(ordered_pair(f19(X1),f20(X1)),X1)
| single_valued_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_480,plain,
( member(ordered_pair(f19(X1),f21(X1)),X1)
| single_valued_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_481,plain,
( member(X1,estin)
| ~ member(first(X1),second(X1))
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_482,plain,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ disjoint(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_483,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_484,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_485,plain,
( member(X1,domain_of(X3))
| X1 != first(X2)
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_486,plain,
( member(X1,sigma(X3))
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_487,plain,
( member(X1,range_of(X3))
| X1 != second(X2)
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_488,plain,
( X1 = first(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_489,plain,
( X1 = second(f27(X1,X2))
| ~ member(X1,range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_490,plain,
( little_set(f4(X1,X2))
| ~ member(X1,first(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_491,plain,
( little_set(f5(X1,X2))
| ~ member(X1,first(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_492,plain,
( little_set(f6(X1,X2))
| ~ member(X1,second(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_493,plain,
( little_set(f7(X1,X2))
| ~ member(X1,second(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_494,plain,
( ordered_pair_predicate(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_495,plain,
( little_set(f9(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_496,plain,
( little_set(f10(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_497,plain,
( little_set(f11(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_498,plain,
( little_set(f12(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_499,plain,
( little_set(f13(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_500,plain,
( little_set(f14(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_501,plain,
( ordered_pair_predicate(f27(X1,X2))
| ~ member(X1,range_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_502,plain,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4)
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_503,plain,
( X1 = X2
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_504,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_505,plain,
( member(ordered_pair(X1,f26(X1)),f25)
| X1 = empty_set
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_506,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_507,plain,
( member(f17(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_508,plain,
( member(f23(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_509,plain,
( member(f23(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_510,plain,
( member(X1,non_ordered_pair(X2,X3))
| X1 != X2
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_511,plain,
( member(X1,non_ordered_pair(X3,X2))
| X1 != X2
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_512,plain,
( member(X1,powerset(X2))
| ~ subset(X1,X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_513,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_514,plain,
( member(first(X1),second(X1))
| ~ member(X1,estin) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_515,plain,
( subset(X1,X2)
| ~ member(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_516,plain,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_517,plain,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_518,plain,
( little_set(image(X1,X2))
| ~ function(X2)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_519,plain,
( ordered_pair_predicate(X1)
| X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2) ),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_520,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_521,plain,
( member(X1,identity_relation)
| first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_522,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_523,plain,
( member(successor(X1),infinity)
| ~ member(X1,infinity) ),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_524,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_525,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,converse(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_526,plain,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_527,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_528,plain,
( X1 = X2
| little_set(f1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_529,plain,
( member(f26(X1),X1)
| X1 = empty_set
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_530,plain,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_531,plain,
( one_to_one_function(X1)
| ~ function(converse(X1))
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_532,plain,
( member(X1,singleton_set(X1))
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_533,plain,
( little_set(X1)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_534,plain,
( little_set(X1)
| ~ closed(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_535,plain,
( little_set(X1)
| ~ closed(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_536,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_537,plain,
( member(f18(X1),X1)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_538,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,estin) ),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_539,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,identity_relation) ),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_540,plain,
( member(f24(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_541,plain,
( disjoint(f24(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_542,plain,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_543,plain,
( member(X1,universal_set)
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_544,plain,
( function(X1)
| ~ single_valued_set(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_545,plain,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_546,plain,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_547,plain,
( little_set(sigma(X1))
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_548,plain,
( little_set(powerset(X1))
| ~ little_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_549,plain,
( function(converse(X1))
| ~ one_to_one_function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_550,plain,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_551,plain,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_552,plain,
( single_valued_set(X1)
| f20(X1) != f21(X1) ),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_553,plain,
( little_set(f19(X1))
| single_valued_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_554,plain,
( little_set(f20(X1))
| single_valued_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_555,plain,
( little_set(f21(X1))
| single_valued_set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_556,plain,
( relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_557,plain,
( single_valued_set(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_558,plain,
( function(X1)
| ~ one_to_one_function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_559,plain,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_560,plain,
( homomorphism(X1,X3,X2,X4,X5)
| apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| ~ maps(X1,X3,X4)
| ~ closed(X4,X5)
| ~ closed(X3,X2) ),
c_0_420,
[final] ).
cnf(c_0_561,plain,
( member(f32(X1,X2,X3,X4,X5),X2)
| homomorphism(X1,X2,X3,X4,X5)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
c_0_421,
[final] ).
cnf(c_0_562,plain,
( member(f33(X1,X2,X3,X4,X5),X2)
| homomorphism(X1,X2,X3,X4,X5)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
c_0_422,
[final] ).
cnf(c_0_563,plain,
( apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
| ~ member(X4,X6)
| ~ member(X3,X6)
| ~ homomorphism(X1,X6,X2,X7,X5) ),
c_0_423,
[final] ).
cnf(c_0_564,plain,
( maps(X1,X2,X3)
| ~ homomorphism(X1,X2,X4,X3,X5) ),
c_0_424,
[final] ).
cnf(c_0_565,plain,
( closed(X1,X2)
| ~ homomorphism(X3,X1,X2,X4,X5) ),
c_0_425,
[final] ).
cnf(c_0_566,plain,
( closed(X1,X2)
| ~ homomorphism(X3,X4,X5,X1,X2) ),
c_0_426,
[final] ).
cnf(c_0_567,plain,
( member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2)
| ~ member(X1,compose(X2,X3)) ),
c_0_427,
[final] ).
cnf(c_0_568,plain,
( member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3)
| ~ member(X1,compose(X2,X3)) ),
c_0_428,
[final] ).
cnf(c_0_569,plain,
( member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2)
| ~ member(X1,rotate_right(X2)) ),
c_0_429,
[final] ).
cnf(c_0_570,plain,
( member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2)
| ~ member(X1,flip_range_of(X2)) ),
c_0_430,
[final] ).
cnf(c_0_571,plain,
( member(first(f22(X1,X2,X3)),X2)
| ~ member(X1,image(X2,X3)) ),
c_0_431,
[final] ).
cnf(c_0_572,plain,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
c_0_432,
[final] ).
cnf(c_0_573,plain,
( ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)) = X1
| ~ member(X1,compose(X2,X3)) ),
c_0_433,
[final] ).
cnf(c_0_574,plain,
( member(X5,rotate_right(X4))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X5) ),
c_0_434,
[final] ).
cnf(c_0_575,plain,
( member(X5,flip_range_of(X4))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ little_set(X2)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X5) ),
c_0_435,
[final] ).
cnf(c_0_576,plain,
( member(X6,compose(X5,X3))
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X4,X1),X5)
| X6 != ordered_pair(X4,X2)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
c_0_436,
[final] ).
cnf(c_0_577,plain,
( ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) = X1
| ~ member(X1,rotate_right(X2)) ),
c_0_437,
[final] ).
cnf(c_0_578,plain,
( ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) = X1
| ~ member(X1,flip_range_of(X2)) ),
c_0_438,
[final] ).
cnf(c_0_579,plain,
( member(f22(X1,X2,X3),X3)
| ~ member(X1,image(X2,X3)) ),
c_0_439,
[final] ).
cnf(c_0_580,plain,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
c_0_440,
[final] ).
cnf(c_0_581,plain,
( second(f22(X1,X2,X3)) = X1
| ~ member(X1,image(X2,X3)) ),
c_0_441,
[final] ).
cnf(c_0_582,plain,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
c_0_442,
[final] ).
cnf(c_0_583,plain,
( ordered_pair_predicate(f22(X1,X2,X3))
| ~ member(X1,image(X2,X3)) ),
c_0_443,
[final] ).
cnf(c_0_584,plain,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
c_0_444,
[final] ).
cnf(c_0_585,plain,
( little_set(f29(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
c_0_445,
[final] ).
cnf(c_0_586,plain,
( little_set(f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
c_0_446,
[final] ).
cnf(c_0_587,plain,
( little_set(f31(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
c_0_447,
[final] ).
cnf(c_0_588,plain,
( X1 = X2
| ~ member(ordered_pair(X3,X2),X4)
| ~ member(ordered_pair(X3,X1),X4)
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
c_0_448,
[final] ).
cnf(c_0_589,plain,
( closed(X2,X1)
| ~ maps(X1,cross_product(X2,X2),X2)
| ~ little_set(X1)
| ~ little_set(X2) ),
c_0_449,
[final] ).
cnf(c_0_590,plain,
( member(X1,converse(X2))
| ~ member(ordered_pair(second(X1),first(X1)),X2)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
c_0_450,
[final] ).
cnf(c_0_591,plain,
( X1 = X2
| ~ member(f1(X1,X2),X2)
| ~ member(f1(X1,X2),X1) ),
c_0_451,
[final] ).
cnf(c_0_592,plain,
( member(X1,cross_product(X3,X2))
| ~ member(second(X1),X2)
| ~ member(first(X1),X3)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
c_0_452,
[final] ).
cnf(c_0_593,plain,
( member(X2,image(X3,X4))
| second(X1) != X2
| ~ member(first(X1),X3)
| ~ member(X1,X4)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X2) ),
c_0_453,
[final] ).
cnf(c_0_594,plain,
( member(X1,apply(X4,X3))
| ~ member(X1,second(X2))
| first(X2) != X3
| ~ member(X2,X4)
| ~ ordered_pair_predicate(X2) ),
c_0_454,
[final] ).
cnf(c_0_595,plain,
( subset(range_of(X1),X2)
| ~ maps(X1,X3,X2) ),
c_0_455,
[final] ).
cnf(c_0_596,plain,
( maps(X1,cross_product(X2,X2),X2)
| ~ closed(X2,X1) ),
c_0_456,
[final] ).
cnf(c_0_597,plain,
( maps(X1,X3,X2)
| ~ subset(range_of(X1),X2)
| domain_of(X1) != X3
| ~ function(X1) ),
c_0_457,
[final] ).
cnf(c_0_598,plain,
( ordered_pair(f4(X2,X1),f5(X2,X1)) = X1
| ~ member(X2,first(X1)) ),
c_0_458,
[final] ).
cnf(c_0_599,plain,
( ordered_pair(f6(X2,X1),f7(X2,X1)) = X1
| ~ member(X2,second(X1)) ),
c_0_459,
[final] ).
cnf(c_0_600,plain,
( member(ordered_pair(second(X1),first(X1)),X2)
| ~ member(X1,converse(X2)) ),
c_0_460,
[final] ).
cnf(c_0_601,plain,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
c_0_461,
[final] ).
cnf(c_0_602,plain,
( function(X1)
| ~ maps(X1,X2,X3) ),
c_0_462,
[final] ).
