TSTP Solution File: SEU161+2 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU161+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n011.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 10:25:28 EDT 2022
% Result : Theorem 0.58s 0.78s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
input ).
fof(t6_boole_0,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(orientation,[status(thm)],[t6_boole]) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
input ).
fof(t4_boole_0,plain,
! [A] :
( set_difference(empty_set,A) = empty_set
| $false ),
inference(orientation,[status(thm)],[t4_boole]) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
input ).
fof(t3_boole_0,plain,
! [A] :
( set_difference(A,empty_set) = A
| $false ),
inference(orientation,[status(thm)],[t3_boole]) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
input ).
fof(t2_tarski_0,plain,
! [A,B] :
( A = B
| ~ ! [C] :
( in(C,A)
<=> in(C,B) ) ),
inference(orientation,[status(thm)],[t2_tarski]) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
input ).
fof(t2_boole_0,plain,
! [A] :
( set_intersection2(A,empty_set) = empty_set
| $false ),
inference(orientation,[status(thm)],[t2_boole]) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
input ).
fof(t1_boole_0,plain,
! [A] :
( set_union2(A,empty_set) = A
| $false ),
inference(orientation,[status(thm)],[t1_boole]) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
input ).
fof(symmetry_r1_xboole_0_0,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(orientation,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
input ).
fof(reflexivity_r1_tarski_0,plain,
! [A] :
( subset(A,A)
| $false ),
inference(orientation,[status(thm)],[reflexivity_r1_tarski]) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
input ).
fof(irreflexivity_r2_xboole_0_0,plain,
! [A] :
( ~ proper_subset(A,A)
| $false ),
inference(orientation,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
input ).
fof(idempotence_k3_xboole_0_0,plain,
! [A] :
( set_intersection2(A,A) = A
| $false ),
inference(orientation,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
input ).
fof(idempotence_k2_xboole_0_0,plain,
! [A] :
( set_union2(A,A) = A
| $false ),
inference(orientation,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
input ).
fof(fc3_xboole_0_0,plain,
! [A,B] :
( empty(A)
| ~ empty(set_union2(B,A)) ),
inference(orientation,[status(thm)],[fc3_xboole_0]) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
input ).
fof(fc2_xboole_0_0,plain,
! [A,B] :
( empty(A)
| ~ empty(set_union2(A,B)) ),
inference(orientation,[status(thm)],[fc2_xboole_0]) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
input ).
fof(fc1_zfmisc_1_0,plain,
! [A,B] :
( ~ empty(ordered_pair(A,B))
| $false ),
inference(orientation,[status(thm)],[fc1_zfmisc_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
input ).
fof(fc1_xboole_0_0,plain,
( empty(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc1_xboole_0]) ).
fof(dt_k4_xboole_0,axiom,
$true,
input ).
fof(dt_k4_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k4_xboole_0]) ).
fof(dt_k4_tarski,axiom,
$true,
input ).
fof(dt_k4_tarski_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k4_tarski]) ).
fof(dt_k3_xboole_0,axiom,
$true,
input ).
fof(dt_k3_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k3_xboole_0]) ).
fof(dt_k3_tarski,axiom,
$true,
input ).
fof(dt_k3_tarski_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k3_tarski]) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
input ).
fof(dt_k2_zfmisc_1_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(dt_k2_xboole_0,axiom,
$true,
input ).
fof(dt_k2_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k2_xboole_0]) ).
fof(dt_k2_tarski,axiom,
$true,
input ).
fof(dt_k2_tarski_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k2_tarski]) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
input ).
fof(dt_k1_zfmisc_1_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(dt_k1_xboole_0,axiom,
$true,
input ).
fof(dt_k1_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k1_xboole_0]) ).
fof(dt_k1_tarski,axiom,
$true,
input ).
fof(dt_k1_tarski_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k1_tarski]) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ),
input ).
fof(d8_xboole_0_0,plain,
! [A,B] :
( proper_subset(A,B)
| ~ ( subset(A,B)
& A != B ) ),
inference(orientation,[status(thm)],[d8_xboole_0]) ).
fof(d8_xboole_0_1,plain,
! [A,B] :
( ~ proper_subset(A,B)
| ( subset(A,B)
& A != B ) ),
inference(orientation,[status(thm)],[d8_xboole_0]) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
input ).
fof(d7_xboole_0_0,plain,
! [A,B] :
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ),
inference(orientation,[status(thm)],[d7_xboole_0]) ).
fof(d7_xboole_0_1,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(orientation,[status(thm)],[d7_xboole_0]) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
input ).
fof(d5_tarski_0,plain,
! [A,B] :
( ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))
| $false ),
inference(orientation,[status(thm)],[d5_tarski]) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
input ).
fof(d4_xboole_0_0,plain,
! [A,B,C] :
( C = set_difference(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(orientation,[status(thm)],[d4_xboole_0]) ).
