%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n012.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 10:25:36 EDT 2022
% Result : Theorem 157.36s 157.57s
% Output : CNFRefutation 157.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 114
% Syntax : Number of formulae : 1004 ( 273 unt; 0 def)
% Number of atoms : 2546 ( 759 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 2640 (1098 ~;1217 |; 177 &)
% ( 70 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 65 ( 65 usr; 11 con; 0-4 aty)
% Number of variables : 2319 ( 135 sgn 717 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('<stdin>',d2_zfmisc_1) ).
fof(c_0_1,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('<stdin>',d3_xboole_0) ).
fof(c_0_2,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('<stdin>',d4_xboole_0) ).
fof(c_0_3,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('<stdin>',d2_xboole_0) ).
fof(c_0_4,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_5,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_6,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_7,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_8,axiom,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('<stdin>',t9_tarski) ).
fof(c_0_9,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_10,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_11,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_12,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_13,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_14,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_15,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_16,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_17,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_18,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('<stdin>',d2_subset_1) ).
fof(c_0_19,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_20,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_21,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_22,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_23,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_24,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_25,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_26,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_27,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_28,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_29,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_30,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_31,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_32,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_33,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_34,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_35,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_36,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_37,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_38,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_39,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_40,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_41,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_42,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_43,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_44,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_45,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_46,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_47,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_48,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_49,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_50,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_51,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_52,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_53,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_54,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
c_0_0 ).
fof(c_0_55,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_1 ).
fof(c_0_56,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_57,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_3 ).
fof(c_0_58,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_4 ).
fof(c_0_59,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_5 ).
fof(c_0_60,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_6 ).
fof(c_0_61,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_7 ).
fof(c_0_62,plain,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_63,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_9 ).
fof(c_0_64,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_10 ).
fof(c_0_65,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_11 ).
fof(c_0_66,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_67,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_68,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_69,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_15 ).
fof(c_0_70,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_71,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_72,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_73,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_19 ).
fof(c_0_74,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_20 ).
fof(c_0_75,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_21 ).
fof(c_0_76,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_77,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_23 ).
fof(c_0_78,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_24 ).
fof(c_0_79,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_25 ).
fof(c_0_80,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_26 ).
fof(c_0_81,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_82,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_83,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_29 ).
fof(c_0_84,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_85,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_31 ).
fof(c_0_86,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_32 ).
fof(c_0_87,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_33 ).
fof(c_0_88,axiom,
! [X1,X2] : subset(X1,X1),
c_0_34 ).
fof(c_0_89,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_35 ).
fof(c_0_90,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_36 ).
fof(c_0_91,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_37 ).
fof(c_0_92,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_38 ).
fof(c_0_93,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_39 ).
fof(c_0_94,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_95,axiom,
? [X1] : empty(X1),
c_0_41 ).
fof(c_0_96,axiom,
empty(empty_set),
c_0_42 ).
fof(c_0_97,axiom,
$true,
c_0_43 ).
fof(c_0_98,axiom,
$true,
c_0_44 ).
fof(c_0_99,axiom,
$true,
c_0_45 ).
fof(c_0_100,axiom,
$true,
c_0_46 ).
fof(c_0_101,axiom,
$true,
c_0_47 ).
fof(c_0_102,axiom,
$true,
c_0_48 ).
fof(c_0_103,axiom,
$true,
c_0_49 ).
fof(c_0_104,axiom,
$true,
c_0_50 ).
fof(c_0_105,axiom,
$true,
c_0_51 ).
fof(c_0_106,axiom,
$true,
c_0_52 ).
fof(c_0_107,axiom,
$true,
c_0_53 ).
fof(c_0_108,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk6_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk7_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk6_4(X7,X8,X9,X10),esk7_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(X14,X7)
| ~ in(X15,X8)
| X13 != ordered_pair(X14,X15)
| in(X13,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(esk8_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk8_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk9_3(X16,X17,X18),X16)
| in(esk8_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk10_3(X16,X17,X18),X17)
| in(esk8_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk8_3(X16,X17,X18) = ordered_pair(esk9_3(X16,X17,X18),esk10_3(X16,X17,X18))
| in(esk8_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])])])]) ).
fof(c_0_109,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X9,X5)
| ~ in(X9,X6)
| in(X9,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk12_3(X10,X11,X12),X12)
| ~ in(esk12_3(X10,X11,X12),X10)
| ~ in(esk12_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk12_3(X10,X11,X12),X10)
| in(esk12_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk12_3(X10,X11,X12),X11)
| in(esk12_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])])]) ).
fof(c_0_110,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X9,X5)
| in(X9,X6)
| in(X9,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk16_3(X10,X11,X12),X12)
| ~ in(esk16_3(X10,X11,X12),X10)
| in(esk16_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk16_3(X10,X11,X12),X10)
| in(esk16_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk16_3(X10,X11,X12),X11)
| in(esk16_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])])])]) ).
fof(c_0_111,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X9,X5)
| in(X9,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X9,X6)
| in(X9,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk5_3(X10,X11,X12),X10)
| ~ in(esk5_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk5_3(X10,X11,X12),X11)
| ~ in(esk5_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk5_3(X10,X11,X12),X12)
| in(esk5_3(X10,X11,X12),X10)
| in(esk5_3(X10,X11,X12),X11)
| X12 = set_union2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])])]) ).
fof(c_0_112,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X9 != X5
| in(X9,X7)
| X7 != unordered_pair(X5,X6) )
& ( X9 != X6
| in(X9,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk4_3(X10,X11,X12) != X10
| ~ in(esk4_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk4_3(X10,X11,X12) != X11
| ~ in(esk4_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk4_3(X10,X11,X12),X12)
| esk4_3(X10,X11,X12) = X10
| esk4_3(X10,X11,X12) = X11
| X12 = unordered_pair(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])])])]) ).
fof(c_0_113,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk13_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk13_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk14_2(X11,X12),X12)
| ~ in(esk14_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk14_2(X11,X12),esk15_2(X11,X12))
| in(esk14_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk15_2(X11,X12),X11)
| in(esk14_2(X11,X12),X12)
| X12 = union(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])])]) ).
fof(c_0_114,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X7,X4)
| in(X7,X5)
| X5 != powerset(X4) )
& ( ~ in(esk3_2(X8,X9),X9)
| ~ subset(esk3_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk3_2(X8,X9),X9)
| subset(esk3_2(X8,X9),X8)
| X9 = powerset(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])])])]) ).
fof(c_0_115,plain,
! [X4,X5] :
( ( ~ in(esk21_2(X4,X5),X4)
| ~ in(esk21_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk21_2(X4,X5),X4)
| in(esk21_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
fof(c_0_116,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk22_1(X6))
& ( ~ in(X8,esk22_1(X6))
| ~ subset(X9,X8)
| in(X9,esk22_1(X6)) )
& ( in(esk23_2(X6,X10),esk22_1(X6))
| ~ in(X10,esk22_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk23_2(X6,X10))
| ~ in(X10,esk22_1(X6)) )
& ( ~ subset(X13,esk22_1(X6))
| are_equipotent(X13,esk22_1(X6))
| in(X13,esk22_1(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])])]) ).
fof(c_0_117,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk1_2(X8,X9),X9)
| esk1_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk1_2(X8,X9),X9)
| esk1_2(X8,X9) = X8
| X9 = singleton(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])])])]) ).
fof(c_0_118,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk11_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk11_2(X7,X8),X8)
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])])])]) ).
fof(c_0_119,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_120,plain,
! [X3,X4] :
( empty(X3)
| ~ empty(set_union2(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])]) ).
fof(c_0_121,plain,
! [X3,X4] :
( empty(X3)
| ~ empty(set_union2(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
fof(c_0_122,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_123,plain,
! [X3,X4,X5,X6] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X5,X6)
| ~ subset(X6,X5)
| X5 = X6 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])])]) ).
fof(c_0_124,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])]) ).
fof(c_0_125,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])]) ).
fof(c_0_126,plain,
! [X3,X4,X5,X6,X7,X8] :
( ( ~ element(X4,X3)
| in(X4,X3)
| empty(X3) )
& ( ~ in(X5,X3)
| element(X5,X3)
| empty(X3) )
& ( ~ element(X7,X6)
| empty(X7)
| ~ empty(X6) )
& ( ~ empty(X8)
| element(X8,X6)
| ~ empty(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])])]) ).
fof(c_0_127,plain,
! [X3,X4,X5,X6] :
( ( subset(X3,X4)
| ~ proper_subset(X3,X4) )
& ( X3 != X4
| ~ proper_subset(X3,X4) )
& ( ~ subset(X5,X6)
| X5 = X6
| proper_subset(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])])]) ).
fof(c_0_128,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])]) ).
fof(c_0_129,plain,
! [X3,X4,X5,X6] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X5,X6) != empty_set
| disjoint(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])]) ).
fof(c_0_130,plain,
! [X3] :
( ( element(esk18_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk18_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])]) ).
fof(c_0_131,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])]) ).
fof(c_0_132,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_78]) ).
fof(c_0_133,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_79]) ).
fof(c_0_134,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_80]) ).
fof(c_0_135,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk2_1(X5),X5)
| X5 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])])])])]) ).
fof(c_0_136,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_82]) ).
fof(c_0_137,plain,
! [X3] : element(esk17_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_83])]) ).
fof(c_0_138,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_84]) ).
fof(c_0_139,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])]) ).
fof(c_0_140,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_86]) ).
fof(c_0_141,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_87]) ).
fof(c_0_142,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_88]) ).
fof(c_0_143,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_89]) ).
fof(c_0_144,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_90]) ).
fof(c_0_145,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_91]) ).
fof(c_0_146,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_92]) ).
fof(c_0_147,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])]) ).
fof(c_0_148,plain,
~ empty(esk20_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_94])]) ).
fof(c_0_149,plain,
empty(esk19_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_95])]) ).
fof(c_0_150,axiom,
empty(empty_set),
c_0_96 ).
fof(c_0_151,axiom,
$true,
c_0_97 ).
fof(c_0_152,axiom,
$true,
c_0_98 ).
fof(c_0_153,axiom,
$true,
c_0_99 ).
fof(c_0_154,axiom,
$true,
c_0_100 ).
fof(c_0_155,axiom,
$true,
c_0_101 ).
fof(c_0_156,axiom,
$true,
c_0_102 ).
fof(c_0_157,axiom,
$true,
c_0_103 ).
fof(c_0_158,axiom,
$true,
c_0_104 ).
fof(c_0_159,axiom,
$true,
c_0_105 ).
fof(c_0_160,axiom,
$true,
c_0_106 ).
fof(c_0_161,axiom,
$true,
c_0_107 ).
cnf(c_0_162,plain,
( X4 = ordered_pair(esk6_4(X2,X3,X1,X4),esk7_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_163,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk12_3(X2,X3,X1),X3)
| ~ in(esk12_3(X2,X3,X1),X2)
| ~ in(esk12_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_164,plain,
( in(esk6_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_165,plain,
( in(esk7_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_166,plain,
( X1 = set_difference(X2,X3)
| in(esk16_3(X2,X3,X1),X3)
| ~ in(esk16_3(X2,X3,X1),X2)
| ~ in(esk16_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_167,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| esk8_3(X2,X3,X1) = ordered_pair(esk9_3(X2,X3,X1),esk10_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_168,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk5_3(X2,X3,X1),X1)
| ~ in(esk5_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_169,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk5_3(X2,X3,X1),X1)
| ~ in(esk5_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_170,plain,
( X1 = set_union2(X2,X3)
| in(esk5_3(X2,X3,X1),X3)
| in(esk5_3(X2,X3,X1),X2)
| in(esk5_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_171,plain,
( X1 = cartesian_product2(X2,X3)
| esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk8_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_172,plain,
( X1 = set_difference(X2,X3)
| in(esk16_3(X2,X3,X1),X1)
| ~ in(esk16_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_173,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk4_3(X2,X3,X1),X1)
| esk4_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_174,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk4_3(X2,X3,X1),X1)
| esk4_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_175,plain,
( X1 = set_difference(X2,X3)
| in(esk16_3(X2,X3,X1),X1)
| in(esk16_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_176,plain,
( X1 = set_intersection2(X2,X3)
| in(esk12_3(X2,X3,X1),X1)
| in(esk12_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_177,plain,
( X1 = set_intersection2(X2,X3)
| in(esk12_3(X2,X3,X1),X1)
| in(esk12_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_178,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| in(esk9_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_179,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| in(esk10_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_180,plain,
( X1 = unordered_pair(X2,X3)
| esk4_3(X2,X3,X1) = X3
| esk4_3(X2,X3,X1) = X2
| in(esk4_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_181,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk14_2(X2,X1),X3)
| ~ in(esk14_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_182,plain,
( in(X3,esk13_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_183,plain,
( in(esk13_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_184,plain,
( X1 = powerset(X2)
| ~ subset(esk3_2(X2,X1),X2)
| ~ in(esk3_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_185,plain,
( X1 = X2
| ~ in(esk21_2(X1,X2),X2)
| ~ in(esk21_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_186,plain,
( X1 = union(X2)
| in(esk14_2(X2,X1),X1)
| in(esk14_2(X2,X1),esk15_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_187,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_188,plain,
( in(X3,esk23_2(X2,X1))
| ~ in(X1,esk22_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_189,plain,
( X1 = singleton(X2)
| esk1_2(X2,X1) != X2
| ~ in(esk1_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_190,plain,
( X1 = union(X2)
| in(esk14_2(X2,X1),X1)
| in(esk15_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_191,plain,
( X1 = powerset(X2)
| subset(esk3_2(X2,X1),X2)
| in(esk3_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_192,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_193,plain,
( X1 = X2
| in(esk21_2(X1,X2),X2)
| in(esk21_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_194,plain,
( in(esk23_2(X2,X1),esk22_1(X2))
| ~ in(X1,esk22_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_195,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_196,plain,
( in(X1,esk22_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk22_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_197,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_198,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_199,plain,
( in(X1,esk22_1(X2))
| are_equipotent(X1,esk22_1(X2))
| ~ subset(X1,esk22_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_200,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_201,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_202,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_203,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_204,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_205,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_206,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_207,plain,
( X1 = singleton(X2)
| esk1_2(X2,X1) = X2
| in(esk1_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_208,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_209,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_210,plain,
( subset(X1,X2)
| in(esk11_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_211,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_212,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_213,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_214,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_215,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_216,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_217,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_218,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_219,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_220,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_221,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_222,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_223,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_224,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_225,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_226,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_227,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_228,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_229,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_230,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_231,plain,
( empty(X1)
| element(esk18_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_232,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_233,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_234,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_235,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_236,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_237,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_238,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_239,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_240,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_241,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_242,plain,
( empty(X1)
| ~ empty(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_243,plain,
in(X1,esk22_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_244,plain,
element(esk17_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_245,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_246,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_247,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_248,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_249,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_250,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_251,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_252,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_253,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_254,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_255,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_256,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_257,plain,
~ empty(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_258,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_259,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_260,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_261,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_262,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_263,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_264,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_155]) ).
cnf(c_0_265,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_266,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_267,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_268,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_269,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_270,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_271,plain,
( ordered_pair(esk6_4(X2,X3,X1,X4),esk7_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_162,
[final] ).