cnf(c_0_603,plain,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
c_0_463,
[final] ).
cnf(c_0_604,plain,
( member(first(X1),X2)
| ~ member(X1,cross_product(X2,X3)) ),
c_0_464,
[final] ).
cnf(c_0_605,plain,
( member(second(X1),X2)
| ~ member(X1,cross_product(X3,X2)) ),
c_0_465,
[final] ).
cnf(c_0_606,plain,
( X1 = X2
| member(f1(X1,X2),X2)
| member(f1(X1,X2),X1) ),
c_0_466,
[final] ).
cnf(c_0_607,plain,
( member(X1,first(X3))
| ~ member(X1,X2)
| X3 != ordered_pair(X2,X4)
| ~ little_set(X4)
| ~ little_set(X2) ),
c_0_467,
[final] ).
cnf(c_0_608,plain,
( member(X1,second(X3))
| ~ member(X1,X2)
| X3 != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4) ),
c_0_468,
[final] ).
cnf(c_0_609,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
c_0_469,
[final] ).
cnf(c_0_610,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
c_0_470,
[final] ).
cnf(c_0_611,plain,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
c_0_471,
[final] ).
cnf(c_0_612,plain,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X1)
| ~ little_set(X3) ),
c_0_472,
[final] ).
cnf(c_0_613,plain,
( member(X1,f4(X1,X2))
| ~ member(X1,first(X2)) ),
c_0_473,
[final] ).
cnf(c_0_614,plain,
( member(X1,f7(X1,X2))
| ~ member(X1,second(X2)) ),
c_0_474,
[final] ).
cnf(c_0_615,plain,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
c_0_475,
[final] ).
cnf(c_0_616,plain,
( member(f16(X1,X2),X2)
| ~ member(X1,sigma(X2)) ),
c_0_476,
[final] ).
cnf(c_0_617,plain,
( member(X1,f16(X1,X2))
| ~ member(X1,sigma(X2)) ),
c_0_477,
[final] ).
cnf(c_0_618,plain,
( member(f27(X1,X2),X2)
| ~ member(X1,range_of(X2)) ),
c_0_478,
[final] ).
cnf(c_0_619,plain,
( member(ordered_pair(f19(X1),f20(X1)),X1)
| single_valued_set(X1) ),
c_0_479,
[final] ).
cnf(c_0_620,plain,
( member(ordered_pair(f19(X1),f21(X1)),X1)
| single_valued_set(X1) ),
c_0_480,
[final] ).
cnf(c_0_621,plain,
( member(X1,estin)
| ~ member(first(X1),second(X1))
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
c_0_481,
[final] ).
cnf(c_0_622,plain,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ disjoint(X3,X2) ),
c_0_482,
[final] ).
cnf(c_0_623,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X3,X2)) ),
c_0_483,
[final] ).
cnf(c_0_624,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,cross_product(X2,X3)) ),
c_0_484,
[final] ).
cnf(c_0_625,plain,
( member(X1,domain_of(X3))
| X1 != first(X2)
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
c_0_485,
[final] ).
cnf(c_0_626,plain,
( member(X1,sigma(X3))
| ~ member(X1,X2)
| ~ member(X2,X3) ),
c_0_486,
[final] ).
cnf(c_0_627,plain,
( member(X1,range_of(X3))
| X1 != second(X2)
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
c_0_487,
[final] ).
cnf(c_0_628,plain,
( first(f8(X1,X2)) = X1
| ~ member(X1,domain_of(X2)) ),
c_0_488,
[final] ).
cnf(c_0_629,plain,
( second(f27(X1,X2)) = X1
| ~ member(X1,range_of(X2)) ),
c_0_489,
[final] ).
cnf(c_0_630,plain,
( little_set(f4(X1,X2))
| ~ member(X1,first(X2)) ),
c_0_490,
[final] ).
cnf(c_0_631,plain,
( little_set(f5(X1,X2))
| ~ member(X1,first(X2)) ),
c_0_491,
[final] ).
cnf(c_0_632,plain,
( little_set(f6(X1,X2))
| ~ member(X1,second(X2)) ),
c_0_492,
[final] ).
cnf(c_0_633,plain,
( little_set(f7(X1,X2))
| ~ member(X1,second(X2)) ),
c_0_493,
[final] ).
cnf(c_0_634,plain,
( ordered_pair_predicate(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
c_0_494,
[final] ).
cnf(c_0_635,plain,
( little_set(f9(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
c_0_495,
[final] ).
cnf(c_0_636,plain,
( little_set(f10(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
c_0_496,
[final] ).
cnf(c_0_637,plain,
( little_set(f11(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
c_0_497,
[final] ).
cnf(c_0_638,plain,
( little_set(f12(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
c_0_498,
[final] ).
cnf(c_0_639,plain,
( little_set(f13(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
c_0_499,
[final] ).
cnf(c_0_640,plain,
( little_set(f14(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
c_0_500,
[final] ).
cnf(c_0_641,plain,
( ordered_pair_predicate(f27(X1,X2))
| ~ member(X1,range_of(X2)) ),
c_0_501,
[final] ).
cnf(c_0_642,plain,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4)
| ~ little_set(X2)
| ~ little_set(X1) ),
c_0_502,
[final] ).
cnf(c_0_643,plain,
( X1 = X2
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| ~ little_set(X2)
| ~ little_set(X1) ),
c_0_503,
[final] ).
cnf(c_0_644,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
c_0_504,
[final] ).
cnf(c_0_645,plain,
( member(ordered_pair(X1,f26(X1)),f25)
| X1 = empty_set
| ~ little_set(X1) ),
c_0_505,
[final] ).
cnf(c_0_646,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_506,
[final] ).
cnf(c_0_647,plain,
( member(f17(X1,X2),X1)
| subset(X1,X2) ),
c_0_507,
[final] ).
cnf(c_0_648,plain,
( member(f23(X1,X2),X1)
| disjoint(X1,X2) ),
c_0_508,
[final] ).
cnf(c_0_649,plain,
( member(f23(X1,X2),X2)
| disjoint(X1,X2) ),
c_0_509,
[final] ).
cnf(c_0_650,plain,
( member(X1,non_ordered_pair(X2,X3))
| X1 != X2
| ~ little_set(X1) ),
c_0_510,
[final] ).
cnf(c_0_651,plain,
( member(X1,non_ordered_pair(X3,X2))
| X1 != X2
| ~ little_set(X1) ),
c_0_511,
[final] ).
cnf(c_0_652,plain,
( member(X1,powerset(X2))
| ~ subset(X1,X2)
| ~ little_set(X1) ),
c_0_512,
[final] ).
cnf(c_0_653,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_513,
[final] ).
cnf(c_0_654,plain,
( member(first(X1),second(X1))
| ~ member(X1,estin) ),
c_0_514,
[final] ).
cnf(c_0_655,plain,
( subset(X1,X2)
| ~ member(X1,powerset(X2)) ),
c_0_515,
[final] ).
cnf(c_0_656,plain,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X2)
| ~ little_set(X1) ),
c_0_516,
[final] ).
cnf(c_0_657,plain,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
c_0_517,
[final] ).
cnf(c_0_658,plain,
( little_set(image(X1,X2))
| ~ function(X2)
| ~ little_set(X1) ),
c_0_518,
[final] ).
cnf(c_0_659,plain,
( ordered_pair_predicate(X1)
| X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2) ),
c_0_519,
[final] ).
cnf(c_0_660,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ little_set(X1) ),
c_0_520,
[final] ).
cnf(c_0_661,plain,
( member(X1,identity_relation)
| first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
c_0_521,
[final] ).
cnf(c_0_662,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
c_0_522,
[final] ).
cnf(c_0_663,plain,
( member(successor(X1),infinity)
| ~ member(X1,infinity) ),
c_0_523,
[final] ).
cnf(c_0_664,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_524,
[final] ).
cnf(c_0_665,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,converse(X2)) ),
c_0_525,
[final] ).
cnf(c_0_666,plain,
( ordered_pair(f2(X1),f3(X1)) = X1
| ~ ordered_pair_predicate(X1) ),
c_0_526,
[final] ).
cnf(c_0_667,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,X2)
| ~ relation(X2) ),
c_0_527,
[final] ).
cnf(c_0_668,plain,
( X1 = X2
| little_set(f1(X1,X2)) ),
c_0_528,
[final] ).
cnf(c_0_669,plain,
( member(f26(X1),X1)
| X1 = empty_set
| ~ little_set(X1) ),
c_0_529,
[final] ).
cnf(c_0_670,plain,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
c_0_530,
[final] ).
cnf(c_0_671,plain,
( one_to_one_function(X1)
| ~ function(converse(X1))
| ~ function(X1) ),
c_0_531,
[final] ).
cnf(c_0_672,plain,
( member(X1,singleton_set(X1))
| ~ little_set(X1) ),
c_0_532,
[final] ).
cnf(c_0_673,plain,
( little_set(X1)
| ~ member(X1,X2) ),
c_0_533,
[final] ).
cnf(c_0_674,plain,
( little_set(X1)
| ~ closed(X1,X2) ),
c_0_534,
[final] ).
cnf(c_0_675,plain,
( little_set(X1)
| ~ closed(X2,X1) ),
c_0_535,
[final] ).
cnf(c_0_676,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
c_0_536,
[final] ).
cnf(c_0_677,plain,
( member(f18(X1),X1)
| relation(X1) ),
c_0_537,
[final] ).
cnf(c_0_678,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,estin) ),
c_0_538,
[final] ).
cnf(c_0_679,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,identity_relation) ),
c_0_539,
[final] ).
cnf(c_0_680,plain,
( member(f24(X1),X1)
| X1 = empty_set ),
c_0_540,
[final] ).
cnf(c_0_681,plain,
( disjoint(f24(X1),X1)
| X1 = empty_set ),
c_0_541,
[final] ).
cnf(c_0_682,plain,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
c_0_542,
[final] ).
cnf(c_0_683,plain,
( member(X1,universal_set)
| ~ little_set(X1) ),
c_0_543,
[final] ).
cnf(c_0_684,plain,
( function(X1)
| ~ single_valued_set(X1)
| ~ relation(X1) ),
c_0_544,
[final] ).
cnf(c_0_685,plain,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
c_0_545,
[final] ).
cnf(c_0_686,plain,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
c_0_546,
[final] ).
cnf(c_0_687,plain,
( little_set(sigma(X1))
| ~ little_set(X1) ),
c_0_547,
[final] ).
cnf(c_0_688,plain,
( little_set(powerset(X1))
| ~ little_set(X1) ),
c_0_548,
[final] ).
cnf(c_0_689,plain,
( function(converse(X1))
| ~ one_to_one_function(X1) ),
c_0_549,
[final] ).
cnf(c_0_690,plain,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
c_0_550,
[final] ).
cnf(c_0_691,plain,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
c_0_551,
[final] ).
cnf(c_0_692,plain,
( single_valued_set(X1)
| f21(X1) != f20(X1) ),
c_0_552,
[final] ).
cnf(c_0_693,plain,
( little_set(f19(X1))
| single_valued_set(X1) ),
c_0_553,
[final] ).
cnf(c_0_694,plain,
( little_set(f20(X1))
| single_valued_set(X1) ),
c_0_554,
[final] ).
cnf(c_0_695,plain,
( little_set(f21(X1))
| single_valued_set(X1) ),
c_0_555,
[final] ).
cnf(c_0_696,plain,
( relation(X1)
| ~ function(X1) ),
c_0_556,
[final] ).
cnf(c_0_697,plain,
( single_valued_set(X1)
| ~ function(X1) ),
c_0_557,
[final] ).
cnf(c_0_698,plain,
( function(X1)
| ~ one_to_one_function(X1) ),
c_0_558,
[final] ).
cnf(c_0_699,plain,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
c_0_559,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_560_0,axiom,
( homomorphism(X1,X3,X2,X4,X5)
| apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| ~ maps(X1,X3,X4)
| ~ closed(X4,X5)
| ~ closed(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_560_1,axiom,
( apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| homomorphism(X1,X3,X2,X4,X5)
| ~ maps(X1,X3,X4)
| ~ closed(X4,X5)
| ~ closed(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_560_2,axiom,
( ~ maps(X1,X3,X4)
| apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| homomorphism(X1,X3,X2,X4,X5)
| ~ closed(X4,X5)
| ~ closed(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_560_3,axiom,
( ~ closed(X4,X5)
| ~ maps(X1,X3,X4)
| apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| homomorphism(X1,X3,X2,X4,X5)
| ~ closed(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_560_4,axiom,
( ~ closed(X3,X2)
| ~ closed(X4,X5)
| ~ maps(X1,X3,X4)
| apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
| homomorphism(X1,X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_561_0,axiom,
( member(f32(X1,X2,X3,X4,X5),X2)
| homomorphism(X1,X2,X3,X4,X5)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_561_1,axiom,
( homomorphism(X1,X2,X3,X4,X5)
| member(f32(X1,X2,X3,X4,X5),X2)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_561_2,axiom,
( ~ maps(X1,X2,X4)
| homomorphism(X1,X2,X3,X4,X5)
| member(f32(X1,X2,X3,X4,X5),X2)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_561_3,axiom,
( ~ closed(X4,X5)
| ~ maps(X1,X2,X4)
| homomorphism(X1,X2,X3,X4,X5)
| member(f32(X1,X2,X3,X4,X5),X2)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_561_4,axiom,
( ~ closed(X2,X3)
| ~ closed(X4,X5)
| ~ maps(X1,X2,X4)
| homomorphism(X1,X2,X3,X4,X5)
| member(f32(X1,X2,X3,X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_562_0,axiom,
( member(f33(X1,X2,X3,X4,X5),X2)
| homomorphism(X1,X2,X3,X4,X5)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_562_1,axiom,
( homomorphism(X1,X2,X3,X4,X5)
| member(f33(X1,X2,X3,X4,X5),X2)
| ~ maps(X1,X2,X4)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_562_2,axiom,
( ~ maps(X1,X2,X4)
| homomorphism(X1,X2,X3,X4,X5)
| member(f33(X1,X2,X3,X4,X5),X2)
| ~ closed(X4,X5)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_562_3,axiom,
( ~ closed(X4,X5)
| ~ maps(X1,X2,X4)
| homomorphism(X1,X2,X3,X4,X5)
| member(f33(X1,X2,X3,X4,X5),X2)
| ~ closed(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_562_4,axiom,
( ~ closed(X2,X3)
| ~ closed(X4,X5)
| ~ maps(X1,X2,X4)
| homomorphism(X1,X2,X3,X4,X5)
| member(f33(X1,X2,X3,X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_563_0,axiom,
( apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
| ~ member(X4,X6)
| ~ member(X3,X6)
| ~ homomorphism(X1,X6,X2,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_563_1,axiom,
( ~ member(X4,X6)
| apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
| ~ member(X3,X6)
| ~ homomorphism(X1,X6,X2,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_563_2,axiom,
( ~ member(X3,X6)
| ~ member(X4,X6)
| apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
| ~ homomorphism(X1,X6,X2,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_563_3,axiom,
( ~ homomorphism(X1,X6,X2,X7,X5)
| ~ member(X3,X6)
| ~ member(X4,X6)
| apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_564_0,axiom,
( maps(X1,X2,X3)
| ~ homomorphism(X1,X2,X4,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_564]) ).
cnf(c_0_564_1,axiom,
( ~ homomorphism(X1,X2,X4,X3,X5)
| maps(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_564]) ).
cnf(c_0_565_0,axiom,
( closed(X1,X2)
| ~ homomorphism(X3,X1,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_565]) ).
cnf(c_0_565_1,axiom,
( ~ homomorphism(X3,X1,X2,X4,X5)
| closed(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_565]) ).
cnf(c_0_566_0,axiom,
( closed(X1,X2)
| ~ homomorphism(X3,X4,X5,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_566]) ).
cnf(c_0_566_1,axiom,
( ~ homomorphism(X3,X4,X5,X1,X2)
| closed(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_566]) ).
cnf(c_0_567_0,axiom,
( member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2)
| ~ member(X1,compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_567]) ).
cnf(c_0_567_1,axiom,
( ~ member(X1,compose(X2,X3))
| member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_567]) ).
cnf(c_0_568_0,axiom,
( member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3)
| ~ member(X1,compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_568_1,axiom,
( ~ member(X1,compose(X2,X3))
| member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_569_0,axiom,
( member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2)
| ~ member(X1,rotate_right(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_1,axiom,
( ~ member(X1,rotate_right(X2))
| member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_570_0,axiom,
( member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2)
| ~ member(X1,flip_range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_1,axiom,
( ~ member(X1,flip_range_of(X2))
| member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_571_0,axiom,
( member(first(f22(X1,X2,X3)),X2)
| ~ member(X1,image(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_571_1,axiom,
( ~ member(X1,image(X2,X3))
| member(first(f22(X1,X2,X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_572_0,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_1,axiom,
( ~ member(X1,apply(X2,X3))
| member(X1,second(f28(X1,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_573_0,axiom,
( ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)) = X1
| ~ member(X1,compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_573_1,axiom,
( ~ member(X1,compose(X2,X3))
| ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_574_0,axiom,
( member(X5,rotate_right(X4))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_1,axiom,
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,rotate_right(X4))
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_2,axiom,
( X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,rotate_right(X4))
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_3,axiom,
( ~ little_set(X2)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,rotate_right(X4))
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_4,axiom,
( ~ little_set(X1)
| ~ little_set(X2)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,rotate_right(X4))
| ~ little_set(X3)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_5,axiom,
( ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X2)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,rotate_right(X4))
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_6,axiom,
( ~ little_set(X5)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X2)
| X5 != ordered_pair(X3,ordered_pair(X1,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,rotate_right(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_575_0,axiom,
( member(X5,flip_range_of(X4))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ little_set(X2)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_1,axiom,
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,flip_range_of(X4))
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ little_set(X2)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_2,axiom,
( X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,flip_range_of(X4))
| ~ little_set(X2)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_3,axiom,
( ~ little_set(X2)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,flip_range_of(X4))
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_4,axiom,
( ~ little_set(X3)
| ~ little_set(X2)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,flip_range_of(X4))
| ~ little_set(X1)
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_5,axiom,
( ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X2)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,flip_range_of(X4))
| ~ little_set(X5) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_6,axiom,
( ~ little_set(X5)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ little_set(X2)
| X5 != ordered_pair(X1,ordered_pair(X3,X2))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
| member(X5,flip_range_of(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_576_0,axiom,
( member(X6,compose(X5,X3))
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X4,X1),X5)
| X6 != ordered_pair(X4,X2)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_1,axiom,
( ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3))
| ~ member(ordered_pair(X4,X1),X5)
| X6 != ordered_pair(X4,X2)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_2,axiom,
( ~ member(ordered_pair(X4,X1),X5)
| ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3))
| X6 != ordered_pair(X4,X2)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_3,axiom,
( X6 != ordered_pair(X4,X2)
| ~ member(ordered_pair(X4,X1),X5)
| ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3))
| ~ little_set(X1)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_4,axiom,
( ~ little_set(X1)
| X6 != ordered_pair(X4,X2)
| ~ member(ordered_pair(X4,X1),X5)
| ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3))
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_5,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| X6 != ordered_pair(X4,X2)
| ~ member(ordered_pair(X4,X1),X5)
| ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3))
| ~ little_set(X4)
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_6,axiom,
( ~ little_set(X4)
| ~ little_set(X2)
| ~ little_set(X1)
| X6 != ordered_pair(X4,X2)
| ~ member(ordered_pair(X4,X1),X5)
| ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3))
| ~ little_set(X6) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_7,axiom,
( ~ little_set(X6)
| ~ little_set(X4)
| ~ little_set(X2)
| ~ little_set(X1)
| X6 != ordered_pair(X4,X2)
| ~ member(ordered_pair(X4,X1),X5)
| ~ member(ordered_pair(X1,X2),X3)
| member(X6,compose(X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_577_0,axiom,
( ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) = X1
| ~ member(X1,rotate_right(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_577_1,axiom,
( ~ member(X1,rotate_right(X2))
| ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_578_0,axiom,
( ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) = X1
| ~ member(X1,flip_range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_578_1,axiom,
( ~ member(X1,flip_range_of(X2))
| ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_579_0,axiom,
( member(f22(X1,X2,X3),X3)
| ~ member(X1,image(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_579_1,axiom,
( ~ member(X1,image(X2,X3))
| member(f22(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_580_0,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_580_1,axiom,
( ~ member(X1,apply(X2,X3))
| member(f28(X1,X2,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_581_0,axiom,
( second(f22(X1,X2,X3)) = X1
| ~ member(X1,image(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_581_1,axiom,
( ~ member(X1,image(X2,X3))
| second(f22(X1,X2,X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_582_0,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_582_1,axiom,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_583_0,axiom,
( ordered_pair_predicate(f22(X1,X2,X3))
| ~ member(X1,image(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_583_1,axiom,
( ~ member(X1,image(X2,X3))
| ordered_pair_predicate(f22(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_584_0,axiom,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_584_1,axiom,
( ~ member(X1,apply(X2,X3))
| ordered_pair_predicate(f28(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_585_0,axiom,
( little_set(f29(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_585_1,axiom,
( ~ member(X1,compose(X2,X3))
| little_set(f29(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_586_0,axiom,
( little_set(f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_586]) ).