cnf(c_0_272,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk12_3(X2,X3,X1),X3)
| ~ in(esk12_3(X2,X3,X1),X2)
| ~ in(esk12_3(X2,X3,X1),X1) ),
c_0_163,
[final] ).
cnf(c_0_273,plain,
( in(esk6_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_164,
[final] ).
cnf(c_0_274,plain,
( in(esk7_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_165,
[final] ).
cnf(c_0_275,plain,
( X1 = set_difference(X2,X3)
| in(esk16_3(X2,X3,X1),X3)
| ~ in(esk16_3(X2,X3,X1),X2)
| ~ in(esk16_3(X2,X3,X1),X1) ),
c_0_166,
[final] ).
cnf(c_0_276,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| ordered_pair(esk9_3(X2,X3,X1),esk10_3(X2,X3,X1)) = esk8_3(X2,X3,X1) ),
c_0_167,
[final] ).
cnf(c_0_277,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk5_3(X2,X3,X1),X1)
| ~ in(esk5_3(X2,X3,X1),X2) ),
c_0_168,
[final] ).
cnf(c_0_278,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk5_3(X2,X3,X1),X1)
| ~ in(esk5_3(X2,X3,X1),X3) ),
c_0_169,
[final] ).
cnf(c_0_279,plain,
( X1 = set_union2(X2,X3)
| in(esk5_3(X2,X3,X1),X3)
| in(esk5_3(X2,X3,X1),X2)
| in(esk5_3(X2,X3,X1),X1) ),
c_0_170,
[final] ).
cnf(c_0_280,plain,
( X1 = cartesian_product2(X2,X3)
| esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk8_3(X2,X3,X1),X1) ),
c_0_171,
[final] ).
cnf(c_0_281,plain,
( X1 = set_difference(X2,X3)
| in(esk16_3(X2,X3,X1),X1)
| ~ in(esk16_3(X2,X3,X1),X3) ),
c_0_172,
[final] ).
cnf(c_0_282,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk4_3(X2,X3,X1),X1)
| esk4_3(X2,X3,X1) != X2 ),
c_0_173,
[final] ).
cnf(c_0_283,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk4_3(X2,X3,X1),X1)
| esk4_3(X2,X3,X1) != X3 ),
c_0_174,
[final] ).
cnf(c_0_284,plain,
( X1 = set_difference(X2,X3)
| in(esk16_3(X2,X3,X1),X1)
| in(esk16_3(X2,X3,X1),X2) ),
c_0_175,
[final] ).
cnf(c_0_285,plain,
( X1 = set_intersection2(X2,X3)
| in(esk12_3(X2,X3,X1),X1)
| in(esk12_3(X2,X3,X1),X2) ),
c_0_176,
[final] ).
cnf(c_0_286,plain,
( X1 = set_intersection2(X2,X3)
| in(esk12_3(X2,X3,X1),X1)
| in(esk12_3(X2,X3,X1),X3) ),
c_0_177,
[final] ).
cnf(c_0_287,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| in(esk9_3(X2,X3,X1),X2) ),
c_0_178,
[final] ).
cnf(c_0_288,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| in(esk10_3(X2,X3,X1),X3) ),
c_0_179,
[final] ).
cnf(c_0_289,plain,
( X1 = unordered_pair(X2,X3)
| esk4_3(X2,X3,X1) = X3
| esk4_3(X2,X3,X1) = X2
| in(esk4_3(X2,X3,X1),X1) ),
c_0_180,
[final] ).
cnf(c_0_290,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk14_2(X2,X1),X3)
| ~ in(esk14_2(X2,X1),X1) ),
c_0_181,
[final] ).
cnf(c_0_291,plain,
( in(X3,esk13_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_182,
[final] ).
cnf(c_0_292,plain,
( in(esk13_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_183,
[final] ).
cnf(c_0_293,plain,
( X1 = powerset(X2)
| ~ subset(esk3_2(X2,X1),X2)
| ~ in(esk3_2(X2,X1),X1) ),
c_0_184,
[final] ).
cnf(c_0_294,plain,
( X1 = X2
| ~ in(esk21_2(X1,X2),X2)
| ~ in(esk21_2(X1,X2),X1) ),
c_0_185,
[final] ).
cnf(c_0_295,plain,
( X1 = union(X2)
| in(esk14_2(X2,X1),X1)
| in(esk14_2(X2,X1),esk15_2(X2,X1)) ),
c_0_186,
[final] ).
cnf(c_0_296,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_187,
[final] ).
cnf(c_0_297,plain,
( in(X3,esk23_2(X2,X1))
| ~ in(X1,esk22_1(X2))
| ~ subset(X3,X1) ),
c_0_188,
[final] ).
cnf(c_0_298,plain,
( X1 = singleton(X2)
| esk1_2(X2,X1) != X2
| ~ in(esk1_2(X2,X1),X1) ),
c_0_189,
[final] ).
cnf(c_0_299,plain,
( X1 = union(X2)
| in(esk14_2(X2,X1),X1)
| in(esk15_2(X2,X1),X2) ),
c_0_190,
[final] ).
cnf(c_0_300,plain,
( X1 = powerset(X2)
| subset(esk3_2(X2,X1),X2)
| in(esk3_2(X2,X1),X1) ),
c_0_191,
[final] ).
cnf(c_0_301,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_192,
[final] ).
cnf(c_0_302,plain,
( X1 = X2
| in(esk21_2(X1,X2),X2)
| in(esk21_2(X1,X2),X1) ),
c_0_193,
[final] ).
cnf(c_0_303,plain,
( in(esk23_2(X2,X1),esk22_1(X2))
| ~ in(X1,esk22_1(X2)) ),
c_0_194,
[final] ).
cnf(c_0_304,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
c_0_195,
[final] ).
cnf(c_0_305,plain,
( in(X1,esk22_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk22_1(X2)) ),
c_0_196,
[final] ).
cnf(c_0_306,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_197,
[final] ).
cnf(c_0_307,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_198,
[final] ).
cnf(c_0_308,plain,
( in(X1,esk22_1(X2))
| are_equipotent(X1,esk22_1(X2))
| ~ subset(X1,esk22_1(X2)) ),
c_0_199,
[final] ).
cnf(c_0_309,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_200,
[final] ).
cnf(c_0_310,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_201,
[final] ).
cnf(c_0_311,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_202,
[final] ).
cnf(c_0_312,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_203,
[final] ).
cnf(c_0_313,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_204,
[final] ).
cnf(c_0_314,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_205,
[final] ).
cnf(c_0_315,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_206,
[final] ).
cnf(c_0_316,plain,
( X1 = singleton(X2)
| esk1_2(X2,X1) = X2
| in(esk1_2(X2,X1),X1) ),
c_0_207,
[final] ).
cnf(c_0_317,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_208,
[final] ).
cnf(c_0_318,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_209,
[final] ).
cnf(c_0_319,plain,
( subset(X1,X2)
| in(esk11_2(X1,X2),X1) ),
c_0_210,
[final] ).
cnf(c_0_320,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_211,
[final] ).
cnf(c_0_321,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_212,
[final] ).
cnf(c_0_322,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_213,
[final] ).
cnf(c_0_323,plain,
~ empty(ordered_pair(X1,X2)),
c_0_214,
[final] ).
cnf(c_0_324,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_215,
[final] ).
cnf(c_0_325,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_216,
[final] ).
cnf(c_0_326,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_217,
[final] ).
cnf(c_0_327,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_218,
[final] ).
cnf(c_0_328,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_219,
[final] ).
cnf(c_0_329,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_220,
[final] ).
cnf(c_0_330,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_221,
[final] ).
cnf(c_0_331,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_222,
[final] ).
cnf(c_0_332,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_223,
[final] ).
cnf(c_0_333,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_224,
[final] ).
cnf(c_0_334,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_225,
[final] ).
cnf(c_0_335,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_226,
[final] ).
cnf(c_0_336,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_227,
[final] ).
cnf(c_0_337,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_228,
[final] ).
cnf(c_0_338,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_229,
[final] ).
cnf(c_0_339,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_230,
[final] ).
cnf(c_0_340,plain,
( empty(X1)
| element(esk18_1(X1),powerset(X1)) ),
c_0_231,
[final] ).
cnf(c_0_341,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_232,
[final] ).
cnf(c_0_342,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_233,
[final] ).
cnf(c_0_343,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_234,
[final] ).
cnf(c_0_344,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_235,
[final] ).
cnf(c_0_345,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_236,
[final] ).
cnf(c_0_346,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_237,
[final] ).
cnf(c_0_347,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_238,
[final] ).
cnf(c_0_348,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_239,
[final] ).
cnf(c_0_349,plain,
~ proper_subset(X1,X1),
c_0_240,
[final] ).
cnf(c_0_350,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
c_0_241,
[final] ).
cnf(c_0_351,plain,
( empty(X1)
| ~ empty(esk18_1(X1)) ),
c_0_242,
[final] ).
cnf(c_0_352,plain,
in(X1,esk22_1(X1)),
c_0_243,
[final] ).
cnf(c_0_353,plain,
element(esk17_1(X1),X1),
c_0_244,
[final] ).
cnf(c_0_354,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_245,
[final] ).
cnf(c_0_355,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_246,
[final] ).
cnf(c_0_356,plain,
~ empty(powerset(X1)),
c_0_247,
[final] ).
cnf(c_0_357,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_248,
[final] ).
cnf(c_0_358,plain,
set_intersection2(X1,X1) = X1,
c_0_249,
[final] ).
cnf(c_0_359,plain,
set_union2(X1,X1) = X1,
c_0_250,
[final] ).
cnf(c_0_360,plain,
subset(X1,X1),
c_0_251,
[final] ).
cnf(c_0_361,plain,
set_difference(X1,empty_set) = X1,
c_0_252,
[final] ).
cnf(c_0_362,plain,
set_union2(X1,empty_set) = X1,
c_0_253,
[final] ).
cnf(c_0_363,plain,
set_difference(empty_set,X1) = empty_set,
c_0_254,
[final] ).
cnf(c_0_364,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_255,
[final] ).
cnf(c_0_365,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_256,
[final] ).
cnf(c_0_366,plain,
~ empty(esk20_0),
c_0_257,
[final] ).
cnf(c_0_367,plain,
empty(esk19_0),
c_0_258,
[final] ).
cnf(c_0_368,plain,
empty(empty_set),
c_0_259,
[final] ).
cnf(c_0_369,plain,
$true,
c_0_260,
[final] ).
cnf(c_0_370,plain,
$true,
c_0_261,
[final] ).
cnf(c_0_371,plain,
$true,
c_0_262,
[final] ).
cnf(c_0_372,plain,
$true,
c_0_263,
[final] ).
cnf(c_0_373,plain,
$true,
c_0_264,
[final] ).
cnf(c_0_374,plain,
$true,
c_0_265,
[final] ).
cnf(c_0_375,plain,
$true,
c_0_266,
[final] ).
cnf(c_0_376,plain,
$true,
c_0_267,
[final] ).
cnf(c_0_377,plain,
$true,
c_0_268,
[final] ).
cnf(c_0_378,plain,
$true,
c_0_269,
[final] ).
cnf(c_0_379,plain,
$true,
c_0_270,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_271_0,axiom,
( ordered_pair(sk1_esk6_4(X2,X3,X1,X4),sk1_esk7_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_271]) ).
cnf(c_0_271_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk6_4(X2,X3,X1,X4),sk1_esk7_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_271]) ).
cnf(c_0_271_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk6_4(X2,X3,X1,X4),sk1_esk7_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_271]) ).
cnf(c_0_272_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk12_3(X2,X3,X1),X3)
| ~ in(sk1_esk12_3(X2,X3,X1),X2)
| ~ in(sk1_esk12_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_272]) ).
cnf(c_0_272_1,axiom,
( ~ in(sk1_esk12_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk12_3(X2,X3,X1),X2)
| ~ in(sk1_esk12_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_272]) ).
cnf(c_0_272_2,axiom,
( ~ in(sk1_esk12_3(X2,X3,X1),X2)
| ~ in(sk1_esk12_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk12_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_272]) ).
cnf(c_0_272_3,axiom,
( ~ in(sk1_esk12_3(X2,X3,X1),X1)
| ~ in(sk1_esk12_3(X2,X3,X1),X2)
| ~ in(sk1_esk12_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_272]) ).
cnf(c_0_273_0,axiom,
( in(sk1_esk6_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_273]) ).
cnf(c_0_273_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk6_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_273]) ).
cnf(c_0_273_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk6_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_273]) ).
cnf(c_0_274_0,axiom,
( in(sk1_esk7_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_274]) ).
cnf(c_0_274_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk7_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_274]) ).
cnf(c_0_274_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk7_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_274]) ).
cnf(c_0_275_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk16_3(X2,X3,X1),X3)
| ~ in(sk1_esk16_3(X2,X3,X1),X2)
| ~ in(sk1_esk16_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_275]) ).
cnf(c_0_275_1,axiom,
( in(sk1_esk16_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk16_3(X2,X3,X1),X2)
| ~ in(sk1_esk16_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_275]) ).
cnf(c_0_275_2,axiom,
( ~ in(sk1_esk16_3(X2,X3,X1),X2)
| in(sk1_esk16_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk16_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_275]) ).
cnf(c_0_275_3,axiom,
( ~ in(sk1_esk16_3(X2,X3,X1),X1)
| ~ in(sk1_esk16_3(X2,X3,X1),X2)
| in(sk1_esk16_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_275]) ).
cnf(c_0_276_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk8_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk9_3(X2,X3,X1),sk1_esk10_3(X2,X3,X1)) = sk1_esk8_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_276]) ).
cnf(c_0_276_1,axiom,
( in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk9_3(X2,X3,X1),sk1_esk10_3(X2,X3,X1)) = sk1_esk8_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_276]) ).
cnf(c_0_276_2,axiom,
( ordered_pair(sk1_esk9_3(X2,X3,X1),sk1_esk10_3(X2,X3,X1)) = sk1_esk8_3(X2,X3,X1)
| in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_276]) ).
cnf(c_0_277_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk5_3(X2,X3,X1),X1)
| ~ in(sk1_esk5_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_277]) ).
cnf(c_0_277_1,axiom,
( ~ in(sk1_esk5_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk5_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_277]) ).
cnf(c_0_277_2,axiom,
( ~ in(sk1_esk5_3(X2,X3,X1),X2)
| ~ in(sk1_esk5_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_277]) ).
cnf(c_0_278_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk5_3(X2,X3,X1),X1)
| ~ in(sk1_esk5_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_278]) ).
cnf(c_0_278_1,axiom,
( ~ in(sk1_esk5_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk5_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_278]) ).
cnf(c_0_278_2,axiom,
( ~ in(sk1_esk5_3(X2,X3,X1),X3)
| ~ in(sk1_esk5_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_278]) ).
cnf(c_0_279_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk5_3(X2,X3,X1),X3)
| in(sk1_esk5_3(X2,X3,X1),X2)
| in(sk1_esk5_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_279]) ).
cnf(c_0_279_1,axiom,
( in(sk1_esk5_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk5_3(X2,X3,X1),X2)
| in(sk1_esk5_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_279]) ).
cnf(c_0_279_2,axiom,
( in(sk1_esk5_3(X2,X3,X1),X2)
| in(sk1_esk5_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk5_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_279]) ).