cnf(c_0_586_1,axiom,
( ~ member(X1,compose(X2,X3))
| little_set(f30(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_586]) ).
cnf(c_0_587_0,axiom,
( little_set(f31(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_587]) ).
cnf(c_0_587_1,axiom,
( ~ member(X1,compose(X2,X3))
| little_set(f31(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_587]) ).
cnf(c_0_588_0,axiom,
( X1 = X2
| ~ member(ordered_pair(X3,X2),X4)
| ~ member(ordered_pair(X3,X1),X4)
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_1,axiom,
( ~ member(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ member(ordered_pair(X3,X1),X4)
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_2,axiom,
( ~ member(ordered_pair(X3,X1),X4)
| ~ member(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ little_set(X2)
| ~ little_set(X1)
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_3,axiom,
( ~ little_set(X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ member(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ little_set(X1)
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_4,axiom,
( ~ little_set(X1)
| ~ little_set(X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ member(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ little_set(X3)
| ~ single_valued_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_5,axiom,
( ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ member(ordered_pair(X3,X2),X4)
| X1 = X2
| ~ single_valued_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_6,axiom,
( ~ single_valued_set(X4)
| ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ member(ordered_pair(X3,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_589_0,axiom,
( closed(X2,X1)
| ~ maps(X1,cross_product(X2,X2),X2)
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_1,axiom,
( ~ maps(X1,cross_product(X2,X2),X2)
| closed(X2,X1)
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_2,axiom,
( ~ little_set(X1)
| ~ maps(X1,cross_product(X2,X2),X2)
| closed(X2,X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_3,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| ~ maps(X1,cross_product(X2,X2),X2)
| closed(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_590_0,axiom,
( member(X1,converse(X2))
| ~ member(ordered_pair(second(X1),first(X1)),X2)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_1,axiom,
( ~ member(ordered_pair(second(X1),first(X1)),X2)
| member(X1,converse(X2))
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_2,axiom,
( ~ ordered_pair_predicate(X1)
| ~ member(ordered_pair(second(X1),first(X1)),X2)
| member(X1,converse(X2))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_3,axiom,
( ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| ~ member(ordered_pair(second(X1),first(X1)),X2)
| member(X1,converse(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_591_0,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X2)
| ~ member(f1(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_591_1,axiom,
( ~ member(f1(X1,X2),X2)
| X1 = X2
| ~ member(f1(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_591_2,axiom,
( ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_592_0,axiom,
( member(X1,cross_product(X3,X2))
| ~ member(second(X1),X2)
| ~ member(first(X1),X3)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_592_1,axiom,
( ~ member(second(X1),X2)
| member(X1,cross_product(X3,X2))
| ~ member(first(X1),X3)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_592_2,axiom,
( ~ member(first(X1),X3)
| ~ member(second(X1),X2)
| member(X1,cross_product(X3,X2))
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_592_3,axiom,
( ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X3)
| ~ member(second(X1),X2)
| member(X1,cross_product(X3,X2))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_592_4,axiom,
( ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X3)
| ~ member(second(X1),X2)
| member(X1,cross_product(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_593_0,axiom,
( member(X2,image(X3,X4))
| second(X1) != X2
| ~ member(first(X1),X3)
| ~ member(X1,X4)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_1,axiom,
( second(X1) != X2
| member(X2,image(X3,X4))
| ~ member(first(X1),X3)
| ~ member(X1,X4)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_2,axiom,
( ~ member(first(X1),X3)
| second(X1) != X2
| member(X2,image(X3,X4))
| ~ member(X1,X4)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_3,axiom,
( ~ member(X1,X4)
| ~ member(first(X1),X3)
| second(X1) != X2
| member(X2,image(X3,X4))
| ~ ordered_pair_predicate(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_4,axiom,
( ~ ordered_pair_predicate(X1)
| ~ member(X1,X4)
| ~ member(first(X1),X3)
| second(X1) != X2
| member(X2,image(X3,X4))
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_5,axiom,
( ~ little_set(X2)
| ~ ordered_pair_predicate(X1)
| ~ member(X1,X4)
| ~ member(first(X1),X3)
| second(X1) != X2
| member(X2,image(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_594_0,axiom,
( member(X1,apply(X4,X3))
| ~ member(X1,second(X2))
| first(X2) != X3
| ~ member(X2,X4)
| ~ ordered_pair_predicate(X2) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_1,axiom,
( ~ member(X1,second(X2))
| member(X1,apply(X4,X3))
| first(X2) != X3
| ~ member(X2,X4)
| ~ ordered_pair_predicate(X2) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_2,axiom,
( first(X2) != X3
| ~ member(X1,second(X2))
| member(X1,apply(X4,X3))
| ~ member(X2,X4)
| ~ ordered_pair_predicate(X2) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_3,axiom,
( ~ member(X2,X4)
| first(X2) != X3
| ~ member(X1,second(X2))
| member(X1,apply(X4,X3))
| ~ ordered_pair_predicate(X2) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_4,axiom,
( ~ ordered_pair_predicate(X2)
| ~ member(X2,X4)
| first(X2) != X3
| ~ member(X1,second(X2))
| member(X1,apply(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_595_0,axiom,
( subset(range_of(X1),X2)
| ~ maps(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_595_1,axiom,
( ~ maps(X1,X3,X2)
| subset(range_of(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_596_0,axiom,
( maps(X1,cross_product(X2,X2),X2)
| ~ closed(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_596_1,axiom,
( ~ closed(X2,X1)
| maps(X1,cross_product(X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_597_0,axiom,
( maps(X1,X3,X2)
| ~ subset(range_of(X1),X2)
| domain_of(X1) != X3
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_1,axiom,
( ~ subset(range_of(X1),X2)
| maps(X1,X3,X2)
| domain_of(X1) != X3
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_2,axiom,
( domain_of(X1) != X3
| ~ subset(range_of(X1),X2)
| maps(X1,X3,X2)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_3,axiom,
( ~ function(X1)
| domain_of(X1) != X3
| ~ subset(range_of(X1),X2)
| maps(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_598_0,axiom,
( ordered_pair(f4(X2,X1),f5(X2,X1)) = X1
| ~ member(X2,first(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_598_1,axiom,
( ~ member(X2,first(X1))
| ordered_pair(f4(X2,X1),f5(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_599_0,axiom,
( ordered_pair(f6(X2,X1),f7(X2,X1)) = X1
| ~ member(X2,second(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_1,axiom,
( ~ member(X2,second(X1))
| ordered_pair(f6(X2,X1),f7(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_600_0,axiom,
( member(ordered_pair(second(X1),first(X1)),X2)
| ~ member(X1,converse(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_600_1,axiom,
( ~ member(X1,converse(X2))
| member(ordered_pair(second(X1),first(X1)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_601_0,axiom,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_601]) ).
cnf(c_0_601_1,axiom,
( ~ maps(X1,X2,X3)
| domain_of(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_601]) ).
cnf(c_0_602_0,axiom,
( function(X1)
| ~ maps(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_602_1,axiom,
( ~ maps(X1,X2,X3)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_603_0,axiom,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_603_1,axiom,
( ~ member(X1,X2)
| member(X1,intersection(X3,X2))
| ~ member(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_603_2,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_604_0,axiom,
( member(first(X1),X2)
| ~ member(X1,cross_product(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_604_1,axiom,
( ~ member(X1,cross_product(X2,X3))
| member(first(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_605_0,axiom,
( member(second(X1),X2)
| ~ member(X1,cross_product(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_605_1,axiom,
( ~ member(X1,cross_product(X3,X2))
| member(second(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_606_0,axiom,
( X1 = X2
| member(f1(X1,X2),X2)
| member(f1(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_606_1,axiom,
( member(f1(X1,X2),X2)
| X1 = X2
| member(f1(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_606_2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_607_0,axiom,
( member(X1,first(X3))
| ~ member(X1,X2)
| X3 != ordered_pair(X2,X4)
| ~ little_set(X4)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_1,axiom,
( ~ member(X1,X2)
| member(X1,first(X3))
| X3 != ordered_pair(X2,X4)
| ~ little_set(X4)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_2,axiom,
( X3 != ordered_pair(X2,X4)
| ~ member(X1,X2)
| member(X1,first(X3))
| ~ little_set(X4)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_3,axiom,
( ~ little_set(X4)
| X3 != ordered_pair(X2,X4)
| ~ member(X1,X2)
| member(X1,first(X3))
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_4,axiom,
( ~ little_set(X2)
| ~ little_set(X4)
| X3 != ordered_pair(X2,X4)
| ~ member(X1,X2)
| member(X1,first(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_608_0,axiom,
( member(X1,second(X3))
| ~ member(X1,X2)
| X3 != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_1,axiom,
( ~ member(X1,X2)
| member(X1,second(X3))
| X3 != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_2,axiom,
( X3 != ordered_pair(X4,X2)
| ~ member(X1,X2)
| member(X1,second(X3))
| ~ little_set(X2)
| ~ little_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_3,axiom,
( ~ little_set(X2)
| X3 != ordered_pair(X4,X2)
| ~ member(X1,X2)
| member(X1,second(X3))
| ~ little_set(X4) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_4,axiom,
( ~ little_set(X4)
| ~ little_set(X2)
| X3 != ordered_pair(X4,X2)
| ~ member(X1,X2)
| member(X1,second(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_609_0,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_609_1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_610_0,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_610_1,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_611_0,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_611_1,axiom,
( ~ member(f17(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_612_0,axiom,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X1)
| ~ little_set(X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_1,axiom,
( ordered_pair(X3,X1) != ordered_pair(X4,X2)
| X1 = X2
| ~ little_set(X2)
| ~ little_set(X4)
| ~ little_set(X1)
| ~ little_set(X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_2,axiom,
( ~ little_set(X2)
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| X1 = X2
| ~ little_set(X4)
| ~ little_set(X1)
| ~ little_set(X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_3,axiom,
( ~ little_set(X4)
| ~ little_set(X2)
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| X1 = X2
| ~ little_set(X1)
| ~ little_set(X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_4,axiom,
( ~ little_set(X1)
| ~ little_set(X4)
| ~ little_set(X2)
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| X1 = X2
| ~ little_set(X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_5,axiom,
( ~ little_set(X3)
| ~ little_set(X1)
| ~ little_set(X4)
| ~ little_set(X2)
| ordered_pair(X3,X1) != ordered_pair(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_613_0,axiom,
( member(X1,f4(X1,X2))
| ~ member(X1,first(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_613_1,axiom,
( ~ member(X1,first(X2))
| member(X1,f4(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_614_0,axiom,
( member(X1,f7(X1,X2))
| ~ member(X1,second(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_1,axiom,