cnf(c_0_279_3,axiom,
( in(sk1_esk5_3(X2,X3,X1),X1)
| in(sk1_esk5_3(X2,X3,X1),X2)
| in(sk1_esk5_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_279]) ).
cnf(c_0_280_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_280]) ).
cnf(c_0_280_1,axiom,
( sk1_esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_280]) ).
cnf(c_0_280_2,axiom,
( ~ in(X5,X3)
| sk1_esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_280]) ).
cnf(c_0_280_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_280]) ).
cnf(c_0_280_4,axiom,
( ~ in(sk1_esk8_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk8_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_280]) ).
cnf(c_0_281_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk16_3(X2,X3,X1),X1)
| ~ in(sk1_esk16_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_281]) ).
cnf(c_0_281_1,axiom,
( in(sk1_esk16_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk16_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_281]) ).
cnf(c_0_281_2,axiom,
( ~ in(sk1_esk16_3(X2,X3,X1),X3)
| in(sk1_esk16_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_281]) ).
cnf(c_0_282_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk4_3(X2,X3,X1),X1)
| sk1_esk4_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_282]) ).
cnf(c_0_282_1,axiom,
( ~ in(sk1_esk4_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk4_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_282]) ).
cnf(c_0_282_2,axiom,
( sk1_esk4_3(X2,X3,X1) != X2
| ~ in(sk1_esk4_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_282]) ).
cnf(c_0_283_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk4_3(X2,X3,X1),X1)
| sk1_esk4_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_283]) ).
cnf(c_0_283_1,axiom,
( ~ in(sk1_esk4_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk4_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_283]) ).
cnf(c_0_283_2,axiom,
( sk1_esk4_3(X2,X3,X1) != X3
| ~ in(sk1_esk4_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_283]) ).
cnf(c_0_284_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk16_3(X2,X3,X1),X1)
| in(sk1_esk16_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_284]) ).
cnf(c_0_284_1,axiom,
( in(sk1_esk16_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk16_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_284]) ).
cnf(c_0_284_2,axiom,
( in(sk1_esk16_3(X2,X3,X1),X2)
| in(sk1_esk16_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_284]) ).
cnf(c_0_285_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk12_3(X2,X3,X1),X1)
| in(sk1_esk12_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_285]) ).
cnf(c_0_285_1,axiom,
( in(sk1_esk12_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk12_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_285]) ).
cnf(c_0_285_2,axiom,
( in(sk1_esk12_3(X2,X3,X1),X2)
| in(sk1_esk12_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_285]) ).
cnf(c_0_286_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk12_3(X2,X3,X1),X1)
| in(sk1_esk12_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_286]) ).
cnf(c_0_286_1,axiom,
( in(sk1_esk12_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk12_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_286]) ).
cnf(c_0_286_2,axiom,
( in(sk1_esk12_3(X2,X3,X1),X3)
| in(sk1_esk12_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_286]) ).
cnf(c_0_287_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk8_3(X2,X3,X1),X1)
| in(sk1_esk9_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_287]) ).
cnf(c_0_287_1,axiom,
( in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk9_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_287]) ).
cnf(c_0_287_2,axiom,
( in(sk1_esk9_3(X2,X3,X1),X2)
| in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_287]) ).
cnf(c_0_288_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk8_3(X2,X3,X1),X1)
| in(sk1_esk10_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_288]) ).
cnf(c_0_288_1,axiom,
( in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk10_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_288]) ).
cnf(c_0_288_2,axiom,
( in(sk1_esk10_3(X2,X3,X1),X3)
| in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_288]) ).
cnf(c_0_289_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk4_3(X2,X3,X1) = X3
| sk1_esk4_3(X2,X3,X1) = X2
| in(sk1_esk4_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_289]) ).
cnf(c_0_289_1,axiom,
( sk1_esk4_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk4_3(X2,X3,X1) = X2
| in(sk1_esk4_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_289]) ).
cnf(c_0_289_2,axiom,
( sk1_esk4_3(X2,X3,X1) = X2
| sk1_esk4_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk4_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_289]) ).
cnf(c_0_289_3,axiom,
( in(sk1_esk4_3(X2,X3,X1),X1)
| sk1_esk4_3(X2,X3,X1) = X2
| sk1_esk4_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_289]) ).
cnf(c_0_290_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk14_2(X2,X1),X3)
| ~ in(sk1_esk14_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_290]) ).
cnf(c_0_290_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk14_2(X2,X1),X3)
| ~ in(sk1_esk14_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_290]) ).
cnf(c_0_290_2,axiom,
( ~ in(sk1_esk14_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk14_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_290]) ).
cnf(c_0_290_3,axiom,
( ~ in(sk1_esk14_2(X2,X1),X1)
| ~ in(sk1_esk14_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_290]) ).
cnf(c_0_291_0,axiom,
( in(X3,sk1_esk13_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_291]) ).
cnf(c_0_291_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk13_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_291]) ).
cnf(c_0_291_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk13_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_291]) ).
cnf(c_0_292_0,axiom,
( in(sk1_esk13_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_292]) ).
cnf(c_0_292_1,axiom,
( X1 != union(X2)
| in(sk1_esk13_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_292]) ).
cnf(c_0_292_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk13_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_292]) ).
cnf(c_0_293_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk3_2(X2,X1),X2)
| ~ in(sk1_esk3_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_293]) ).
cnf(c_0_293_1,axiom,
( ~ subset(sk1_esk3_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk3_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_293]) ).
cnf(c_0_293_2,axiom,
( ~ in(sk1_esk3_2(X2,X1),X1)
| ~ subset(sk1_esk3_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_293]) ).
cnf(c_0_294_0,axiom,
( X1 = X2
| ~ in(sk1_esk21_2(X1,X2),X2)
| ~ in(sk1_esk21_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_294]) ).
cnf(c_0_294_1,axiom,
( ~ in(sk1_esk21_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk21_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_294]) ).
cnf(c_0_294_2,axiom,
( ~ in(sk1_esk21_2(X1,X2),X1)
| ~ in(sk1_esk21_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_294]) ).
cnf(c_0_295_0,axiom,
( X1 = union(X2)
| in(sk1_esk14_2(X2,X1),X1)
| in(sk1_esk14_2(X2,X1),sk1_esk15_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_295]) ).
cnf(c_0_295_1,axiom,
( in(sk1_esk14_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk14_2(X2,X1),sk1_esk15_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_295]) ).
cnf(c_0_295_2,axiom,
( in(sk1_esk14_2(X2,X1),sk1_esk15_2(X2,X1))
| in(sk1_esk14_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_295]) ).
cnf(c_0_296_0,axiom,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_296]) ).
cnf(c_0_296_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_296]) ).
cnf(c_0_296_2,axiom,
( X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_296]) ).
cnf(c_0_296_3,axiom,
( ~ in(X6,X3)
| X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_296]) ).
cnf(c_0_296_4,axiom,
( ~ in(X5,X2)
| ~ in(X6,X3)
| X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_296]) ).
cnf(c_0_297_0,axiom,
( in(X3,sk1_esk23_2(X2,X1))
| ~ in(X1,sk1_esk22_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_297]) ).
cnf(c_0_297_1,axiom,
( ~ in(X1,sk1_esk22_1(X2))
| in(X3,sk1_esk23_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_297]) ).
cnf(c_0_297_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk22_1(X2))
| in(X3,sk1_esk23_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_297]) ).
cnf(c_0_298_0,axiom,
( X1 = singleton(X2)
| sk1_esk1_2(X2,X1) != X2
| ~ in(sk1_esk1_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_298]) ).
cnf(c_0_298_1,axiom,
( sk1_esk1_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk1_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_298]) ).
cnf(c_0_298_2,axiom,
( ~ in(sk1_esk1_2(X2,X1),X1)
| sk1_esk1_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_298]) ).
cnf(c_0_299_0,axiom,
( X1 = union(X2)
| in(sk1_esk14_2(X2,X1),X1)
| in(sk1_esk15_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_299]) ).
cnf(c_0_299_1,axiom,
( in(sk1_esk14_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk15_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_299]) ).
cnf(c_0_299_2,axiom,
( in(sk1_esk15_2(X2,X1),X2)
| in(sk1_esk14_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_299]) ).
cnf(c_0_300_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk3_2(X2,X1),X2)
| in(sk1_esk3_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_300]) ).
cnf(c_0_300_1,axiom,
( subset(sk1_esk3_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk3_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_300]) ).
cnf(c_0_300_2,axiom,
( in(sk1_esk3_2(X2,X1),X1)
| subset(sk1_esk3_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_300]) ).
cnf(c_0_301_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_301]) ).
cnf(c_0_301_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_301]) ).
cnf(c_0_301_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_301]) ).
cnf(c_0_301_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_301]) ).
cnf(c_0_302_0,axiom,
( X1 = X2
| in(sk1_esk21_2(X1,X2),X2)
| in(sk1_esk21_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_302]) ).
cnf(c_0_302_1,axiom,
( in(sk1_esk21_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk21_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_302]) ).
cnf(c_0_302_2,axiom,
( in(sk1_esk21_2(X1,X2),X1)
| in(sk1_esk21_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_302]) ).
cnf(c_0_303_0,axiom,
( in(sk1_esk23_2(X2,X1),sk1_esk22_1(X2))
| ~ in(X1,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_303]) ).
cnf(c_0_303_1,axiom,
( ~ in(X1,sk1_esk22_1(X2))
| in(sk1_esk23_2(X2,X1),sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_303]) ).
cnf(c_0_304_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk11_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_304]) ).
cnf(c_0_304_1,axiom,
( ~ in(sk1_esk11_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_304]) ).
cnf(c_0_305_0,axiom,
( in(X1,sk1_esk22_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_305]) ).
cnf(c_0_305_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk22_1(X2))
| ~ in(X3,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_305]) ).
cnf(c_0_305_2,axiom,
( ~ in(X3,sk1_esk22_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_305]) ).
cnf(c_0_306_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_306]) ).
cnf(c_0_306_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_306]) ).
cnf(c_0_306_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_306]) ).
cnf(c_0_306_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_306]) ).
cnf(c_0_307_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_307]) ).
cnf(c_0_307_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_307]) ).
cnf(c_0_307_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_307]) ).
cnf(c_0_307_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_307]) ).
cnf(c_0_308_0,axiom,
( in(X1,sk1_esk22_1(X2))
| are_equipotent(X1,sk1_esk22_1(X2))
| ~ subset(X1,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_308]) ).
cnf(c_0_308_1,axiom,
( are_equipotent(X1,sk1_esk22_1(X2))
| in(X1,sk1_esk22_1(X2))
| ~ subset(X1,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_308]) ).
cnf(c_0_308_2,axiom,
( ~ subset(X1,sk1_esk22_1(X2))
| are_equipotent(X1,sk1_esk22_1(X2))
| in(X1,sk1_esk22_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_308]) ).
cnf(c_0_309_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_309]) ).
cnf(c_0_309_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_309]) ).
cnf(c_0_309_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_309]) ).
cnf(c_0_310_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_310]) ).
cnf(c_0_310_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_310]) ).
cnf(c_0_310_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_310]) ).
cnf(c_0_310_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_310]) ).
cnf(c_0_311_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_311]) ).
cnf(c_0_311_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_311]) ).
cnf(c_0_311_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_311]) ).
cnf(c_0_312_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_312]) ).
cnf(c_0_312_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_312]) ).
cnf(c_0_312_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_312]) ).
cnf(c_0_313_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_313]) ).
cnf(c_0_313_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_313]) ).
cnf(c_0_313_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_313]) ).
cnf(c_0_314_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_314]) ).
cnf(c_0_314_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_314]) ).
cnf(c_0_314_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_314]) ).
cnf(c_0_315_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_315]) ).
cnf(c_0_315_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_315]) ).
cnf(c_0_315_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_315]) ).
cnf(c_0_316_0,axiom,
( X1 = singleton(X2)
| sk1_esk1_2(X2,X1) = X2
| in(sk1_esk1_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_316]) ).
cnf(c_0_316_1,axiom,
( sk1_esk1_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk1_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_316]) ).
cnf(c_0_316_2,axiom,
( in(sk1_esk1_2(X2,X1),X1)
| sk1_esk1_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_316]) ).
cnf(c_0_318_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_318]) ).
cnf(c_0_318_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_318]) ).
cnf(c_0_318_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_318]) ).
cnf(c_0_319_0,axiom,
( subset(X1,X2)
| in(sk1_esk11_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_319]) ).
cnf(c_0_319_1,axiom,
( in(sk1_esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_319]) ).
cnf(c_0_320_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_320]) ).
cnf(c_0_320_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_320]) ).
cnf(c_0_321_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_321]) ).
cnf(c_0_321_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_321]) ).
cnf(c_0_322_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_322]) ).
cnf(c_0_322_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_322]) ).
cnf(c_0_322_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_322]) ).
cnf(c_0_322_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_322]) ).
cnf(c_0_324_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_324]) ).
cnf(c_0_324_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_324]) ).
cnf(c_0_324_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_324]) ).
cnf(c_0_325_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_325]) ).
cnf(c_0_325_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_325]) ).
cnf(c_0_325_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_325]) ).
cnf(c_0_326_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_326]) ).
cnf(c_0_326_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_326]) ).
cnf(c_0_326_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_326]) ).
cnf(c_0_327_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_327]) ).
cnf(c_0_327_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_327]) ).
cnf(c_0_328_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_328]) ).
cnf(c_0_328_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_328]) ).
cnf(c_0_329_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_329]) ).
cnf(c_0_329_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_329]) ).
cnf(c_0_329_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_329]) ).
cnf(c_0_330_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_330]) ).
cnf(c_0_330_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_330]) ).
cnf(c_0_330_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_330]) ).
cnf(c_0_331_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_331]) ).
cnf(c_0_331_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_331]) ).
cnf(c_0_331_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_331]) ).
cnf(c_0_332_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_332]) ).
cnf(c_0_332_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_332]) ).
cnf(c_0_332_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_332]) ).
cnf(c_0_333_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_333]) ).
cnf(c_0_333_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_333]) ).
cnf(c_0_333_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_333]) ).
cnf(c_0_334_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_334]) ).
cnf(c_0_334_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_334]) ).
cnf(c_0_335_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_335]) ).
cnf(c_0_335_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_335]) ).
cnf(c_0_336_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_336]) ).
cnf(c_0_336_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_336]) ).
cnf(c_0_337_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_337]) ).
cnf(c_0_337_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_337]) ).
cnf(c_0_338_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_338]) ).
cnf(c_0_338_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_338]) ).
cnf(c_0_338_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_338]) ).
cnf(c_0_339_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_339]) ).
cnf(c_0_339_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_339]) ).
cnf(c_0_339_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_339]) ).
cnf(c_0_340_0,axiom,
( empty(X1)
| element(sk1_esk18_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_340]) ).
cnf(c_0_340_1,axiom,
( element(sk1_esk18_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_340]) ).
cnf(c_0_341_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_341]) ).
cnf(c_0_341_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_341]) ).
cnf(c_0_342_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_342]) ).
cnf(c_0_342_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_342]) ).
cnf(c_0_342_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_342]) ).
cnf(c_0_346_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_346]) ).
cnf(c_0_346_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_346]) ).
cnf(c_0_346_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_346]) ).
cnf(c_0_347_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_347]) ).