( ~ member(X1,second(X2))
| member(X1,f7(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_615_0,axiom,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_615_1,axiom,
( ~ member(X1,domain_of(X2))
| member(f8(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_616_0,axiom,
( member(f16(X1,X2),X2)
| ~ member(X1,sigma(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_616_1,axiom,
( ~ member(X1,sigma(X2))
| member(f16(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_617_0,axiom,
( member(X1,f16(X1,X2))
| ~ member(X1,sigma(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_617_1,axiom,
( ~ member(X1,sigma(X2))
| member(X1,f16(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_618_0,axiom,
( member(f27(X1,X2),X2)
| ~ member(X1,range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_618_1,axiom,
( ~ member(X1,range_of(X2))
| member(f27(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_619_0,axiom,
( member(ordered_pair(f19(X1),f20(X1)),X1)
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_1,axiom,
( single_valued_set(X1)
| member(ordered_pair(f19(X1),f20(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_620_0,axiom,
( member(ordered_pair(f19(X1),f21(X1)),X1)
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_620_1,axiom,
( single_valued_set(X1)
| member(ordered_pair(f19(X1),f21(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_621_0,axiom,
( member(X1,estin)
| ~ member(first(X1),second(X1))
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_1,axiom,
( ~ member(first(X1),second(X1))
| member(X1,estin)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_2,axiom,
( ~ ordered_pair_predicate(X1)
| ~ member(first(X1),second(X1))
| member(X1,estin)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_3,axiom,
( ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),second(X1))
| member(X1,estin) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_622_0,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ disjoint(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_1,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| ~ disjoint(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_2,axiom,
( ~ disjoint(X3,X2)
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_623_0,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_623_1,axiom,
( X1 = X3
| X1 = X2
| ~ member(X1,non_ordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_623_2,axiom,
( ~ member(X1,non_ordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_624_0,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,cross_product(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_624_1,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_625_0,axiom,
( member(X1,domain_of(X3))
| X1 != first(X2)
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_1,axiom,
( X1 != first(X2)
| member(X1,domain_of(X3))
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_2,axiom,
( ~ member(X2,X3)
| X1 != first(X2)
| member(X1,domain_of(X3))
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_3,axiom,
( ~ ordered_pair_predicate(X2)
| ~ member(X2,X3)
| X1 != first(X2)
| member(X1,domain_of(X3))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_4,axiom,
( ~ little_set(X1)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X3)
| X1 != first(X2)
| member(X1,domain_of(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_626_0,axiom,
( member(X1,sigma(X3))
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_1,axiom,
( ~ member(X1,X2)
| member(X1,sigma(X3))
| ~ member(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_2,axiom,
( ~ member(X2,X3)
| ~ member(X1,X2)
| member(X1,sigma(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_627_0,axiom,
( member(X1,range_of(X3))
| X1 != second(X2)
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_1,axiom,
( X1 != second(X2)
| member(X1,range_of(X3))
| ~ member(X2,X3)
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_2,axiom,
( ~ member(X2,X3)
| X1 != second(X2)
| member(X1,range_of(X3))
| ~ ordered_pair_predicate(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_3,axiom,
( ~ ordered_pair_predicate(X2)
| ~ member(X2,X3)
| X1 != second(X2)
| member(X1,range_of(X3))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_4,axiom,
( ~ little_set(X1)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X3)
| X1 != second(X2)
| member(X1,range_of(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_628_0,axiom,
( first(f8(X1,X2)) = X1
| ~ member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_1,axiom,
( ~ member(X1,domain_of(X2))
| first(f8(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_629_0,axiom,
( second(f27(X1,X2)) = X1
| ~ member(X1,range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_1,axiom,
( ~ member(X1,range_of(X2))
| second(f27(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_630_0,axiom,
( little_set(f4(X1,X2))
| ~ member(X1,first(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_630_1,axiom,
( ~ member(X1,first(X2))
| little_set(f4(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_631_0,axiom,
( little_set(f5(X1,X2))
| ~ member(X1,first(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_631_1,axiom,
( ~ member(X1,first(X2))
| little_set(f5(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_632_0,axiom,
( little_set(f6(X1,X2))
| ~ member(X1,second(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_1,axiom,
( ~ member(X1,second(X2))
| little_set(f6(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_633_0,axiom,
( little_set(f7(X1,X2))
| ~ member(X1,second(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_1,axiom,
( ~ member(X1,second(X2))
| little_set(f7(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_634_0,axiom,
( ordered_pair_predicate(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_1,axiom,
( ~ member(X1,domain_of(X2))
| ordered_pair_predicate(f8(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_635_0,axiom,
( little_set(f9(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_1,axiom,
( ~ member(X1,rotate_right(X2))
| little_set(f9(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_636_0,axiom,
( little_set(f10(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_1,axiom,
( ~ member(X1,rotate_right(X2))
| little_set(f10(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_637_0,axiom,
( little_set(f11(X1,X2))
| ~ member(X1,rotate_right(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_1,axiom,
( ~ member(X1,rotate_right(X2))
| little_set(f11(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_638_0,axiom,
( little_set(f12(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_1,axiom,
( ~ member(X1,flip_range_of(X2))
| little_set(f12(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_639_0,axiom,
( little_set(f13(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_1,axiom,
( ~ member(X1,flip_range_of(X2))
| little_set(f13(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_640_0,axiom,
( little_set(f14(X1,X2))
| ~ member(X1,flip_range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_1,axiom,
( ~ member(X1,flip_range_of(X2))
| little_set(f14(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_641_0,axiom,
( ordered_pair_predicate(f27(X1,X2))
| ~ member(X1,range_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_1,axiom,
( ~ member(X1,range_of(X2))
| ordered_pair_predicate(f27(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_642_0,axiom,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4)
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_1,axiom,
( ordered_pair(X1,X3) != ordered_pair(X2,X4)
| X1 = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_2,axiom,
( ~ little_set(X2)
| ordered_pair(X1,X3) != ordered_pair(X2,X4)
| X1 = X2
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_3,axiom,
( ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X3) != ordered_pair(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_643_0,axiom,
( X1 = X2
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_1,axiom,
( non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| X1 = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_2,axiom,
( ~ little_set(X2)
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| X1 = X2
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_3,axiom,
( ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_644_0,axiom,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_1,axiom,
( ~ member(X1,X3)
| member(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_2,axiom,
( ~ subset(X3,X2)
| ~ member(X1,X3)
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_645_0,axiom,
( member(ordered_pair(X1,f26(X1)),f25)
| X1 = empty_set
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_1,axiom,
( X1 = empty_set
| member(ordered_pair(X1,f26(X1)),f25)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_2,axiom,
( ~ little_set(X1)
| X1 = empty_set
| member(ordered_pair(X1,f26(X1)),f25) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_646_0,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_647_0,axiom,
( member(f17(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_1,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_648_0,axiom,
( member(f23(X1,X2),X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_1,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_649_0,axiom,
( member(f23(X1,X2),X2)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_649_1,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_650_0,axiom,
( member(X1,non_ordered_pair(X2,X3))
| X1 != X2
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_1,axiom,
( X1 != X2
| member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_2,axiom,
( ~ little_set(X1)
| X1 != X2
| member(X1,non_ordered_pair(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_651_0,axiom,
( member(X1,non_ordered_pair(X3,X2))
| X1 != X2
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_651_1,axiom,
( X1 != X2
| member(X1,non_ordered_pair(X3,X2))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_651_2,axiom,
( ~ little_set(X1)
| X1 != X2
| member(X1,non_ordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_652_0,axiom,
( member(X1,powerset(X2))
| ~ subset(X1,X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_652_1,axiom,
( ~ subset(X1,X2)
| member(X1,powerset(X2))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_652_2,axiom,
( ~ little_set(X1)
| ~ subset(X1,X2)
| member(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_653_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_653_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_653_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_654_0,axiom,
( member(first(X1),second(X1))
| ~ member(X1,estin) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_654_1,axiom,
( ~ member(X1,estin)
| member(first(X1),second(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_655_0,axiom,
( subset(X1,X2)
| ~ member(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_655_1,axiom,
( ~ member(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_656_0,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_1,axiom,
( ~ little_set(X2)
| first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_2,axiom,
( ~ little_set(X1)
| ~ little_set(X2)
| first(ordered_pair(X1,X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_657_0,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_657_1,axiom,
( ~ little_set(X2)
| second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_657_2,axiom,
( ~ little_set(X1)
| ~ little_set(X2)
| second(ordered_pair(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_658_0,axiom,
( little_set(image(X1,X2))
| ~ function(X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_1,axiom,
( ~ function(X2)
| little_set(image(X1,X2))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_2,axiom,
( ~ little_set(X1)
| ~ function(X2)
| little_set(image(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_659_0,axiom,
( ordered_pair_predicate(X1)
| X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_1,axiom,
( X1 != ordered_pair(X2,X3)
| ordered_pair_predicate(X1)
| ~ little_set(X3)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_2,axiom,
( ~ little_set(X3)
| X1 != ordered_pair(X2,X3)
| ordered_pair_predicate(X1)
| ~ little_set(X2) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_3,axiom,
( ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3)
| ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_660_0,axiom,
( member(X1,X2)
| member(X1,complement(X2))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_1,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_2,axiom,
( ~ little_set(X1)
| member(X1,complement(X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_661_0,axiom,
( member(X1,identity_relation)
| first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_661_1,axiom,
( first(X1) != second(X1)
| member(X1,identity_relation)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_661_2,axiom,
( ~ ordered_pair_predicate(X1)
| first(X1) != second(X1)
| member(X1,identity_relation)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_661_3,axiom,
( ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| first(X1) != second(X1)
| member(X1,identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_662_0,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_1,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_2,axiom,
( ~ subset(X1,X2)
| proper_subset(X1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_663_0,axiom,
( member(successor(X1),infinity)
| ~ member(X1,infinity) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_663_1,axiom,
( ~ member(X1,infinity)
| member(successor(X1),infinity) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_664_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_665_0,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,converse(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_665_1,axiom,
( ~ member(X1,converse(X2))
| ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_666_0,axiom,
( ordered_pair(f2(X1),f3(X1)) = X1
| ~ ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_666_1,axiom,
( ~ ordered_pair_predicate(X1)
| ordered_pair(f2(X1),f3(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_667_0,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_667_1,axiom,
( ~ member(X1,X2)
| ordered_pair_predicate(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_667_2,axiom,
( ~ relation(X2)
| ~ member(X1,X2)
| ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_668_0,axiom,
( X1 = X2
| little_set(f1(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_668_1,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_669_0,axiom,
( member(f26(X1),X1)
| X1 = empty_set
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_669_1,axiom,
( X1 = empty_set
| member(f26(X1),X1)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_669_2,axiom,
( ~ little_set(X1)
| X1 = empty_set
| member(f26(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_670_0,axiom,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_670_1,axiom,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_671_0,axiom,
( one_to_one_function(X1)
| ~ function(converse(X1))
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_1,axiom,
( ~ function(converse(X1))
| one_to_one_function(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_2,axiom,
( ~ function(X1)
| ~ function(converse(X1))
| one_to_one_function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_672_0,axiom,
( member(X1,singleton_set(X1))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_672_1,axiom,
( ~ little_set(X1)
| member(X1,singleton_set(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_673_0,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_673_1,axiom,
( ~ member(X1,X2)
| little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_674_0,axiom,
( little_set(X1)
| ~ closed(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_1,axiom,
( ~ closed(X1,X2)
| little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_675_0,axiom,
( little_set(X1)
| ~ closed(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_675_1,axiom,
( ~ closed(X2,X1)
| little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_676_0,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_676_1,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_677_0,axiom,
( member(f18(X1),X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_1,axiom,
( relation(X1)
| member(f18(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_678_0,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,estin) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_1,axiom,
( ~ member(X1,estin)
| ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_679_0,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_1,axiom,
( ~ member(X1,identity_relation)
| ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_680_0,axiom,
( member(f24(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_1,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_681_0,axiom,
( disjoint(f24(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_1,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_682_0,axiom,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_1,axiom,
( ~ ordered_pair_predicate(f18(X1))
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_683_0,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_1,axiom,
( ~ little_set(X1)
| member(X1,universal_set) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_684_0,axiom,
( function(X1)
| ~ single_valued_set(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_1,axiom,
( ~ single_valued_set(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_2,axiom,
( ~ relation(X1)
| ~ single_valued_set(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_685_0,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_1,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(f2(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_686_0,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_1,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(f3(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_687_0,axiom,
( little_set(sigma(X1))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_1,axiom,
( ~ little_set(X1)
| little_set(sigma(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_688_0,axiom,
( little_set(powerset(X1))
| ~ little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_688_1,axiom,
( ~ little_set(X1)
| little_set(powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_689_0,axiom,
( function(converse(X1))
| ~ one_to_one_function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_1,axiom,
( ~ one_to_one_function(X1)
| function(converse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_690_0,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_1,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_691_0,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_1,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_692_0,axiom,
( single_valued_set(X1)
| f21(X1) != f20(X1) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_1,axiom,
( f21(X1) != f20(X1)
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_693_0,axiom,
( little_set(f19(X1))
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_1,axiom,
( single_valued_set(X1)
| little_set(f19(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_694_0,axiom,
( little_set(f20(X1))
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_1,axiom,
( single_valued_set(X1)
| little_set(f20(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_695_0,axiom,
( little_set(f21(X1))
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_1,axiom,
( single_valued_set(X1)
| little_set(f21(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_696_0,axiom,
( relation(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_1,axiom,
( ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_697_0,axiom,
( single_valued_set(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_1,axiom,
( ~ function(X1)
| single_valued_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_698_0,axiom,
( function(X1)
| ~ one_to_one_function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_1,axiom,
( ~ one_to_one_function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_699_0,axiom,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_699_1,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_061,negated_conjecture,
~ subset(a,c),
file('<stdin>',prove_a_subset_c) ).
fof(c_0_1_062,hypothesis,
subset(b,c),
file('<stdin>',b_subset_c) ).
fof(c_0_2_063,hypothesis,
subset(a,b),
file('<stdin>',a_subset_b) ).
fof(c_0_3_064,negated_conjecture,
~ subset(a,c),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_4_065,hypothesis,
subset(b,c),
c_0_1 ).
fof(c_0_5_066,hypothesis,
subset(a,b),
c_0_2 ).
fof(c_0_6_067,negated_conjecture,
~ subset(a,c),
c_0_3 ).
fof(c_0_7_068,hypothesis,
subset(b,c),
c_0_4 ).
fof(c_0_8_069,hypothesis,
subset(a,b),
c_0_5 ).
cnf(c_0_9_070,negated_conjecture,
~ subset(a,c),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10_071,hypothesis,
subset(b,c),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11_072,hypothesis,
subset(a,b),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12_073,negated_conjecture,
~ subset(a,c),
c_0_9,
[final] ).
cnf(c_0_13_074,hypothesis,
subset(b,c),
c_0_10,
[final] ).
cnf(c_0_14_075,hypothesis,
subset(a,b),
c_0_11,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_246,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p',c_0_644_2) ).
cnf(c_782,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ subset(X2,X1) ),
inference(copy,[status(esa)],[c_246]) ).
cnf(c_62911,plain,
( ~ member(f17(a,c),b)
| member(f17(a,c),X0)
| ~ subset(b,X0) ),
inference(instantiation,[status(thm)],[c_782]) ).
cnf(c_165897,plain,
( member(f17(a,c),c)
| ~ member(f17(a,c),b)
| ~ subset(b,c) ),
inference(instantiation,[status(thm)],[c_62911]) ).
cnf(c_24952,plain,
( ~ member(f17(a,c),a)
| member(f17(a,c),X0)
| ~ subset(a,X0) ),
inference(instantiation,[status(thm)],[c_782]) ).
cnf(c_61524,plain,
( ~ member(f17(a,c),a)
| member(f17(a,c),b)
| ~ subset(a,b) ),
inference(instantiation,[status(thm)],[c_24952]) ).
cnf(c_252,plain,
( subset(X0,X1)
| member(f17(X0,X1),X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p',c_0_647_0) ).
cnf(c_788,plain,
( subset(X0,X1)
| member(f17(X0,X1),X0) ),
inference(copy,[status(esa)],[c_252]) ).
cnf(c_24381,plain,
( member(f17(a,c),a)
| subset(a,c) ),
inference(instantiation,[status(thm)],[c_788]) ).
cnf(c_159,plain,
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p',c_0_611_0) ).
cnf(c_695,plain,
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) ),
inference(copy,[status(esa)],[c_159]) ).
cnf(c_24379,plain,
( ~ member(f17(a,c),c)
| subset(a,c) ),
inference(instantiation,[status(thm)],[c_695]) ).
cnf(c_388,plain,
subset(b,c),
file('/export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p',c_0_13) ).
cnf(c_389,plain,
subset(a,b),
file('/export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p',c_0_14) ).
cnf(c_387,negated_conjecture,
~ subset(a,c),
file('/export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p',c_0_12) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_165897,c_61524,c_24381,c_24379,c_388,c_389,c_387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SET027-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 12:24:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.42 % Orientation found
% 0.20/0.42 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_7ff647.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_c81bf9.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_7aec22 | grep -v "SZS"
% 0.20/0.44
% 0.20/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ iProver source info
% 0.20/0.44
% 0.20/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.44 % git: non_committed_changes: true
% 0.20/0.44 % git: last_make_outside_of_git: true
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ Input Options
% 0.20/0.44
% 0.20/0.44 % --out_options all
% 0.20/0.44 % --tptp_safe_out true
% 0.20/0.44 % --problem_path ""
% 0.20/0.44 % --include_path ""
% 0.20/0.44 % --clausifier .//eprover
% 0.20/0.44 % --clausifier_options --tstp-format
% 0.20/0.44 % --stdin false
% 0.20/0.44 % --dbg_backtrace false
% 0.20/0.44 % --dbg_dump_prop_clauses false
% 0.20/0.44 % --dbg_dump_prop_clauses_file -
% 0.20/0.44 % --dbg_out_stat false
% 0.20/0.44
% 0.20/0.44 % ------ General Options
% 0.20/0.44
% 0.20/0.44 % --fof false
% 0.20/0.44 % --time_out_real 150.
% 0.20/0.44 % --time_out_prep_mult 0.2
% 0.20/0.44 % --time_out_virtual -1.