cnf(c_0_347_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_347]) ).
cnf(c_0_348_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_348]) ).
cnf(c_0_348_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_348]) ).
cnf(c_0_350_0,axiom,
( X1 = empty_set
| in(sk1_esk2_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_350]) ).
cnf(c_0_350_1,axiom,
( in(sk1_esk2_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_350]) ).
cnf(c_0_351_0,axiom,
( empty(X1)
| ~ empty(sk1_esk18_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_351]) ).
cnf(c_0_351_1,axiom,
( ~ empty(sk1_esk18_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_351]) ).
cnf(c_0_354_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_354]) ).
cnf(c_0_354_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_354]) ).
cnf(c_0_355_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_355]) ).
cnf(c_0_355_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_355]) ).
cnf(c_0_357_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_357]) ).
cnf(c_0_357_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_357]) ).
cnf(c_0_357_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_357]) ).
cnf(c_0_365_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_365]) ).
cnf(c_0_365_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_365]) ).
cnf(c_0_323_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_323]) ).
cnf(c_0_349_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_349]) ).
cnf(c_0_356_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_356]) ).
cnf(c_0_366_0,axiom,
~ empty(sk1_esk20_0),
inference(literals_permutation,[status(thm)],[c_0_366]) ).
cnf(c_0_317_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_317]) ).
cnf(c_0_343_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_343]) ).
cnf(c_0_344_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_344]) ).
cnf(c_0_345_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_345]) ).
cnf(c_0_352_0,axiom,
in(X1,sk1_esk22_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_352]) ).
cnf(c_0_353_0,axiom,
element(sk1_esk17_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_353]) ).
cnf(c_0_358_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_358]) ).
cnf(c_0_359_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_359]) ).
cnf(c_0_360_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_360]) ).
cnf(c_0_361_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_361]) ).
cnf(c_0_362_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_362]) ).
cnf(c_0_363_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_363]) ).
cnf(c_0_364_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_364]) ).
cnf(c_0_367_0,axiom,
empty(sk1_esk19_0),
inference(literals_permutation,[status(thm)],[c_0_367]) ).
cnf(c_0_368_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_368]) ).
cnf(c_0_369_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_369]) ).
cnf(c_0_370_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_370]) ).
cnf(c_0_371_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_371]) ).
cnf(c_0_372_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_372]) ).
cnf(c_0_373_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_373]) ).
cnf(c_0_374_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_374]) ).
cnf(c_0_375_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_375]) ).
cnf(c_0_376_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_376]) ).
cnf(c_0_377_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_377]) ).
cnf(c_0_378_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_378]) ).
cnf(c_0_379_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_379]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('<stdin>',t106_zfmisc_1) ).
fof(c_0_1_002,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('<stdin>',l55_zfmisc_1) ).
fof(c_0_2_003,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('<stdin>',t119_zfmisc_1) ).
fof(c_0_3_004,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('<stdin>',l3_zfmisc_1) ).
fof(c_0_4_005,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_5_006,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_6_007,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('<stdin>',t118_zfmisc_1) ).
fof(c_0_7_008,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('<stdin>',t4_xboole_0) ).
fof(c_0_8_009,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_9_010,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_10_011,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_11_012,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('<stdin>',t136_zfmisc_1) ).
fof(c_0_12_013,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('<stdin>',t3_xboole_0) ).
fof(c_0_13_014,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_14_015,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_15_016,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_16_017,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_17_018,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_18_019,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_19_020,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_20_021,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_21_022,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('<stdin>',t10_zfmisc_1) ).
fof(c_0_22_023,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_23_024,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_24_025,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('<stdin>',t33_zfmisc_1) ).
fof(c_0_25_026,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_26_027,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_27_028,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_28_029,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_29_030,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_30_031,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_31_032,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_32_033,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_33_034,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_34_035,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_35_036,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_36_037,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_37_038,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_38_039,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_39_040,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_40_041,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_41_042,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_42_043,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_43_044,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_44_045,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_45_046,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_46_047,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_47_048,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_48_049,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_49_050,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_50_051,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_51_052,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_0 ).
fof(c_0_52_053,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_1 ).
fof(c_0_53_054,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_2 ).
fof(c_0_54_055,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_3 ).
fof(c_0_55_056,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_4 ).
fof(c_0_56_057,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_5 ).
fof(c_0_57_058,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
c_0_6 ).
fof(c_0_58_059,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_59_060,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_8 ).
fof(c_0_60_061,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_9 ).
fof(c_0_61_062,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_10 ).
fof(c_0_62_063,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_63_064,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_64_065,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_13 ).
fof(c_0_65_066,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_14 ).
fof(c_0_66_067,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_15 ).
fof(c_0_67_068,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_68_069,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_17 ).
fof(c_0_69_070,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_18 ).
fof(c_0_70_071,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_19 ).
fof(c_0_71_072,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_20 ).
fof(c_0_72_073,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_21 ).
fof(c_0_73_074,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_22 ).
fof(c_0_74_075,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_23 ).
fof(c_0_75_076,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_24 ).
fof(c_0_76_077,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_25 ).
fof(c_0_77_078,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_26 ).
fof(c_0_78_079,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_27 ).
fof(c_0_79_080,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_28 ).
fof(c_0_80_081,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_29 ).
fof(c_0_81_082,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_30 ).
fof(c_0_82_083,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_31 ).
fof(c_0_83_084,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_32 ).
fof(c_0_84_085,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_33 ).
fof(c_0_85_086,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_34 ).
fof(c_0_86_087,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_35 ).
fof(c_0_87_088,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_36 ).
fof(c_0_88_089,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_37 ).
fof(c_0_89_090,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_38 ).
fof(c_0_90_091,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_39 ).
fof(c_0_91_092,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_40 ).
fof(c_0_92_093,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_93_094,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_42 ).
fof(c_0_94_095,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_43 ).
fof(c_0_95_096,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_44 ).
fof(c_0_96_097,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_45 ).
fof(c_0_97_098,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
inference(assume_negation,[status(cth)],[c_0_46]) ).
fof(c_0_98_099,lemma,
! [X1] : subset(empty_set,X1),
c_0_47 ).
fof(c_0_99_100,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_48 ).
fof(c_0_100_101,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_49 ).
fof(c_0_101_102,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_50 ).
fof(c_0_102_103,lemma,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X9,X11)
| ~ in(X10,X12)
| in(ordered_pair(X9,X10),cartesian_product2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])])]) ).
fof(c_0_103_104,lemma,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X9,X11)
| ~ in(X10,X12)
| in(ordered_pair(X9,X10),cartesian_product2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])]) ).
fof(c_0_104_105,lemma,
! [X5,X6,X7,X8] :
( ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])]) ).
fof(c_0_105_106,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| in(X6,X4)
| subset(X4,set_difference(X5,singleton(X6))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
fof(c_0_106_107,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_difference(X4,X6),set_difference(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_107_108,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_intersection2(X4,X6),set_intersection2(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
fof(c_0_108_109,lemma,
! [X4,X5,X6,X7] :
( ( subset(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
| ~ subset(X4,X5) )
& ( subset(cartesian_product2(X7,X4),cartesian_product2(X7,X5))
| ~ subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])]) ).
fof(c_0_109_110,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk6_2(X4,X5),set_intersection2(X4,X5)) )
& ( ~ in(X9,set_intersection2(X7,X8))
| ~ disjoint(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])])]) ).
fof(c_0_110_111,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])]) ).
fof(c_0_111_112,lemma,
! [X4,X5,X6,X7,X8,X9] :
( ( in(X4,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( in(X5,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( ~ in(X7,X9)
| ~ in(X8,X9)
| subset(unordered_pair(X7,X8),X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])])]) ).
fof(c_0_112_113,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,set_intersection2(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])]) ).
fof(c_0_113_114,lemma,
! [X5,X7,X8,X9,X10] :
( in(X5,esk4_1(X5))
& ( ~ in(X7,esk4_1(X5))
| ~ subset(X8,X7)
| in(X8,esk4_1(X5)) )
& ( ~ in(X9,esk4_1(X5))
| in(powerset(X9),esk4_1(X5)) )
& ( ~ subset(X10,esk4_1(X5))
| are_equipotent(X10,esk4_1(X5))
| in(X10,esk4_1(X5)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
fof(c_0_114_115,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk5_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk5_2(X4,X5),X5)
| disjoint(X4,X5) )
& ( ~ in(X9,X7)
| ~ in(X9,X8)
| ~ disjoint(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])])])]) ).
fof(c_0_115_116,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| X4 = set_union2(X3,set_difference(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])]) ).
fof(c_0_116_117,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ disjoint(X5,X6)
| disjoint(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])]) ).
fof(c_0_117_118,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])]) ).
fof(c_0_118_119,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,singleton(X4)) != X3
| ~ in(X4,X3) )
& ( in(X6,X5)
| set_difference(X5,singleton(X6)) = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
fof(c_0_119_120,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])]) ).
fof(c_0_120_121,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_121_122,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_70]) ).
fof(c_0_122_123,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_71]) ).
fof(c_0_123_124,lemma,
! [X5,X6,X7,X8] :
( unordered_pair(X5,X6) != unordered_pair(X7,X8)
| X5 = X7
| X5 = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])]) ).
fof(c_0_124_125,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X5,X6)
| subset(singleton(X5),X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])]) ).
fof(c_0_125_126,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X5,X6)
| subset(singleton(X5),X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])]) ).
fof(c_0_126_127,lemma,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ordered_pair(X5,X6) != ordered_pair(X7,X8) )
& ( X6 = X8
| ordered_pair(X5,X6) != ordered_pair(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])]) ).
fof(c_0_127_128,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])]) ).
fof(c_0_128_129,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])]) ).
fof(c_0_129_130,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])]) ).
fof(c_0_130_131,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])]) ).
fof(c_0_131_132,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])]) ).
fof(c_0_132_133,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])]) ).
fof(c_0_133_134,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_82]) ).
fof(c_0_134_135,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_83]) ).
fof(c_0_135_136,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_84]) ).
fof(c_0_136_137,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X5 != empty_set
| subset(X5,singleton(X6)) )
& ( X5 != singleton(X6)
| subset(X5,singleton(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])])]) ).
fof(c_0_137_138,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X5 != empty_set
| subset(X5,singleton(X6)) )
& ( X5 != singleton(X6)
| subset(X5,singleton(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])])])]) ).
fof(c_0_138_139,lemma,
! [X3,X4,X5,X6] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X5,X6) != X5
| disjoint(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])])]) ).
fof(c_0_139_140,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])]) ).
fof(c_0_140_141,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])]) ).
fof(c_0_141_142,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])])]) ).
fof(c_0_142_143,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])])]) ).
fof(c_0_143_144,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])]) ).
fof(c_0_144_145,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])]) ).
fof(c_0_145_146,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X4 = X5 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])]) ).
fof(c_0_146_147,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])]) ).
fof(c_0_147_148,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_96]) ).
fof(c_0_148_149,negated_conjecture,
( element(esk2_0,powerset(esk1_0))
& in(esk3_0,esk2_0)
& ~ in(esk3_0,esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])]) ).
fof(c_0_149_150,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_98]) ).
fof(c_0_150_151,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_99]) ).
fof(c_0_151_152,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_100]) ).
fof(c_0_152_153,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_101 ).
cnf(c_0_153_154,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_154_155,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_155_156,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_156_157,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_157_158,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_158_159,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_159_160,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_160_161,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_161_162,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_162_163,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_163_164,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_164_165,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_165_166,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_166_167,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_167_168,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_168_169,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_169_170,lemma,
( in(esk6_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_170_171,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_171_172,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_172_173,lemma,
( in(X1,esk4_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk4_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_173_174,lemma,
( in(X1,esk4_1(X2))
| are_equipotent(X1,esk4_1(X2))
| ~ subset(X1,esk4_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_174_175,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_175_176,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_176_177,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_177_178,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_178_179,lemma,
( in(powerset(X1),esk4_1(X2))
| ~ in(X1,esk4_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_179_180,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_180_181,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_181_182,lemma,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_182_183,lemma,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_183_184,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_184_185,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_185_186,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_186_187,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_187_188,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_188_189,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_189_190,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_190_191,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_191_192,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_192_193,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_193_194,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_194_195,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_195_196,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_196_197,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_197_198,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_198_199,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_199_200,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_200_201,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_201_202,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_202_203,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_203_204,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_204_205,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_205_206,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_206_207,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_207_208,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_208_209,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_209_210,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_210_211,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_211_212,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_212_213,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_213_214,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_214_215,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_215_216,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_216_217,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_217_218,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_218_219,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_219_220,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_220_221,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_221_222,lemma,
in(X1,esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_222_223,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_223_224,negated_conjecture,
~ in(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_224_225,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_225_226,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_226_227,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_227_228,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_228_229,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_229_230,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_230_231,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_153,
[final] ).
cnf(c_0_231_232,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_154,
[final] ).
cnf(c_0_232_233,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_155,
[final] ).
cnf(c_0_233_234,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_156,
[final] ).
cnf(c_0_234_235,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_157,
[final] ).
cnf(c_0_235_236,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_158,
[final] ).
cnf(c_0_236_237,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_159,
[final] ).
cnf(c_0_237_238,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_160,
[final] ).
cnf(c_0_238_239,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_161,
[final] ).
cnf(c_0_239_240,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_162,
[final] ).
cnf(c_0_240_241,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_163,
[final] ).
cnf(c_0_241_242,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_164,
[final] ).
cnf(c_0_242_243,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_165,
[final] ).
cnf(c_0_243_244,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_166,
[final] ).
cnf(c_0_244_245,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_167,
[final] ).
cnf(c_0_245_246,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_168,
[final] ).
cnf(c_0_246_247,lemma,
( in(esk6_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_169,
[final] ).
cnf(c_0_247_248,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_170,
[final] ).
cnf(c_0_248_249,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_171,
[final] ).
cnf(c_0_249_250,lemma,
( in(X1,esk4_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk4_1(X2)) ),
c_0_172,
[final] ).
cnf(c_0_250_251,lemma,
( in(X1,esk4_1(X2))
| are_equipotent(X1,esk4_1(X2))
| ~ subset(X1,esk4_1(X2)) ),
c_0_173,
[final] ).
cnf(c_0_251_252,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_174,
[final] ).
cnf(c_0_252_253,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_175,
[final] ).
cnf(c_0_253_254,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_176,
[final] ).
cnf(c_0_254_255,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_177,
[final] ).
cnf(c_0_255_256,lemma,
( in(powerset(X1),esk4_1(X2))
| ~ in(X1,esk4_1(X2)) ),
c_0_178,
[final] ).
cnf(c_0_256_257,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_179,
[final] ).
cnf(c_0_257_258,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_180,
[final] ).
cnf(c_0_258_259,lemma,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),X1) ),
c_0_181,
[final] ).
cnf(c_0_259_260,lemma,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),X2) ),
c_0_182,
[final] ).
cnf(c_0_260_261,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_183,
[final] ).
cnf(c_0_261_262,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_184,
[final] ).
cnf(c_0_262_263,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_185,
[final] ).
cnf(c_0_263_264,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_186,
[final] ).
cnf(c_0_264_265,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_187,
[final] ).
cnf(c_0_265_266,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_188,
[final] ).
cnf(c_0_266_267,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_189,
[final] ).
cnf(c_0_267_268,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_190,
[final] ).
cnf(c_0_268_269,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_191,
[final] ).
cnf(c_0_269_270,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_192,
[final] ).
cnf(c_0_270_271,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_193,
[final] ).
cnf(c_0_271_272,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_194,
[final] ).
cnf(c_0_272_273,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_195,
[final] ).
cnf(c_0_273_274,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_196,
[final] ).
cnf(c_0_274_275,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_197,
[final] ).
cnf(c_0_275_276,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_198,
[final] ).
cnf(c_0_276_277,lemma,
subset(X1,set_union2(X1,X2)),
c_0_199,
[final] ).
cnf(c_0_277_278,lemma,
subset(set_difference(X1,X2),X1),
c_0_200,
[final] ).
cnf(c_0_278_279,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_201,
[final] ).
cnf(c_0_279_280,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_202,
[final] ).
cnf(c_0_280_281,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_203,
[final] ).
cnf(c_0_281_282,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_204,
[final] ).
cnf(c_0_282_283,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_205,
[final] ).
cnf(c_0_283_284,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_206,
[final] ).
cnf(c_0_284_285,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_207,
[final] ).
cnf(c_0_285_286,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_208,
[final] ).
cnf(c_0_286_287,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_209,
[final] ).
cnf(c_0_287_288,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_210,
[final] ).
cnf(c_0_288_289,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_211,
[final] ).
cnf(c_0_289_290,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_212,
[final] ).
cnf(c_0_290_291,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_213,
[final] ).
cnf(c_0_291_292,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_214,
[final] ).
cnf(c_0_292_293,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_215,
[final] ).
cnf(c_0_293_294,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_216,
[final] ).
cnf(c_0_294_295,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_217,
[final] ).
cnf(c_0_295_296,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_218,
[final] ).
cnf(c_0_296_297,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_219,
[final] ).
cnf(c_0_297_298,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_220,
[final] ).
cnf(c_0_298_299,lemma,
in(X1,esk4_1(X1)),
c_0_221,
[final] ).
cnf(c_0_299_300,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_222,
[final] ).
cnf(c_0_300_301,negated_conjecture,
~ in(esk3_0,esk1_0),
c_0_223,
[final] ).
cnf(c_0_301_302,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
c_0_224,
[final] ).
cnf(c_0_302_303,lemma,
subset(empty_set,X1),
c_0_225,
[final] ).
cnf(c_0_303_304,lemma,
union(powerset(X1)) = X1,
c_0_226,
[final] ).
cnf(c_0_304_305,negated_conjecture,
in(esk3_0,esk2_0),
c_0_227,
[final] ).
cnf(c_0_305_306,lemma,
singleton(X1) != empty_set,
c_0_228,
[final] ).
cnf(c_0_306_307,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_229,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_335,plain,
union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_303) ).
cnf(c_586,plain,
union(powerset(X0)) = X0,
inference(copy,[status(esa)],[c_335]) ).
cnf(c_664,plain,
union(powerset(X0)) = X0,
inference(copy,[status(esa)],[c_586]) ).
cnf(c_669,plain,
union(powerset(X0)) = X0,
inference(copy,[status(esa)],[c_664]) ).
cnf(c_785,plain,
union(powerset(X0)) = X0,
inference(copy,[status(esa)],[c_669]) ).
cnf(c_1740,plain,
union(powerset(X0)) = X0,
inference(copy,[status(esa)],[c_785]) ).
cnf(c_132,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| in(X0,X3)
| X3 != union(X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_310_1) ).
cnf(c_1376,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| in(X0,X3)
| X3 != union(X2) ),
inference(copy,[status(esa)],[c_132]) ).
cnf(c_2434,plain,
( in(X0,union(powerset(union(X1))))
| ~ in(X0,X2)
| ~ in(X2,X1) ),
inference(resolution,[status(thm)],[c_1740,c_1376]) ).
cnf(c_2435,plain,
( in(X0,union(powerset(union(X1))))
| ~ in(X0,X2)
| ~ in(X2,X1) ),
inference(rewriting,[status(thm)],[c_2434]) ).
cnf(c_333,negated_conjecture,
element(sk2_esk2_0,powerset(sk2_esk1_0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_301) ).
cnf(c_592,negated_conjecture,
element(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(copy,[status(esa)],[c_333]) ).
cnf(c_662,negated_conjecture,
element(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(copy,[status(esa)],[c_592]) ).
cnf(c_671,negated_conjecture,
element(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(copy,[status(esa)],[c_662]) ).
cnf(c_783,negated_conjecture,
element(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(copy,[status(esa)],[c_671]) ).
cnf(c_1736,plain,
element(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(copy,[status(esa)],[c_783]) ).
cnf(c_77,plain,
( empty(X0)
| in(X1,X0)
| ~ element(X1,X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_331_2) ).
cnf(c_1266,plain,
( empty(X0)
| in(X1,X0)
| ~ element(X1,X0) ),
inference(copy,[status(esa)],[c_77]) ).
cnf(c_1267,plain,
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(rewriting,[status(thm)],[c_1266]) ).
cnf(c_1826,plain,
( empty(powerset(sk2_esk1_0))
| in(sk2_esk2_0,powerset(sk2_esk1_0)) ),
inference(resolution,[status(thm)],[c_1736,c_1267]) ).
cnf(c_1827,plain,
( empty(powerset(sk2_esk1_0))
| in(sk2_esk2_0,powerset(sk2_esk1_0)) ),
inference(rewriting,[status(thm)],[c_1826]) ).
cnf(c_27,plain,
~ empty(powerset(X0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_356_0) ).
cnf(c_1166,plain,
~ empty(powerset(X0)),
inference(copy,[status(esa)],[c_27]) ).
cnf(c_1853,plain,
in(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(forward_subsumption_resolution,[status(thm)],[c_1827,c_1166]) ).
cnf(c_1854,plain,
in(sk2_esk2_0,powerset(sk2_esk1_0)),
inference(rewriting,[status(thm)],[c_1853]) ).
cnf(c_28491,plain,
( in(X0,union(powerset(union(powerset(sk2_esk1_0)))))
| ~ in(X0,sk2_esk2_0) ),
inference(resolution,[status(thm)],[c_2435,c_1854]) ).
cnf(c_28492,plain,
( in(X0,union(powerset(union(powerset(sk2_esk1_0)))))
| ~ in(X0,sk2_esk2_0) ),
inference(rewriting,[status(thm)],[c_28491]) ).
cnf(c_323,negated_conjecture,
~ in(sk2_esk3_0,sk2_esk1_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_300) ).
cnf(c_590,negated_conjecture,
~ in(sk2_esk3_0,sk2_esk1_0),
inference(copy,[status(esa)],[c_323]) ).
cnf(c_652,negated_conjecture,
~ in(sk2_esk3_0,sk2_esk1_0),
inference(copy,[status(esa)],[c_590]) ).
cnf(c_681,negated_conjecture,
~ in(sk2_esk3_0,sk2_esk1_0),
inference(copy,[status(esa)],[c_652]) ).
cnf(c_773,negated_conjecture,
~ in(sk2_esk3_0,sk2_esk1_0),
inference(copy,[status(esa)],[c_681]) ).
cnf(c_1716,plain,
~ in(sk2_esk3_0,sk2_esk1_0),
inference(copy,[status(esa)],[c_773]) ).
cnf(c_111,plain,
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_318_0) ).
cnf(c_1334,plain,
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(copy,[status(esa)],[c_111]) ).
cnf(c_1822,plain,
( ~ subset(X0,sk2_esk1_0)
| ~ in(sk2_esk3_0,X0) ),
inference(resolution,[status(thm)],[c_1716,c_1334]) ).
cnf(c_1823,plain,
( ~ subset(X0,sk2_esk1_0)
| ~ in(sk2_esk3_0,X0) ),
inference(rewriting,[status(thm)],[c_1822]) ).
cnf(c_1920,plain,
( ~ subset(X0,sk2_esk1_0)
| ~ subset(X1,X0)
| ~ in(sk2_esk3_0,X1) ),
inference(resolution,[status(thm)],[c_1823,c_1334]) ).
cnf(c_1921,plain,
( ~ subset(X0,sk2_esk1_0)
| ~ subset(X1,X0)
| ~ in(sk2_esk3_0,X1) ),
inference(rewriting,[status(thm)],[c_1920]) ).
cnf(c_74472,plain,
( ~ subset(union(powerset(union(powerset(sk2_esk1_0)))),X0)
| ~ subset(X0,sk2_esk1_0)
| ~ in(sk2_esk3_0,sk2_esk2_0) ),
inference(resolution,[status(thm)],[c_28492,c_1921]) ).
cnf(c_74473,plain,
( ~ subset(union(powerset(union(powerset(sk2_esk1_0)))),X0)
| ~ subset(X0,sk2_esk1_0)
| ~ in(sk2_esk3_0,sk2_esk2_0) ),
inference(rewriting,[status(thm)],[c_74472]) ).
cnf(c_336,negated_conjecture,
in(sk2_esk3_0,sk2_esk2_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_304) ).
cnf(c_594,negated_conjecture,
in(sk2_esk3_0,sk2_esk2_0),
inference(copy,[status(esa)],[c_336]) ).
cnf(c_665,negated_conjecture,
in(sk2_esk3_0,sk2_esk2_0),
inference(copy,[status(esa)],[c_594]) ).
cnf(c_668,negated_conjecture,
in(sk2_esk3_0,sk2_esk2_0),
inference(copy,[status(esa)],[c_665]) ).
cnf(c_786,negated_conjecture,
in(sk2_esk3_0,sk2_esk2_0),
inference(copy,[status(esa)],[c_668]) ).
cnf(c_1742,plain,
in(sk2_esk3_0,sk2_esk2_0),
inference(copy,[status(esa)],[c_786]) ).
cnf(c_171973,plain,
( ~ subset(union(powerset(union(powerset(sk2_esk1_0)))),X0)
| ~ subset(X0,sk2_esk1_0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_74473,c_1742]) ).
cnf(c_171974,plain,
( ~ subset(union(powerset(union(powerset(sk2_esk1_0)))),X0)
| ~ subset(X0,sk2_esk1_0) ),
inference(rewriting,[status(thm)],[c_171973]) ).
cnf(c_37,plain,
( subset(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p',c_0_354_1) ).
cnf(c_1186,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(copy,[status(esa)],[c_37]) ).
cnf(c_2409,plain,
subset(union(powerset(X0)),X0),
inference(resolution,[status(thm)],[c_1740,c_1186]) ).
cnf(c_2410,plain,
subset(union(powerset(X0)),X0),
inference(rewriting,[status(thm)],[c_2409]) ).
cnf(c_171995,plain,
~ subset(union(powerset(sk2_esk1_0)),sk2_esk1_0),
inference(resolution,[status(thm)],[c_171974,c_2410]) ).
cnf(c_171996,plain,
~ subset(union(powerset(sk2_esk1_0)),sk2_esk1_0),
inference(rewriting,[status(thm)],[c_171995]) ).
cnf(c_205271,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_171996,c_2410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 04:22:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.42 % FOF problem with conjecture
% 0.19/0.42 % 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_bdcdeb.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_d0cf6a | grep -v "SZS"
% 0.19/0.44
% 0.19/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.44
% 0.19/0.44 %
% 0.19/0.44 % ------ iProver source info
% 0.19/0.44
% 0.19/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.44 % git: non_committed_changes: true
% 0.19/0.44 % git: last_make_outside_of_git: true
% 0.19/0.44
% 0.19/0.44 %
% 0.19/0.44 % ------ Input Options
% 0.19/0.44
% 0.19/0.44 % --out_options all
% 0.19/0.44 % --tptp_safe_out true
% 0.19/0.44 % --problem_path ""
% 0.19/0.44 % --include_path ""
% 0.19/0.44 % --clausifier .//eprover
% 0.19/0.44 % --clausifier_options --tstp-format
% 0.19/0.44 % --stdin false
% 0.19/0.44 % --dbg_backtrace false
% 0.19/0.44 % --dbg_dump_prop_clauses false
% 0.19/0.44 % --dbg_dump_prop_clauses_file -
% 0.19/0.44 % --dbg_out_stat false
% 0.19/0.44
% 0.19/0.44 % ------ General Options
% 0.19/0.44
% 0.19/0.44 % --fof false
% 0.19/0.44 % --time_out_real 150.
% 0.19/0.44 % --time_out_prep_mult 0.2
% 0.19/0.44 % --time_out_virtual -1.