% 0.20/0.44 % --schedule none
% 0.20/0.44 % --ground_splitting input
% 0.20/0.44 % --splitting_nvd 16
% 0.20/0.44 % --non_eq_to_eq false
% 0.20/0.44 % --prep_gs_sim true
% 0.20/0.44 % --prep_unflatten false
% 0.20/0.44 % --prep_res_sim true
% 0.20/0.44 % --prep_upred true
% 0.20/0.44 % --res_sim_input true
% 0.20/0.44 % --clause_weak_htbl true
% 0.20/0.44 % --gc_record_bc_elim false
% 0.20/0.44 % --symbol_type_check false
% 0.20/0.44 % --clausify_out false
% 0.20/0.44 % --large_theory_mode false
% 0.20/0.44 % --prep_sem_filter none
% 0.20/0.44 % --prep_sem_filter_out false
% 0.20/0.44 % --preprocessed_out false
% 0.20/0.44 % --sub_typing false
% 0.20/0.44 % --brand_transform false
% 0.20/0.44 % --pure_diseq_elim true
% 0.20/0.44 % --min_unsat_core false
% 0.20/0.44 % --pred_elim true
% 0.20/0.44 % --add_important_lit false
% 0.20/0.44 % --soft_assumptions false
% 0.20/0.44 % --reset_solvers false
% 0.20/0.44 % --bc_imp_inh []
% 0.20/0.44 % --conj_cone_tolerance 1.5
% 0.20/0.44 % --prolific_symb_bound 500
% 0.20/0.44 % --lt_threshold 2000
% 0.20/0.44
% 0.20/0.44 % ------ SAT Options
% 0.20/0.44
% 0.20/0.44 % --sat_mode false
% 0.20/0.44 % --sat_fm_restart_options ""
% 0.20/0.44 % --sat_gr_def false
% 0.20/0.44 % --sat_epr_types true
% 0.20/0.44 % --sat_non_cyclic_types false
% 0.20/0.44 % --sat_finite_models false
% 0.20/0.44 % --sat_fm_lemmas false
% 0.20/0.44 % --sat_fm_prep false
% 0.20/0.44 % --sat_fm_uc_incr true
% 0.20/0.44 % --sat_out_model small
% 0.20/0.44 % --sat_out_clauses false
% 0.20/0.44
% 0.20/0.44 % ------ QBF Options
% 0.20/0.44
% 0.20/0.44 % --qbf_mode false
% 0.20/0.44 % --qbf_elim_univ true
% 0.20/0.44 % --qbf_sk_in true
% 0.20/0.44 % --qbf_pred_elim true
% 0.20/0.44 % --qbf_split 32
% 0.20/0.44
% 0.20/0.44 % ------ BMC1 Options
% 0.20/0.44
% 0.20/0.44 % --bmc1_incremental false
% 0.20/0.44 % --bmc1_axioms reachable_all
% 0.20/0.44 % --bmc1_min_bound 0
% 0.20/0.44 % --bmc1_max_bound -1
% 0.20/0.44 % --bmc1_max_bound_default -1
% 0.20/0.44 % --bmc1_symbol_reachability true
% 0.20/0.44 % --bmc1_property_lemmas false
% 0.20/0.44 % --bmc1_k_induction false
% 0.20/0.44 % --bmc1_non_equiv_states false
% 0.20/0.44 % --bmc1_deadlock false
% 0.20/0.44 % --bmc1_ucm false
% 0.20/0.44 % --bmc1_add_unsat_core none
% 0.20/0.44 % --bmc1_unsat_core_children false
% 0.20/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.44 % --bmc1_out_stat full
% 0.20/0.44 % --bmc1_ground_init false
% 0.20/0.44 % --bmc1_pre_inst_next_state false
% 0.20/0.44 % --bmc1_pre_inst_state false
% 0.20/0.44 % --bmc1_pre_inst_reach_state false
% 0.20/0.44 % --bmc1_out_unsat_core false
% 0.20/0.44 % --bmc1_aig_witness_out false
% 0.20/0.44 % --bmc1_verbose false
% 0.20/0.44 % --bmc1_dump_clauses_tptp false
% 0.50/0.81 % --bmc1_dump_unsat_core_tptp false
% 0.50/0.81 % --bmc1_dump_file -
% 0.50/0.81 % --bmc1_ucm_expand_uc_limit 128
% 0.50/0.81 % --bmc1_ucm_n_expand_iterations 6
% 0.50/0.81 % --bmc1_ucm_extend_mode 1
% 0.50/0.81 % --bmc1_ucm_init_mode 2
% 0.50/0.81 % --bmc1_ucm_cone_mode none
% 0.50/0.81 % --bmc1_ucm_reduced_relation_type 0
% 0.50/0.81 % --bmc1_ucm_relax_model 4
% 0.50/0.81 % --bmc1_ucm_full_tr_after_sat true
% 0.50/0.81 % --bmc1_ucm_expand_neg_assumptions false
% 0.50/0.81 % --bmc1_ucm_layered_model none
% 0.50/0.81 % --bmc1_ucm_max_lemma_size 10
% 0.50/0.81
% 0.50/0.81 % ------ AIG Options
% 0.50/0.81
% 0.50/0.81 % --aig_mode false
% 0.50/0.81
% 0.50/0.81 % ------ Instantiation Options
% 0.50/0.81
% 0.50/0.81 % --instantiation_flag true
% 0.50/0.81 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.50/0.81 % --inst_solver_per_active 750
% 0.50/0.81 % --inst_solver_calls_frac 0.5
% 0.50/0.81 % --inst_passive_queue_type priority_queues
% 0.50/0.81 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.50/0.81 % --inst_passive_queues_freq [25;2]
% 0.50/0.81 % --inst_dismatching true
% 0.50/0.81 % --inst_eager_unprocessed_to_passive true
% 0.50/0.81 % --inst_prop_sim_given true
% 0.50/0.81 % --inst_prop_sim_new false
% 0.50/0.81 % --inst_orphan_elimination true
% 0.50/0.81 % --inst_learning_loop_flag true
% 0.50/0.81 % --inst_learning_start 3000
% 0.50/0.81 % --inst_learning_factor 2
% 0.50/0.81 % --inst_start_prop_sim_after_learn 3
% 0.50/0.81 % --inst_sel_renew solver
% 0.50/0.81 % --inst_lit_activity_flag true
% 0.50/0.81 % --inst_out_proof true
% 0.50/0.81
% 0.50/0.81 % ------ Resolution Options
% 0.50/0.81
% 0.50/0.81 % --resolution_flag true
% 0.50/0.81 % --res_lit_sel kbo_max
% 0.50/0.81 % --res_to_prop_solver none
% 0.50/0.81 % --res_prop_simpl_new false
% 0.50/0.81 % --res_prop_simpl_given false
% 0.50/0.81 % --res_passive_queue_type priority_queues
% 0.50/0.81 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.50/0.81 % --res_passive_queues_freq [15;5]
% 0.50/0.81 % --res_forward_subs full
% 0.50/0.81 % --res_backward_subs full
% 0.50/0.81 % --res_forward_subs_resolution true
% 0.50/0.81 % --res_backward_subs_resolution true
% 0.50/0.81 % --res_orphan_elimination false
% 0.50/0.81 % --res_time_limit 1000.
% 0.50/0.81 % --res_out_proof true
% 0.50/0.81 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_7ff647.s
% 0.50/0.81 % --modulo true
% 0.50/0.81
% 0.50/0.81 % ------ Combination Options
% 0.50/0.81
% 0.50/0.81 % --comb_res_mult 1000
% 0.50/0.81 % --comb_inst_mult 300
% 0.50/0.81 % ------
% 0.50/0.81
% 0.50/0.81 % ------ Parsing...% successful
% 0.50/0.81
% 0.50/0.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.50/0.81
% 0.50/0.81 % ------ Proving...
% 0.50/0.81 % ------ Problem Properties
% 0.50/0.81
% 0.50/0.81 %
% 0.50/0.81 % EPR false
% 0.50/0.81 % Horn false
% 0.50/0.81 % Has equality true
% 0.50/0.81
% 0.50/0.81 % % ------ Input Options Time Limit: Unbounded
% 0.50/0.81
% 0.50/0.81
% 0.50/0.81 Compiling...
% 0.50/0.81 Loading plugin: done.
% 0.50/0.81 Compiling...
% 0.50/0.81 Loading plugin: done.
% 0.50/0.81 Compiling...
% 0.50/0.81 Loading plugin: done.
% 0.50/0.81 % % ------ Current options:
% 0.50/0.81
% 0.50/0.81 % ------ Input Options
% 0.50/0.81
% 0.50/0.81 % --out_options all
% 0.50/0.81 % --tptp_safe_out true
% 0.50/0.81 % --problem_path ""
% 0.50/0.81 % --include_path ""
% 0.50/0.81 % --clausifier .//eprover
% 0.50/0.81 % --clausifier_options --tstp-format
% 0.50/0.81 % --stdin false
% 0.50/0.81 % --dbg_backtrace false
% 0.50/0.81 % --dbg_dump_prop_clauses false
% 0.50/0.81 % --dbg_dump_prop_clauses_file -
% 0.50/0.81 % --dbg_out_stat false
% 0.50/0.81
% 0.50/0.81 % ------ General Options
% 0.50/0.81
% 0.50/0.81 % --fof false
% 0.50/0.81 % --time_out_real 150.
% 0.50/0.81 % --time_out_prep_mult 0.2
% 0.50/0.81 % --time_out_virtual -1.
% 0.50/0.81 % --schedule none
% 0.50/0.81 % --ground_splitting input
% 0.50/0.81 % --splitting_nvd 16
% 0.50/0.81 % --non_eq_to_eq false
% 0.50/0.81 % --prep_gs_sim true
% 0.50/0.81 % --prep_unflatten false
% 0.50/0.81 % --prep_res_sim true
% 0.50/0.81 % --prep_upred true
% 0.50/0.81 % --res_sim_input true
% 0.50/0.81 % --clause_weak_htbl true
% 0.50/0.81 % --gc_record_bc_elim false
% 0.50/0.81 % --symbol_type_check false
% 0.50/0.81 % --clausify_out false
% 0.50/0.81 % --large_theory_mode false
% 0.50/0.81 % --prep_sem_filter none
% 0.50/0.81 % --prep_sem_filter_out false
% 0.50/0.81 % --preprocessed_out false
% 0.50/0.81 % --sub_typing false
% 0.50/0.81 % --brand_transform false
% 0.50/0.81 % --pure_diseq_elim true
% 0.50/0.81 % --min_unsat_core false
% 0.50/0.81 % --pred_elim true
% 0.50/0.81 % --add_important_lit false
% 0.50/0.81 % --soft_assumptions false
% 0.50/0.81 % --reset_solvers false
% 0.50/0.81 % --bc_imp_inh []
% 0.50/0.81 % --conj_cone_tolerance 1.5
% 0.50/0.81 % --prolific_symb_bound 500
% 0.50/0.81 % --lt_threshold 2000
% 0.50/0.81
% 0.50/0.81 % ------ SAT Options
% 0.50/0.81
% 0.50/0.81 % --sat_mode false
% 0.50/0.81 % --sat_fm_restart_options ""
% 0.50/0.81 % --sat_gr_def false
% 0.50/0.81 % --sat_epr_types true
% 0.50/0.81 % --sat_non_cyclic_types false
% 0.50/0.81 % --sat_finite_models false
% 0.50/0.81 % --sat_fm_lemmas false