% 0.19/0.44 % --schedule none
% 0.19/0.44 % --ground_splitting input
% 0.19/0.44 % --splitting_nvd 16
% 0.19/0.44 % --non_eq_to_eq false
% 0.19/0.44 % --prep_gs_sim true
% 0.19/0.44 % --prep_unflatten false
% 0.19/0.44 % --prep_res_sim true
% 0.19/0.44 % --prep_upred true
% 0.19/0.44 % --res_sim_input true
% 0.19/0.44 % --clause_weak_htbl true
% 0.19/0.44 % --gc_record_bc_elim false
% 0.19/0.44 % --symbol_type_check false
% 0.19/0.44 % --clausify_out false
% 0.19/0.44 % --large_theory_mode false
% 0.19/0.44 % --prep_sem_filter none
% 0.19/0.44 % --prep_sem_filter_out false
% 0.19/0.44 % --preprocessed_out false
% 0.19/0.44 % --sub_typing false
% 0.19/0.44 % --brand_transform false
% 0.19/0.44 % --pure_diseq_elim true
% 0.19/0.44 % --min_unsat_core false
% 0.19/0.44 % --pred_elim true
% 0.19/0.44 % --add_important_lit false
% 0.19/0.44 % --soft_assumptions false
% 0.19/0.44 % --reset_solvers false
% 0.19/0.44 % --bc_imp_inh []
% 0.19/0.44 % --conj_cone_tolerance 1.5
% 0.19/0.44 % --prolific_symb_bound 500
% 0.19/0.44 % --lt_threshold 2000
% 0.19/0.44
% 0.19/0.44 % ------ SAT Options
% 0.19/0.44
% 0.19/0.44 % --sat_mode false
% 0.19/0.44 % --sat_fm_restart_options ""
% 0.19/0.44 % --sat_gr_def false
% 0.19/0.44 % --sat_epr_types true
% 0.19/0.44 % --sat_non_cyclic_types false
% 0.19/0.44 % --sat_finite_models false
% 0.19/0.44 % --sat_fm_lemmas false
% 0.19/0.44 % --sat_fm_prep false
% 0.19/0.44 % --sat_fm_uc_incr true
% 0.19/0.44 % --sat_out_model small
% 0.19/0.44 % --sat_out_clauses false
% 0.19/0.44
% 0.19/0.44 % ------ QBF Options
% 0.19/0.44
% 0.19/0.44 % --qbf_mode false
% 0.19/0.44 % --qbf_elim_univ true
% 0.19/0.44 % --qbf_sk_in true
% 0.19/0.44 % --qbf_pred_elim true
% 0.19/0.44 % --qbf_split 32
% 0.19/0.44
% 0.19/0.44 % ------ BMC1 Options
% 0.19/0.44
% 0.19/0.44 % --bmc1_incremental false
% 0.19/0.44 % --bmc1_axioms reachable_all
% 0.19/0.44 % --bmc1_min_bound 0
% 0.19/0.44 % --bmc1_max_bound -1
% 0.19/0.44 % --bmc1_max_bound_default -1
% 0.19/0.44 % --bmc1_symbol_reachability true
% 0.19/0.44 % --bmc1_property_lemmas false
% 0.19/0.44 % --bmc1_k_induction false
% 0.19/0.44 % --bmc1_non_equiv_states false
% 0.19/0.44 % --bmc1_deadlock false
% 0.19/0.44 % --bmc1_ucm false
% 0.19/0.44 % --bmc1_add_unsat_core none
% 0.19/0.44 % --bmc1_unsat_core_children false
% 0.19/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.44 % --bmc1_out_stat full
% 0.19/0.44 % --bmc1_ground_init false
% 0.19/0.44 % --bmc1_pre_inst_next_state false
% 0.19/0.44 % --bmc1_pre_inst_state false
% 0.19/0.44 % --bmc1_pre_inst_reach_state false
% 0.19/0.44 % --bmc1_out_unsat_core false
% 0.19/0.44 % --bmc1_aig_witness_out false
% 0.19/0.44 % --bmc1_verbose false
% 0.19/0.44 % --bmc1_dump_clauses_tptp false
% 0.46/0.78 % --bmc1_dump_unsat_core_tptp false
% 0.46/0.78 % --bmc1_dump_file -
% 0.46/0.78 % --bmc1_ucm_expand_uc_limit 128
% 0.46/0.78 % --bmc1_ucm_n_expand_iterations 6
% 0.46/0.78 % --bmc1_ucm_extend_mode 1
% 0.46/0.78 % --bmc1_ucm_init_mode 2
% 0.46/0.78 % --bmc1_ucm_cone_mode none
% 0.46/0.78 % --bmc1_ucm_reduced_relation_type 0
% 0.46/0.78 % --bmc1_ucm_relax_model 4
% 0.46/0.78 % --bmc1_ucm_full_tr_after_sat true
% 0.46/0.78 % --bmc1_ucm_expand_neg_assumptions false
% 0.46/0.78 % --bmc1_ucm_layered_model none
% 0.46/0.78 % --bmc1_ucm_max_lemma_size 10
% 0.46/0.78
% 0.46/0.78 % ------ AIG Options
% 0.46/0.78
% 0.46/0.78 % --aig_mode false
% 0.46/0.78
% 0.46/0.78 % ------ Instantiation Options
% 0.46/0.78
% 0.46/0.78 % --instantiation_flag true
% 0.46/0.78 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.46/0.78 % --inst_solver_per_active 750
% 0.46/0.78 % --inst_solver_calls_frac 0.5
% 0.46/0.78 % --inst_passive_queue_type priority_queues
% 0.46/0.78 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.46/0.78 % --inst_passive_queues_freq [25;2]
% 0.46/0.78 % --inst_dismatching true
% 0.46/0.78 % --inst_eager_unprocessed_to_passive true
% 0.46/0.78 % --inst_prop_sim_given true
% 0.46/0.78 % --inst_prop_sim_new false
% 0.46/0.78 % --inst_orphan_elimination true
% 0.46/0.78 % --inst_learning_loop_flag true
% 0.46/0.78 % --inst_learning_start 3000
% 0.46/0.78 % --inst_learning_factor 2
% 0.46/0.78 % --inst_start_prop_sim_after_learn 3
% 0.46/0.78 % --inst_sel_renew solver
% 0.46/0.78 % --inst_lit_activity_flag true
% 0.46/0.78 % --inst_out_proof true
% 0.46/0.78
% 0.46/0.78 % ------ Resolution Options
% 0.46/0.78
% 0.46/0.78 % --resolution_flag true
% 0.46/0.78 % --res_lit_sel kbo_max
% 0.46/0.78 % --res_to_prop_solver none
% 0.46/0.78 % --res_prop_simpl_new false
% 0.46/0.78 % --res_prop_simpl_given false
% 0.46/0.78 % --res_passive_queue_type priority_queues
% 0.46/0.78 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.46/0.78 % --res_passive_queues_freq [15;5]
% 0.46/0.78 % --res_forward_subs full
% 0.46/0.78 % --res_backward_subs full
% 0.46/0.78 % --res_forward_subs_resolution true
% 0.46/0.78 % --res_backward_subs_resolution true
% 0.46/0.78 % --res_orphan_elimination false
% 0.46/0.78 % --res_time_limit 1000.
% 0.46/0.78 % --res_out_proof true
% 0.46/0.78 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_bdcdeb.s
% 0.46/0.78 % --modulo true
% 0.46/0.78
% 0.46/0.78 % ------ Combination Options
% 0.46/0.78
% 0.46/0.78 % --comb_res_mult 1000
% 0.46/0.78 % --comb_inst_mult 300
% 0.46/0.78 % ------
% 0.46/0.78
% 0.46/0.78 % ------ Parsing...% successful
% 0.46/0.78
% 0.46/0.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe_e snvd_s sp: 0 0s snvd_e %
% 0.46/0.78
% 0.46/0.78 % ------ Proving...
% 0.46/0.78 % ------ Problem Properties
% 0.46/0.78
% 0.46/0.78 %
% 0.46/0.78 % EPR false
% 0.46/0.78 % Horn false
% 0.46/0.78 % Has equality true
% 0.46/0.78
% 0.46/0.78 % % ------ Input Options Time Limit: Unbounded
% 0.46/0.78
% 0.46/0.78
% 0.46/0.78 Compiling...
% 0.46/0.78 Loading plugin: done.
% 0.46/0.78 Compiling...
% 0.46/0.78 Loading plugin: done.
% 0.46/0.78 Compiling...
% 0.46/0.78 Loading plugin: done.
% 0.46/0.78 % % ------ Current options:
% 0.46/0.78
% 0.46/0.78 % ------ Input Options
% 0.46/0.78
% 0.46/0.78 % --out_options all
% 0.46/0.78 % --tptp_safe_out true
% 0.46/0.78 % --problem_path ""
% 0.46/0.78 % --include_path ""
% 0.46/0.78 % --clausifier .//eprover
% 0.46/0.78 % --clausifier_options --tstp-format
% 0.46/0.78 % --stdin false
% 0.46/0.78 % --dbg_backtrace false
% 0.46/0.78 % --dbg_dump_prop_clauses false
% 0.46/0.78 % --dbg_dump_prop_clauses_file -
% 0.46/0.78 % --dbg_out_stat false
% 0.46/0.78
% 0.46/0.78 % ------ General Options
% 0.46/0.78
% 0.46/0.78 % --fof false
% 0.46/0.78 % --time_out_real 150.
% 0.46/0.78 % --time_out_prep_mult 0.2
% 0.46/0.78 % --time_out_virtual -1.
% 0.46/0.78 % --schedule none
% 0.46/0.78 % --ground_splitting input
% 0.46/0.78 % --splitting_nvd 16
% 0.46/0.78 % --non_eq_to_eq false
% 0.46/0.78 % --prep_gs_sim true
% 0.46/0.78 % --prep_unflatten false
% 0.46/0.78 % --prep_res_sim true
% 0.46/0.78 % --prep_upred true
% 0.46/0.78 % --res_sim_input true
% 0.46/0.78 % --clause_weak_htbl true
% 0.46/0.78 % --gc_record_bc_elim false
% 0.46/0.78 % --symbol_type_check false
% 0.46/0.78 % --clausify_out false
% 0.46/0.78 % --large_theory_mode false
% 0.46/0.78 % --prep_sem_filter none
% 0.46/0.78 % --prep_sem_filter_out false
% 0.46/0.78 % --preprocessed_out false
% 0.46/0.78 % --sub_typing false
% 0.46/0.78 % --brand_transform false
% 0.46/0.78 % --pure_diseq_elim true
% 0.46/0.78 % --min_unsat_core false
% 0.46/0.78 % --pred_elim true
% 0.46/0.78 % --add_important_lit false
% 0.46/0.78 % --soft_assumptions false
% 0.46/0.78 % --reset_solvers false
% 0.46/0.78 % --bc_imp_inh []
% 0.46/0.79 % --conj_cone_tolerance 1.5
% 0.46/0.79 % --prolific_symb_bound 500
% 0.46/0.79 % --lt_threshold 2000
% 0.46/0.79
% 0.46/0.79 % ------ SAT Options
% 0.46/0.79
% 0.46/0.79 % --sat_mode false
% 0.46/0.79 % --sat_fm_restart_options ""
% 0.46/0.79 % --sat_gr_def false
% 0.46/0.79 % --sat_epr_types true
% 0.46/0.79 % --sat_non_cyclic_types false
% 0.46/0.79 % --sat_finite_models false
% 0.46/0.79 % --sat_fm_lemmas false
% 0.46/0.79 % --sat_fm_prep false
% 0.46/0.79 % --sat_fm_uc_incr true
% 0.46/0.79 % --sat_out_model small
% 0.46/0.79 % --sat_out_clauses false
% 0.46/0.79
% 0.46/0.79 % ------ QBF Options
% 0.46/0.79
% 0.46/0.79 % --qbf_mode false
% 0.46/0.79 % --qbf_elim_univ true
% 0.46/0.79 % --qbf_sk_in true
% 0.46/0.79 % --qbf_pred_elim true
% 0.46/0.79 % --qbf_split 32
% 0.46/0.79
% 0.46/0.79 % ------ BMC1 Options
% 0.46/0.79
% 0.46/0.79 % --bmc1_incremental false
% 0.46/0.79 % --bmc1_axioms reachable_all
% 0.46/0.79 % --bmc1_min_bound 0
% 0.46/0.79 % --bmc1_max_bound -1
% 0.46/0.79 % --bmc1_max_bound_default -1
% 0.46/0.79 % --bmc1_symbol_reachability true
% 0.46/0.79 % --bmc1_property_lemmas false
% 0.46/0.79 % --bmc1_k_induction false
% 0.46/0.79 % --bmc1_non_equiv_states false
% 0.46/0.79 % --bmc1_deadlock false
% 0.46/0.79 % --bmc1_ucm false
% 0.46/0.79 % --bmc1_add_unsat_core none
% 0.46/0.79 % --bmc1_unsat_core_children false
% 0.46/0.79 % --bmc1_unsat_core_extrapolate_axioms false
% 0.46/0.79 % --bmc1_out_stat full
% 0.46/0.79 % --bmc1_ground_init false
% 0.46/0.79 % --bmc1_pre_inst_next_state false
% 0.46/0.79 % --bmc1_pre_inst_state false
% 0.46/0.79 % --bmc1_pre_inst_reach_state false
% 0.46/0.79 % --bmc1_out_unsat_core false
% 0.46/0.79 % --bmc1_aig_witness_out false
% 0.46/0.79 % --bmc1_verbose false
% 0.46/0.79 % --bmc1_dump_clauses_tptp false
% 0.46/0.79 % --bmc1_dump_unsat_core_tptp false
% 0.46/0.79 % --bmc1_dump_file -
% 0.46/0.79 % --bmc1_ucm_expand_uc_limit 128
% 0.46/0.79 % --bmc1_ucm_n_expand_iterations 6
% 0.46/0.79 % --bmc1_ucm_extend_mode 1
% 0.46/0.79 % --bmc1_ucm_init_mode 2
% 0.46/0.79 % --bmc1_ucm_cone_mode none
% 0.46/0.79 % --bmc1_ucm_reduced_relation_type 0
% 0.46/0.79 % --bmc1_ucm_relax_model 4
% 0.46/0.79 % --bmc1_ucm_full_tr_after_sat true
% 0.46/0.79 % --bmc1_ucm_expand_neg_assumptions false
% 0.46/0.79 % --bmc1_ucm_layered_model none
% 0.46/0.79 % --bmc1_ucm_max_lemma_size 10
% 0.46/0.79
% 0.46/0.79 % ------ AIG Options
% 0.46/0.79
% 0.46/0.79 % --aig_mode false
% 0.46/0.79
% 0.46/0.79 % ------ Instantiation Options
% 0.46/0.79
% 0.46/0.79 % --instantiation_flag true
% 0.46/0.79 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.46/0.79 % --inst_solver_per_active 750
% 0.46/0.79 % --inst_solver_calls_frac 0.5
% 0.46/0.79 % --inst_passive_queue_type priority_queues
% 0.46/0.79 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.46/0.79 % --inst_passive_queues_freq [25;2]
% 150.17/150.44 % --inst_dismatching true
% 150.17/150.44 % --inst_eager_unprocessed_to_passive true
% 150.17/150.44 % --inst_prop_sim_given true
% 150.17/150.44 % --inst_prop_sim_new false
% 150.17/150.44 % --inst_orphan_elimination true
% 150.17/150.44 % --inst_learning_loop_flag true
% 150.17/150.44 % --inst_learning_start 3000
% 150.17/150.44 % --inst_learning_factor 2
% 150.17/150.44 % --inst_start_prop_sim_after_learn 3
% 150.17/150.44 % --inst_sel_renew solver
% 150.17/150.44 % --inst_lit_activity_flag true
% 150.17/150.44 % --inst_out_proof true
% 150.17/150.44
% 150.17/150.44 % ------ Resolution Options
% 150.17/150.44
% 150.17/150.44 % --resolution_flag true
% 150.17/150.44 % --res_lit_sel kbo_max
% 150.17/150.44 % --res_to_prop_solver none
% 150.17/150.44 % --res_prop_simpl_new false
% 150.17/150.44 % --res_prop_simpl_given false
% 150.17/150.44 % --res_passive_queue_type priority_queues
% 150.17/150.44 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.17/150.44 % --res_passive_queues_freq [15;5]
% 150.17/150.44 % --res_forward_subs full
% 150.17/150.44 % --res_backward_subs full
% 150.17/150.44 % --res_forward_subs_resolution true
% 150.17/150.44 % --res_backward_subs_resolution true
% 150.17/150.44 % --res_orphan_elimination false
% 150.17/150.44 % --res_time_limit 1000.
% 150.17/150.44 % --res_out_proof true
% 150.17/150.44 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_bdcdeb.s
% 150.17/150.44 % --modulo true
% 150.17/150.44
% 150.17/150.44 % ------ Combination Options
% 150.17/150.44
% 150.17/150.44 % --comb_res_mult 1000
% 150.17/150.44 % --comb_inst_mult 300
% 150.17/150.44 % ------
% 150.17/150.44
% 150.17/150.44
% 150.17/150.44
% 150.17/150.44 % ------ Proving...
% 150.17/150.44 %
% 150.17/150.44
% 150.17/150.44
% 150.17/150.44 % Time Out Real
% 150.17/150.44
% 150.17/150.44 % ------ Statistics
% 150.17/150.44
% 150.17/150.44 % ------ General
% 150.17/150.44
% 150.17/150.44 % num_of_input_clauses: 196
% 150.17/150.44 % num_of_input_neg_conjectures: 3
% 150.17/150.44 % num_of_splits: 0
% 150.17/150.44 % num_of_split_atoms: 0
% 150.17/150.44 % num_of_sem_filtered_clauses: 0
% 150.17/150.44 % num_of_subtypes: 0
% 150.17/150.44 % monotx_restored_types: 0
% 150.17/150.44 % sat_num_of_epr_types: 0
% 150.17/150.44 % sat_num_of_non_cyclic_types: 0
% 150.17/150.44 % sat_guarded_non_collapsed_types: 0
% 150.17/150.44 % is_epr: 0
% 150.17/150.44 % is_horn: 0
% 150.17/150.44 % has_eq: 1
% 150.17/150.44 % num_pure_diseq_elim: 0
% 150.17/150.44 % simp_replaced_by: 1
% 150.17/150.44 % res_preprocessed: 80
% 150.17/150.44 % prep_upred: 0
% 150.17/150.44 % prep_unflattend: 0
% 150.17/150.44 % pred_elim_cands: 4
% 150.17/150.44 % pred_elim: 2
% 150.17/150.44 % pred_elim_cl: 2
% 150.17/150.44 % pred_elim_cycles: 3
% 150.17/150.44 % forced_gc_time: 0
% 150.17/150.44 % gc_basic_clause_elim: 0
% 150.17/150.44 % parsing_time: 0.007
% 150.17/150.44 % sem_filter_time: 0.
% 150.17/150.44 % pred_elim_time: 0.
% 150.17/150.44 % out_proof_time: 0.
% 150.17/150.44 % monotx_time: 0.
% 150.17/150.44 % subtype_inf_time: 0.
% 150.17/150.44 % unif_index_cands_time: 1.47
% 150.17/150.44 % unif_index_add_time: 0.056
% 150.17/150.44 % total_time: 150.016
% 150.17/150.44 % num_of_symbols: 71
% 150.17/150.44 % num_of_terms: 3680510
% 150.17/150.44
% 150.17/150.44 % ------ Propositional Solver
% 150.17/150.44
% 150.17/150.44 % prop_solver_calls: 34
% 150.17/150.44 % prop_fast_solver_calls: 285
% 150.17/150.44 % prop_num_of_clauses: 79242
% 150.17/150.44 % prop_preprocess_simplified: 72728
% 150.17/150.44 % prop_fo_subsumed: 0
% 150.17/150.44 % prop_solver_time: 0.034
% 150.17/150.44 % prop_fast_solver_time: 0.
% 150.17/150.44 % prop_unsat_core_time: 0.
% 150.17/150.44
% 150.17/150.44 % ------ QBF
% 150.17/150.44
% 150.17/150.44 % qbf_q_res: 0
% 150.17/150.44 % qbf_num_tautologies: 0
% 150.17/150.44 % qbf_prep_cycles: 0
% 150.17/150.44
% 150.17/150.44 % ------ BMC1
% 150.17/150.44
% 150.17/150.44 % bmc1_current_bound: -1
% 150.17/150.44 % bmc1_last_solved_bound: -1
% 150.17/150.44 % bmc1_unsat_core_size: -1
% 150.17/150.44 % bmc1_unsat_core_parents_size: -1
% 150.17/150.44 % bmc1_merge_next_fun: 0
% 150.17/150.44 % bmc1_unsat_core_clauses_time: 0.
% 150.17/150.44
% 150.17/150.44 % ------ Instantiation
% 150.17/150.44
% 150.17/150.44 % inst_num_of_clauses: 950
% 150.17/150.44 % inst_num_in_passive: 607
% 150.17/150.47 % inst_num_in_active: 295
% 150.17/150.47 % inst_num_in_unprocessed: 46
% 150.17/150.47 % inst_num_of_loops: 299
% 150.17/150.47 % inst_num_of_learning_restarts: 1
% 150.17/150.47 % inst_num_moves_active_passive: 1
% 150.17/150.47 % inst_lit_activity: 181
% 150.17/150.47 % inst_lit_activity_moves: 0
% 150.17/150.47 % inst_num_tautologies: 2
% 150.17/150.47 % inst_num_prop_implied: 0
% 150.17/150.47 % inst_num_existing_simplified: 0
% 150.17/150.47 % inst_num_eq_res_simplified: 0
% 150.17/150.47 % inst_num_child_elim: 0
% 150.17/150.47 % inst_num_of_dismatching_blockings: 242
% 150.17/150.47 % inst_num_of_non_proper_insts: 552
% 150.17/150.47 % inst_num_of_duplicates: 173
% 150.17/150.47 % inst_inst_num_from_inst_to_res: 0
% 150.17/150.47 % inst_dismatching_checking_time: 1.385
% 150.17/150.47
% 150.17/150.47 % ------ Resolution
% 150.17/150.47
% 150.17/150.47 % res_num_of_clauses: 2652317
% 150.17/150.47 % res_num_in_passive: 2652406
% 150.17/150.47 % res_num_in_active: 10131
% 150.17/150.47 % res_num_of_loops: 11564
% 150.17/150.47 % res_forward_subset_subsumed: 221106
% 150.17/150.47 % res_backward_subset_subsumed: 10566
% 150.17/150.47 % res_forward_subsumed: 1156
% 150.17/150.47 % res_backward_subsumed: 202
% 150.17/150.47 % res_forward_subsumption_resolution: 166
% 150.17/150.47 % res_backward_subsumption_resolution: 8
% 150.17/150.47 % res_clause_to_clause_subsumption: 195549
% 150.17/150.47 % res_orphan_elimination: 0
% 150.17/150.47 % res_tautology_del: 2039
% 150.17/150.47 % res_num_eq_res_simplified: 23
% 150.17/150.47 % res_num_sel_changes: 0
% 150.17/150.47 % res_moves_from_active_to_pass: 0
% 150.17/150.47
% 150.17/150.47 % Status Unknown
% 150.27/150.53 % Orienting using strategy ClausalAll
% 150.27/150.53 % FOF problem with conjecture
% 150.27/150.53 % 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_bdcdeb.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_1c30a7.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_a3a51a | grep -v "SZS"
% 150.27/150.55
% 150.27/150.55 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.27/150.55
% 150.27/150.55 %
% 150.27/150.55 % ------ iProver source info
% 150.27/150.55
% 150.27/150.55 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.27/150.55 % git: non_committed_changes: true
% 150.27/150.55 % git: last_make_outside_of_git: true
% 150.27/150.55
% 150.27/150.55 %
% 150.27/150.55 % ------ Input Options
% 150.27/150.55
% 150.27/150.55 % --out_options all
% 150.27/150.55 % --tptp_safe_out true
% 150.27/150.55 % --problem_path ""
% 150.27/150.55 % --include_path ""
% 150.27/150.55 % --clausifier .//eprover
% 150.27/150.55 % --clausifier_options --tstp-format
% 150.27/150.55 % --stdin false
% 150.27/150.55 % --dbg_backtrace false
% 150.27/150.55 % --dbg_dump_prop_clauses false
% 150.27/150.55 % --dbg_dump_prop_clauses_file -
% 150.27/150.55 % --dbg_out_stat false
% 150.27/150.55
% 150.27/150.55 % ------ General Options
% 150.27/150.55
% 150.27/150.55 % --fof false
% 150.27/150.55 % --time_out_real 150.
% 150.27/150.55 % --time_out_prep_mult 0.2
% 150.27/150.55 % --time_out_virtual -1.
% 150.27/150.55 % --schedule none
% 150.27/150.55 % --ground_splitting input
% 150.27/150.55 % --splitting_nvd 16
% 150.27/150.55 % --non_eq_to_eq false
% 150.27/150.55 % --prep_gs_sim true
% 150.27/150.55 % --prep_unflatten false
% 150.27/150.55 % --prep_res_sim true
% 150.27/150.55 % --prep_upred true
% 150.27/150.55 % --res_sim_input true
% 150.27/150.55 % --clause_weak_htbl true
% 150.27/150.55 % --gc_record_bc_elim false
% 150.27/150.55 % --symbol_type_check false
% 150.27/150.55 % --clausify_out false
% 150.27/150.55 % --large_theory_mode false
% 150.27/150.55 % --prep_sem_filter none
% 150.27/150.55 % --prep_sem_filter_out false
% 150.27/150.55 % --preprocessed_out false
% 150.27/150.55 % --sub_typing false
% 150.27/150.55 % --brand_transform false
% 150.27/150.55 % --pure_diseq_elim true
% 150.27/150.55 % --min_unsat_core false
% 150.27/150.55 % --pred_elim true
% 150.27/150.55 % --add_important_lit false
% 150.27/150.55 % --soft_assumptions false
% 150.27/150.55 % --reset_solvers false
% 150.27/150.55 % --bc_imp_inh []
% 150.27/150.55 % --conj_cone_tolerance 1.5
% 150.27/150.55 % --prolific_symb_bound 500
% 150.27/150.55 % --lt_threshold 2000
% 150.27/150.55
% 150.27/150.55 % ------ SAT Options
% 150.27/150.55
% 150.27/150.55 % --sat_mode false
% 150.27/150.55 % --sat_fm_restart_options ""
% 150.27/150.55 % --sat_gr_def false
% 150.27/150.55 % --sat_epr_types true
% 150.27/150.55 % --sat_non_cyclic_types false
% 150.27/150.55 % --sat_finite_models false
% 150.27/150.55 % --sat_fm_lemmas false
% 150.27/150.55 % --sat_fm_prep false
% 150.27/150.55 % --sat_fm_uc_incr true
% 150.27/150.55 % --sat_out_model small
% 150.27/150.55 % --sat_out_clauses false
% 150.27/150.55
% 150.27/150.55 % ------ QBF Options
% 150.27/150.55
% 150.27/150.55 % --qbf_mode false
% 150.27/150.55 % --qbf_elim_univ true
% 150.27/150.55 % --qbf_sk_in true
% 150.27/150.55 % --qbf_pred_elim true
% 150.27/150.55 % --qbf_split 32
% 150.27/150.55
% 150.27/150.55 % ------ BMC1 Options
% 150.27/150.55
% 150.27/150.55 % --bmc1_incremental false
% 150.27/150.55 % --bmc1_axioms reachable_all
% 150.27/150.55 % --bmc1_min_bound 0
% 150.27/150.55 % --bmc1_max_bound -1
% 150.27/150.55 % --bmc1_max_bound_default -1
% 150.27/150.55 % --bmc1_symbol_reachability true
% 150.27/150.55 % --bmc1_property_lemmas false
% 150.27/150.55 % --bmc1_k_induction false
% 150.27/150.55 % --bmc1_non_equiv_states false
% 150.27/150.55 % --bmc1_deadlock false
% 150.27/150.55 % --bmc1_ucm false
% 150.27/150.55 % --bmc1_add_unsat_core none
% 150.27/150.55 % --bmc1_unsat_core_children false
% 150.27/150.55 % --bmc1_unsat_core_extrapolate_axioms false
% 150.27/150.55 % --bmc1_out_stat full
% 150.27/150.55 % --bmc1_ground_init false
% 150.27/150.55 % --bmc1_pre_inst_next_state false
% 150.27/150.55 % --bmc1_pre_inst_state false
% 150.27/150.55 % --bmc1_pre_inst_reach_state false
% 150.27/150.55 % --bmc1_out_unsat_core false
% 150.27/150.55 % --bmc1_aig_witness_out false
% 150.27/150.55 % --bmc1_verbose false
% 150.27/150.55 % --bmc1_dump_clauses_tptp false
% 150.34/150.90 % --bmc1_dump_unsat_core_tptp false
% 150.34/150.90 % --bmc1_dump_file -
% 150.34/150.90 % --bmc1_ucm_expand_uc_limit 128
% 150.34/150.90 % --bmc1_ucm_n_expand_iterations 6
% 150.34/150.90 % --bmc1_ucm_extend_mode 1
% 150.34/150.90 % --bmc1_ucm_init_mode 2
% 150.34/150.90 % --bmc1_ucm_cone_mode none
% 150.34/150.90 % --bmc1_ucm_reduced_relation_type 0
% 150.34/150.90 % --bmc1_ucm_relax_model 4
% 150.34/150.90 % --bmc1_ucm_full_tr_after_sat true
% 150.34/150.90 % --bmc1_ucm_expand_neg_assumptions false
% 150.34/150.90 % --bmc1_ucm_layered_model none
% 150.34/150.90 % --bmc1_ucm_max_lemma_size 10
% 150.34/150.90
% 150.34/150.90 % ------ AIG Options
% 150.34/150.90
% 150.34/150.90 % --aig_mode false
% 150.34/150.90
% 150.34/150.90 % ------ Instantiation Options
% 150.34/150.90
% 150.34/150.90 % --instantiation_flag true
% 150.34/150.90 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.34/150.90 % --inst_solver_per_active 750
% 150.34/150.90 % --inst_solver_calls_frac 0.5
% 150.34/150.90 % --inst_passive_queue_type priority_queues
% 150.34/150.90 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.34/150.90 % --inst_passive_queues_freq [25;2]
% 150.34/150.90 % --inst_dismatching true
% 150.34/150.90 % --inst_eager_unprocessed_to_passive true
% 150.34/150.90 % --inst_prop_sim_given true
% 150.34/150.90 % --inst_prop_sim_new false
% 150.34/150.90 % --inst_orphan_elimination true
% 150.34/150.90 % --inst_learning_loop_flag true
% 150.34/150.90 % --inst_learning_start 3000
% 150.34/150.90 % --inst_learning_factor 2
% 150.34/150.90 % --inst_start_prop_sim_after_learn 3
% 150.34/150.90 % --inst_sel_renew solver
% 150.34/150.90 % --inst_lit_activity_flag true
% 150.34/150.90 % --inst_out_proof true
% 150.34/150.90
% 150.34/150.90 % ------ Resolution Options
% 150.34/150.90
% 150.34/150.90 % --resolution_flag true
% 150.34/150.90 % --res_lit_sel kbo_max
% 150.34/150.90 % --res_to_prop_solver none
% 150.34/150.90 % --res_prop_simpl_new false
% 150.34/150.90 % --res_prop_simpl_given false
% 150.34/150.90 % --res_passive_queue_type priority_queues
% 150.34/150.90 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.34/150.90 % --res_passive_queues_freq [15;5]
% 150.34/150.90 % --res_forward_subs full
% 150.34/150.90 % --res_backward_subs full
% 150.34/150.90 % --res_forward_subs_resolution true
% 150.34/150.90 % --res_backward_subs_resolution true
% 150.34/150.90 % --res_orphan_elimination false
% 150.34/150.90 % --res_time_limit 1000.
% 150.34/150.90 % --res_out_proof true
% 150.34/150.90 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_bdcdeb.s
% 150.34/150.90 % --modulo true
% 150.34/150.90
% 150.34/150.90 % ------ Combination Options
% 150.34/150.90
% 150.34/150.90 % --comb_res_mult 1000
% 150.34/150.90 % --comb_inst_mult 300
% 150.34/150.90 % ------
% 150.34/150.90
% 150.34/150.90 % ------ Parsing...% successful
% 150.34/150.90
% 150.34/150.90 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe_e snvd_s sp: 0 0s snvd_e %
% 150.34/150.90
% 150.34/150.90 % ------ Proving...
% 150.34/150.90 % ------ Problem Properties
% 150.34/150.90
% 150.34/150.90 %
% 150.34/150.90 % EPR false
% 150.34/150.90 % Horn false
% 150.34/150.90 % Has equality true
% 150.34/150.90
% 150.34/150.90 % % ------ Input Options Time Limit: Unbounded
% 150.34/150.90
% 150.34/150.90
% 150.34/150.90 Compiling...