% 0.50/0.81 % --sat_fm_prep false
% 0.50/0.81 % --sat_fm_uc_incr true
% 0.50/0.81 % --sat_out_model small
% 0.50/0.81 % --sat_out_clauses false
% 0.50/0.81
% 0.50/0.81 % ------ QBF Options
% 0.50/0.81
% 0.50/0.81 % --qbf_mode false
% 0.50/0.81 % --qbf_elim_univ true
% 0.50/0.81 % --qbf_sk_in true
% 0.50/0.81 % --qbf_pred_elim true
% 0.50/0.81 % --qbf_split 32
% 0.50/0.81
% 0.50/0.81 % ------ BMC1 Options
% 0.50/0.81
% 0.50/0.81 % --bmc1_incremental false
% 0.50/0.81 % --bmc1_axioms reachable_all
% 0.50/0.81 % --bmc1_min_bound 0
% 0.50/0.81 % --bmc1_max_bound -1
% 0.50/0.81 % --bmc1_max_bound_default -1
% 0.50/0.81 % --bmc1_symbol_reachability true
% 0.50/0.81 % --bmc1_property_lemmas false
% 0.50/0.81 % --bmc1_k_induction false
% 0.50/0.81 % --bmc1_non_equiv_states false
% 0.50/0.81 % --bmc1_deadlock false
% 0.50/0.81 % --bmc1_ucm false
% 0.50/0.81 % --bmc1_add_unsat_core none
% 0.50/0.81 % --bmc1_unsat_core_children false
% 0.50/0.81 % --bmc1_unsat_core_extrapolate_axioms false
% 0.50/0.81 % --bmc1_out_stat full
% 0.50/0.81 % --bmc1_ground_init false
% 0.50/0.81 % --bmc1_pre_inst_next_state false
% 0.50/0.81 % --bmc1_pre_inst_state false
% 0.50/0.81 % --bmc1_pre_inst_reach_state false
% 0.50/0.81 % --bmc1_out_unsat_core false
% 0.50/0.81 % --bmc1_aig_witness_out false
% 0.50/0.81 % --bmc1_verbose false
% 0.50/0.81 % --bmc1_dump_clauses_tptp false
% 0.50/0.81 % --bmc1_dump_unsat_core_tptp false
% 0.50/0.81 % --bmc1_dump_file -
% 0.50/0.81 % --bmc1_ucm_expand_uc_limit 128
% 0.50/0.81 % --bmc1_ucm_n_expand_iterations 6
% 0.50/0.81 % --bmc1_ucm_extend_mode 1
% 0.50/0.81 % --bmc1_ucm_init_mode 2
% 0.50/0.81 % --bmc1_ucm_cone_mode none
% 0.50/0.81 % --bmc1_ucm_reduced_relation_type 0
% 0.50/0.81 % --bmc1_ucm_relax_model 4
% 0.50/0.81 % --bmc1_ucm_full_tr_after_sat true
% 0.50/0.81 % --bmc1_ucm_expand_neg_assumptions false
% 0.50/0.81 % --bmc1_ucm_layered_model none
% 0.50/0.81 % --bmc1_ucm_max_lemma_size 10
% 0.50/0.81
% 0.50/0.81 % ------ AIG Options
% 0.50/0.81
% 0.50/0.81 % --aig_mode false
% 0.50/0.81
% 0.50/0.81 % ------ Instantiation Options
% 0.50/0.81
% 0.50/0.81 % --instantiation_flag true
% 0.50/0.81 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.50/0.81 % --inst_solver_per_active 750
% 0.50/0.81 % --inst_solver_calls_frac 0.5
% 0.50/0.81 % --inst_passive_queue_type priority_queues
% 0.50/0.81 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.50/0.81 % --inst_passive_queues_freq [25;2]
% 0.50/0.81 % --inst_dismatching true
% 5.69/5.96 % --inst_eager_unprocessed_to_passive true
% 5.69/5.96 % --inst_prop_sim_given true
% 5.69/5.96 % --inst_prop_sim_new false
% 5.69/5.96 % --inst_orphan_elimination true
% 5.69/5.96 % --inst_learning_loop_flag true
% 5.69/5.96 % --inst_learning_start 3000
% 5.69/5.96 % --inst_learning_factor 2
% 5.69/5.96 % --inst_start_prop_sim_after_learn 3
% 5.69/5.96 % --inst_sel_renew solver
% 5.69/5.96 % --inst_lit_activity_flag true
% 5.69/5.96 % --inst_out_proof true
% 5.69/5.96
% 5.69/5.96 % ------ Resolution Options
% 5.69/5.96
% 5.69/5.96 % --resolution_flag true
% 5.69/5.96 % --res_lit_sel kbo_max
% 5.69/5.96 % --res_to_prop_solver none
% 5.69/5.96 % --res_prop_simpl_new false
% 5.69/5.96 % --res_prop_simpl_given false
% 5.69/5.96 % --res_passive_queue_type priority_queues
% 5.69/5.96 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 5.69/5.96 % --res_passive_queues_freq [15;5]
% 5.69/5.96 % --res_forward_subs full
% 5.69/5.96 % --res_backward_subs full
% 5.69/5.96 % --res_forward_subs_resolution true
% 5.69/5.96 % --res_backward_subs_resolution true
% 5.69/5.96 % --res_orphan_elimination false
% 5.69/5.96 % --res_time_limit 1000.
% 5.69/5.96 % --res_out_proof true
% 5.69/5.96 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_7ff647.s
% 5.69/5.96 % --modulo true
% 5.69/5.96
% 5.69/5.96 % ------ Combination Options
% 5.69/5.96
% 5.69/5.96 % --comb_res_mult 1000
% 5.69/5.96 % --comb_inst_mult 300
% 5.69/5.96 % ------
% 5.69/5.96
% 5.69/5.96
% 5.69/5.96
% 5.69/5.96 % ------ Proving...
% 5.69/5.96 %
% 5.69/5.96
% 5.69/5.96
% 5.69/5.96 % ------ Statistics
% 5.69/5.96
% 5.69/5.96 % ------ General
% 5.69/5.96
% 5.69/5.96 % num_of_input_clauses: 390
% 5.69/5.96 % num_of_input_neg_conjectures: 1
% 5.69/5.96 % num_of_splits: 0
% 5.69/5.96 % num_of_split_atoms: 0
% 5.69/5.96 % num_of_sem_filtered_clauses: 0
% 5.69/5.96 % num_of_subtypes: 0
% 5.69/5.96 % monotx_restored_types: 0
% 5.69/5.96 % sat_num_of_epr_types: 0
% 5.69/5.96 % sat_num_of_non_cyclic_types: 0
% 5.69/5.96 % sat_guarded_non_collapsed_types: 0
% 5.69/5.96 % is_epr: 0
% 5.69/5.96 % is_horn: 0
% 5.69/5.96 % has_eq: 1
% 5.69/5.96 % num_pure_diseq_elim: 0
% 5.69/5.96 % simp_replaced_by: 0
% 5.69/5.96 % res_preprocessed: 4
% 5.69/5.96 % prep_upred: 0
% 5.69/5.96 % prep_unflattend: 0
% 5.69/5.96 % pred_elim_cands: 0
% 5.69/5.96 % pred_elim: 0
% 5.69/5.96 % pred_elim_cl: 0
% 5.69/5.96 % pred_elim_cycles: 0
% 5.69/5.96 % forced_gc_time: 0
% 5.69/5.96 % gc_basic_clause_elim: 0
% 5.69/5.96 % parsing_time: 0.017
% 5.69/5.96 % sem_filter_time: 0.
% 5.69/5.96 % pred_elim_time: 0.
% 5.69/5.96 % out_proof_time: 0.
% 5.69/5.96 % monotx_time: 0.
% 5.69/5.96 % subtype_inf_time: 0.
% 5.69/5.96 % unif_index_cands_time: 0.039
% 5.69/5.96 % unif_index_add_time: 0.011
% 5.69/5.96 % total_time: 5.535
% 5.69/5.96 % num_of_symbols: 100
% 5.69/5.96 % num_of_terms: 82417
% 5.69/5.96
% 5.69/5.96 % ------ Propositional Solver
% 5.69/5.96
% 5.69/5.96 % prop_solver_calls: 6
% 5.69/5.96 % prop_fast_solver_calls: 7
% 5.69/5.96 % prop_num_of_clauses: 3247
% 5.69/5.96 % prop_preprocess_simplified: 5147
% 5.69/5.96 % prop_fo_subsumed: 0
% 5.69/5.96 % prop_solver_time: 0.001
% 5.69/5.96 % prop_fast_solver_time: 0.
% 5.69/5.96 % prop_unsat_core_time: 0.
% 5.69/5.96
% 5.69/5.96 % ------ QBF
% 5.69/5.96
% 5.69/5.96 % qbf_q_res: 0
% 5.69/5.96 % qbf_num_tautologies: 0
% 5.69/5.96 % qbf_prep_cycles: 0
% 5.69/5.96
% 5.69/5.96 % ------ BMC1
% 5.69/5.96
% 5.69/5.96 % bmc1_current_bound: -1
% 5.69/5.96 % bmc1_last_solved_bound: -1
% 5.69/5.96 % bmc1_unsat_core_size: -1
% 5.69/5.96 % bmc1_unsat_core_parents_size: -1
% 5.69/5.96 % bmc1_merge_next_fun: 0
% 5.69/5.96 % bmc1_unsat_core_clauses_time: 0.
% 5.69/5.96
% 5.69/5.96 % ------ Instantiation
% 5.69/5.96
% 5.69/5.96 % inst_num_of_clauses: 2179
% 5.69/5.96 % inst_num_in_passive: 1168
% 5.69/5.96 % inst_num_in_active: 834
% 5.69/5.97 % inst_num_in_unprocessed: 175
% 5.69/5.97 % inst_num_of_loops: 986
% 5.69/5.97 % inst_num_of_learning_restarts: 0
% 5.69/5.97 % inst_num_moves_active_passive: 150
% 5.69/5.97 % inst_lit_activity: 306
% 5.69/5.97 % inst_lit_activity_moves: 0
% 5.69/5.97 % inst_num_tautologies: 0
% 5.69/5.97 % inst_num_prop_implied: 0
% 5.69/5.97 % inst_num_existing_simplified: 0
% 5.69/5.97 % inst_num_eq_res_simplified: 0
% 5.69/5.97 % inst_num_child_elim: 0
% 5.69/5.97 % inst_num_of_dismatching_blockings: 1536
% 5.69/5.97 % inst_num_of_non_proper_insts: 1881
% 5.69/5.97 % inst_num_of_duplicates: 1888
% 5.69/5.97 % inst_inst_num_from_inst_to_res: 0
% 5.69/5.97 % inst_dismatching_checking_time: 0.004
% 5.69/5.97
% 5.69/5.97 % ------ Resolution
% 5.69/5.97
% 5.69/5.97 % res_num_of_clauses: 54923
% 5.69/5.97 % res_num_in_passive: 51686
% 5.69/5.97 % res_num_in_active: 2977
% 5.69/5.97 % res_num_of_loops: 4000
% 5.69/5.97 % res_forward_subset_subsumed: 11017
% 5.69/5.97 % res_backward_subset_subsumed: 9
% 5.69/5.97 % res_forward_subsumed: 1203
% 5.69/5.97 % res_backward_subsumed: 2
% 5.69/5.97 % res_forward_subsumption_resolution: 515
% 5.69/5.97 % res_backward_subsumption_resolution: 0
% 5.69/5.97 % res_clause_to_clause_subsumption: 89748
% 5.69/5.97 % res_orphan_elimination: 0
% 5.69/5.97 % res_tautology_del: 9
% 5.69/5.97 % res_num_eq_res_simplified: 0
% 5.69/5.97 % res_num_sel_changes: 0
% 5.69/5.97 % res_moves_from_active_to_pass: 0
% 5.69/5.97
% 5.69/5.97 % Status Unsatisfiable
% 5.69/5.97 % SZS status Unsatisfiable
% 5.69/5.97 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------