% 150.34/150.90 Loading plugin: done.
% 150.34/150.90 Compiling...
% 150.34/150.90 Loading plugin: done.
% 150.34/150.90 Compiling...
% 150.34/150.90 Loading plugin: done.
% 150.34/150.90 % % ------ Current options:
% 150.34/150.90
% 150.34/150.90 % ------ Input Options
% 150.34/150.90
% 150.34/150.90 % --out_options all
% 150.34/150.90 % --tptp_safe_out true
% 150.34/150.90 % --problem_path ""
% 150.34/150.90 % --include_path ""
% 150.34/150.90 % --clausifier .//eprover
% 150.34/150.90 % --clausifier_options --tstp-format
% 150.34/150.90 % --stdin false
% 150.34/150.90 % --dbg_backtrace false
% 150.34/150.90 % --dbg_dump_prop_clauses false
% 150.34/150.90 % --dbg_dump_prop_clauses_file -
% 150.34/150.90 % --dbg_out_stat false
% 150.34/150.90
% 150.34/150.90 % ------ General Options
% 150.34/150.90
% 150.34/150.90 % --fof false
% 150.34/150.90 % --time_out_real 150.
% 150.34/150.90 % --time_out_prep_mult 0.2
% 150.34/150.90 % --time_out_virtual -1.
% 150.34/150.90 % --schedule none
% 150.34/150.90 % --ground_splitting input
% 150.34/150.90 % --splitting_nvd 16
% 150.34/150.90 % --non_eq_to_eq false
% 150.34/150.90 % --prep_gs_sim true
% 150.34/150.90 % --prep_unflatten false
% 150.34/150.90 % --prep_res_sim true
% 150.34/150.90 % --prep_upred true
% 150.34/150.90 % --res_sim_input true
% 150.34/150.90 % --clause_weak_htbl true
% 150.34/150.90 % --gc_record_bc_elim false
% 150.34/150.90 % --symbol_type_check false
% 150.34/150.90 % --clausify_out false
% 150.34/150.90 % --large_theory_mode false
% 150.34/150.90 % --prep_sem_filter none
% 150.34/150.90 % --prep_sem_filter_out false
% 150.34/150.90 % --preprocessed_out false
% 150.34/150.90 % --sub_typing false
% 150.34/150.90 % --brand_transform false
% 150.34/150.90 % --pure_diseq_elim true
% 150.34/150.90 % --min_unsat_core false
% 150.34/150.90 % --pred_elim true
% 150.34/150.90 % --add_important_lit false
% 150.34/150.90 % --soft_assumptions false
% 150.34/150.90 % --reset_solvers false
% 150.34/150.90 % --bc_imp_inh []
% 150.34/150.90 % --conj_cone_tolerance 1.5
% 150.34/150.90 % --prolific_symb_bound 500
% 150.34/150.90 % --lt_threshold 2000
% 150.34/150.90
% 150.34/150.90 % ------ SAT Options
% 150.34/150.90
% 150.34/150.90 % --sat_mode false
% 150.34/150.90 % --sat_fm_restart_options ""
% 150.34/150.90 % --sat_gr_def false
% 150.34/150.90 % --sat_epr_types true
% 150.34/150.90 % --sat_non_cyclic_types false
% 150.34/150.90 % --sat_finite_models false
% 150.34/150.90 % --sat_fm_lemmas false
% 150.34/150.90 % --sat_fm_prep false
% 150.34/150.90 % --sat_fm_uc_incr true
% 150.34/150.90 % --sat_out_model small
% 150.34/150.90 % --sat_out_clauses false
% 150.34/150.90
% 150.34/150.90 % ------ QBF Options
% 150.34/150.90
% 150.34/150.90 % --qbf_mode false
% 150.34/150.90 % --qbf_elim_univ true
% 150.34/150.90 % --qbf_sk_in true
% 150.34/150.90 % --qbf_pred_elim true
% 150.34/150.90 % --qbf_split 32
% 150.34/150.90
% 150.34/150.90 % ------ BMC1 Options
% 150.34/150.90
% 150.34/150.90 % --bmc1_incremental false
% 150.34/150.90 % --bmc1_axioms reachable_all
% 150.34/150.90 % --bmc1_min_bound 0
% 150.34/150.90 % --bmc1_max_bound -1
% 150.34/150.90 % --bmc1_max_bound_default -1
% 150.34/150.90 % --bmc1_symbol_reachability true
% 150.34/150.90 % --bmc1_property_lemmas false
% 150.34/150.90 % --bmc1_k_induction false
% 150.34/150.90 % --bmc1_non_equiv_states false
% 150.34/150.90 % --bmc1_deadlock false
% 150.34/150.90 % --bmc1_ucm false
% 150.34/150.90 % --bmc1_add_unsat_core none
% 150.34/150.90 % --bmc1_unsat_core_children false
% 150.34/150.90 % --bmc1_unsat_core_extrapolate_axioms false
% 150.34/150.90 % --bmc1_out_stat full
% 150.34/150.90 % --bmc1_ground_init false
% 150.34/150.90 % --bmc1_pre_inst_next_state false
% 150.34/150.90 % --bmc1_pre_inst_state false
% 150.34/150.90 % --bmc1_pre_inst_reach_state false
% 150.34/150.90 % --bmc1_out_unsat_core false
% 150.34/150.90 % --bmc1_aig_witness_out false
% 150.34/150.90 % --bmc1_verbose false
% 150.34/150.90 % --bmc1_dump_clauses_tptp false
% 150.34/150.90 % --bmc1_dump_unsat_core_tptp false
% 150.34/150.90 % --bmc1_dump_file -
% 150.34/150.90 % --bmc1_ucm_expand_uc_limit 128
% 150.34/150.90 % --bmc1_ucm_n_expand_iterations 6
% 150.34/150.90 % --bmc1_ucm_extend_mode 1
% 150.34/150.90 % --bmc1_ucm_init_mode 2
% 150.34/150.90 % --bmc1_ucm_cone_mode none
% 150.34/150.90 % --bmc1_ucm_reduced_relation_type 0
% 150.34/150.90 % --bmc1_ucm_relax_model 4
% 150.34/150.90 % --bmc1_ucm_full_tr_after_sat true
% 150.34/150.90 % --bmc1_ucm_expand_neg_assumptions false
% 150.34/150.90 % --bmc1_ucm_layered_model none
% 150.34/150.90 % --bmc1_ucm_max_lemma_size 10
% 150.34/150.90
% 150.34/150.90 % ------ AIG Options
% 150.34/150.90
% 150.34/150.90 % --aig_mode false
% 150.34/150.90
% 150.34/150.90 % ------ Instantiation Options
% 150.34/150.90
% 150.34/150.90 % --instantiation_flag true
% 150.34/150.90 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.34/150.90 % --inst_solver_per_active 750
% 150.34/150.90 % --inst_solver_calls_frac 0.5
% 150.34/150.90 % --inst_passive_queue_type priority_queues
% 150.34/150.90 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.34/150.90 % --inst_passive_queues_freq [25;2]
% 157.26/157.57 % --inst_dismatching true
% 157.26/157.57 % --inst_eager_unprocessed_to_passive true
% 157.26/157.57 % --inst_prop_sim_given true
% 157.26/157.57 % --inst_prop_sim_new false
% 157.26/157.57 % --inst_orphan_elimination true
% 157.26/157.57 % --inst_learning_loop_flag true
% 157.26/157.57 % --inst_learning_start 3000
% 157.26/157.57 % --inst_learning_factor 2
% 157.26/157.57 % --inst_start_prop_sim_after_learn 3
% 157.26/157.57 % --inst_sel_renew solver
% 157.26/157.57 % --inst_lit_activity_flag true
% 157.26/157.57 % --inst_out_proof true
% 157.26/157.57
% 157.26/157.57 % ------ Resolution Options
% 157.26/157.57
% 157.26/157.57 % --resolution_flag true
% 157.26/157.57 % --res_lit_sel kbo_max
% 157.26/157.57 % --res_to_prop_solver none
% 157.26/157.57 % --res_prop_simpl_new false
% 157.26/157.57 % --res_prop_simpl_given false
% 157.26/157.57 % --res_passive_queue_type priority_queues
% 157.26/157.57 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 157.26/157.57 % --res_passive_queues_freq [15;5]
% 157.26/157.57 % --res_forward_subs full
% 157.26/157.57 % --res_backward_subs full
% 157.26/157.57 % --res_forward_subs_resolution true
% 157.26/157.57 % --res_backward_subs_resolution true
% 157.26/157.57 % --res_orphan_elimination false
% 157.26/157.57 % --res_time_limit 1000.
% 157.26/157.57 % --res_out_proof true
% 157.26/157.57 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_bdcdeb.s
% 157.26/157.57 % --modulo true
% 157.26/157.57
% 157.26/157.57 % ------ Combination Options
% 157.26/157.57
% 157.26/157.57 % --comb_res_mult 1000
% 157.26/157.57 % --comb_inst_mult 300
% 157.26/157.57 % ------
% 157.26/157.57
% 157.26/157.57
% 157.26/157.57
% 157.26/157.57 % ------ Proving...
% 157.26/157.57 %
% 157.26/157.57
% 157.26/157.57
% 157.26/157.57 % Resolution empty clause
% 157.26/157.57
% 157.26/157.57 % ------ Statistics
% 157.26/157.57
% 157.26/157.57 % ------ General
% 157.26/157.57
% 157.26/157.57 % num_of_input_clauses: 338
% 157.26/157.57 % num_of_input_neg_conjectures: 3
% 157.26/157.57 % num_of_splits: 0
% 157.26/157.57 % num_of_split_atoms: 0
% 157.26/157.57 % num_of_sem_filtered_clauses: 0
% 157.26/157.57 % num_of_subtypes: 0
% 157.26/157.57 % monotx_restored_types: 0
% 157.26/157.57 % sat_num_of_epr_types: 0
% 157.26/157.57 % sat_num_of_non_cyclic_types: 0
% 157.26/157.57 % sat_guarded_non_collapsed_types: 0
% 157.26/157.57 % is_epr: 0
% 157.26/157.57 % is_horn: 0
% 157.26/157.57 % has_eq: 1
% 157.26/157.57 % num_pure_diseq_elim: 0
% 157.26/157.57 % simp_replaced_by: 0
% 157.26/157.57 % res_preprocessed: 80
% 157.26/157.57 % prep_upred: 0
% 157.26/157.57 % prep_unflattend: 0
% 157.26/157.57 % pred_elim_cands: 4
% 157.26/157.57 % pred_elim: 2
% 157.26/157.57 % pred_elim_cl: 2
% 157.26/157.57 % pred_elim_cycles: 3
% 157.26/157.57 % forced_gc_time: 0
% 157.26/157.57 % gc_basic_clause_elim: 0
% 157.26/157.57 % parsing_time: 0.006
% 157.26/157.57 % sem_filter_time: 0.
% 157.26/157.57 % pred_elim_time: 0.
% 157.26/157.57 % out_proof_time: 0.001
% 157.26/157.57 % monotx_time: 0.
% 157.26/157.57 % subtype_inf_time: 0.
% 157.26/157.57 % unif_index_cands_time: 0.045
% 157.26/157.57 % unif_index_add_time: 0.008
% 157.26/157.57 % total_time: 7.029
% 157.26/157.57 % num_of_symbols: 71
% 157.26/157.57 % num_of_terms: 259125
% 157.26/157.57
% 157.26/157.57 % ------ Propositional Solver
% 157.26/157.57
% 157.26/157.57 % prop_solver_calls: 6
% 157.26/157.57 % prop_fast_solver_calls: 285
% 157.26/157.57 % prop_num_of_clauses: 3566
% 157.26/157.57 % prop_preprocess_simplified: 5029
% 157.26/157.57 % prop_fo_subsumed: 0
% 157.26/157.57 % prop_solver_time: 0.
% 157.26/157.57 % prop_fast_solver_time: 0.
% 157.26/157.57 % prop_unsat_core_time: 0.
% 157.26/157.57
% 157.26/157.57 % ------ QBF
% 157.26/157.57
% 157.26/157.57 % qbf_q_res: 0
% 157.26/157.57 % qbf_num_tautologies: 0
% 157.26/157.57 % qbf_prep_cycles: 0
% 157.26/157.57
% 157.26/157.57 % ------ BMC1
% 157.26/157.57
% 157.26/157.57 % bmc1_current_bound: -1
% 157.26/157.57 % bmc1_last_solved_bound: -1
% 157.26/157.57 % bmc1_unsat_core_size: -1
% 157.26/157.57 % bmc1_unsat_core_parents_size: -1
% 157.26/157.57 % bmc1_merge_next_fun: 0
% 157.26/157.57 % bmc1_unsat_core_clauses_time: 0.
% 157.26/157.57
% 157.26/157.57 % ------ Instantiation
% 157.26/157.57
% 157.26/157.57 % inst_num_of_clauses: 2277
% 157.26/157.57 % inst_num_in_passive: 1079
% 157.26/157.57 % inst_num_in_active: 558
% 157.26/157.57 % inst_num_in_unprocessed: 636
% 157.26/157.57 % inst_num_of_loops: 600
% 157.26/157.57 % inst_num_of_learning_restarts: 0
% 157.26/157.57 % inst_num_moves_active_passive: 37
% 157.26/157.57 % inst_lit_activity: 376
% 157.26/157.57 % inst_lit_activity_moves: 0
% 157.26/157.57 % inst_num_tautologies: 4
% 157.26/157.57 % inst_num_prop_implied: 0
% 157.26/157.57 % inst_num_existing_simplified: 0
% 157.26/157.57 % inst_num_eq_res_simplified: 0
% 157.26/157.57 % inst_num_child_elim: 0
% 157.26/157.57 % inst_num_of_dismatching_blockings: 2063
% 157.26/157.57 % inst_num_of_non_proper_insts: 1975
% 157.26/157.57 % inst_num_of_duplicates: 1444
% 157.26/157.57 % inst_inst_num_from_inst_to_res: 0
% 157.26/157.57 % inst_dismatching_checking_time: 0.004
% 157.26/157.57
% 157.26/157.57 % ------ Resolution
% 157.26/157.57
% 157.26/157.57 % res_num_of_clauses: 86858
% 157.26/157.57 % res_num_in_passive: 84533
% 157.26/157.57 % res_num_in_active: 2200
% 157.26/157.57 % res_num_of_loops: 2528
% 157.26/157.57 % res_forward_subset_subsumed: 3807
% 157.26/157.57 % res_backward_subset_subsumed: 61
% 157.26/157.57 % res_forward_subsumed: 405
% 157.26/157.57 % res_backward_subsumed: 15
% 157.26/157.57 % res_forward_subsumption_resolution: 62
% 157.26/157.57 % res_backward_subsumption_resolution: 29
% 157.26/157.57 % res_clause_to_clause_subsumption: 36233
% 157.26/157.57 % res_orphan_elimination: 0
% 157.26/157.57 % res_tautology_del: 529
% 157.26/157.57 % res_num_eq_res_simplified: 5
% 157.26/157.57 % res_num_sel_changes: 0
% 157.26/157.57 % res_moves_from_active_to_pass: 0
% 157.26/157.57
% 157.36/157.57 % Status Unsatisfiable
% 157.36/157.57 % SZS status Theorem
% 157.36/157.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------