fof(d4_xboole_0_1,plain,
! [A,B,C] :
( C != set_difference(A,B)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(orientation,[status(thm)],[d4_xboole_0]) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
input ).
fof(d4_tarski_0,plain,
! [A,B] :
( B = union(A)
| ~ ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(orientation,[status(thm)],[d4_tarski]) ).
fof(d4_tarski_1,plain,
! [A,B] :
( B != union(A)
| ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(orientation,[status(thm)],[d4_tarski]) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
input ).
fof(d3_xboole_0_0,plain,
! [A,B,C] :
( C = set_intersection2(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(orientation,[status(thm)],[d3_xboole_0]) ).
fof(d3_xboole_0_1,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(orientation,[status(thm)],[d3_xboole_0]) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
input ).
fof(d3_tarski_0,plain,
! [A,B] :
( subset(A,B)
| ~ ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(orientation,[status(thm)],[d3_tarski]) ).
fof(d3_tarski_1,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(orientation,[status(thm)],[d3_tarski]) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
input ).
fof(d2_zfmisc_1_0,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
| ~ ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
inference(orientation,[status(thm)],[d2_zfmisc_1]) ).
fof(d2_zfmisc_1_1,plain,
! [A,B,C] :
( C != cartesian_product2(A,B)
| ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
inference(orientation,[status(thm)],[d2_zfmisc_1]) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
input ).
fof(d2_xboole_0_0,plain,
! [A,B,C] :
( C = set_union2(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(orientation,[status(thm)],[d2_xboole_0]) ).
fof(d2_xboole_0_1,plain,
! [A,B,C] :
( C != set_union2(A,B)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(orientation,[status(thm)],[d2_xboole_0]) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
input ).
fof(d2_tarski_0,plain,
! [A,B,C] :
( C = unordered_pair(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(orientation,[status(thm)],[d2_tarski]) ).
fof(d2_tarski_1,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
| ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(orientation,[status(thm)],[d2_tarski]) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
input ).
fof(d1_zfmisc_1_0,plain,
! [A,B] :
( B = powerset(A)
| ~ ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
inference(orientation,[status(thm)],[d1_zfmisc_1]) ).
fof(d1_zfmisc_1_1,plain,
! [A,B] :
( B != powerset(A)
| ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
inference(orientation,[status(thm)],[d1_zfmisc_1]) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
input ).
fof(d1_xboole_0_0,plain,
! [A] :
( A = empty_set
| ~ ! [B] : ~ in(B,A) ),
inference(orientation,[status(thm)],[d1_xboole_0]) ).
fof(d1_xboole_0_1,plain,
! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) ),
inference(orientation,[status(thm)],[d1_xboole_0]) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
input ).
fof(d1_tarski_0,plain,
! [A,B] :
( B = singleton(A)
| ~ ! [C] :
( in(C,B)
<=> C = A ) ),
inference(orientation,[status(thm)],[d1_tarski]) ).
fof(d1_tarski_1,plain,
! [A,B] :
( B != singleton(A)
| ! [C] :
( in(C,B)
<=> C = A ) ),
inference(orientation,[status(thm)],[d1_tarski]) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
input ).
fof(d10_xboole_0_0,plain,
! [A,B] :
( A = B
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[d10_xboole_0]) ).
fof(d10_xboole_0_1,plain,
! [A,B] :
( A != B
| ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[d10_xboole_0]) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
input ).
fof(commutativity_k3_xboole_0_0,plain,
! [A,B] :
( set_intersection2(A,B) = set_intersection2(B,A)
| $false ),
inference(orientation,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
input ).
fof(commutativity_k2_xboole_0_0,plain,
! [A,B] :
( set_union2(A,B) = set_union2(B,A)
| $false ),
inference(orientation,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
input ).
fof(commutativity_k2_tarski_0,plain,
! [A,B] :
( unordered_pair(A,B) = unordered_pair(B,A)
| $false ),
inference(orientation,[status(thm)],[commutativity_k2_tarski]) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
input ).
fof(antisymmetry_r2_xboole_0_0,plain,
! [A,B] :
( ~ proper_subset(A,B)
| ~ proper_subset(B,A) ),
inference(orientation,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
input ).
fof(antisymmetry_r2_hidden_0,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(orientation,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(def_lhs_atom1,axiom,
! [B,A] :
( lhs_atom1(B,A)
<=> ~ in(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [A,B] :
( lhs_atom1(B,A)
| ~ in(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [B,A] :
( lhs_atom2(B,A)
<=> ~ proper_subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A,B] :
( lhs_atom2(B,A)
| ~ proper_subset(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_xboole_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [B,A] :
( lhs_atom3(B,A)
<=> unordered_pair(A,B) = unordered_pair(B,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A,B] :
( lhs_atom3(B,A)
| $false ),
inference(fold_definition,[status(thm)],[commutativity_k2_tarski_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [B,A] :
( lhs_atom4(B,A)
<=> set_union2(A,B) = set_union2(B,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [A,B] :
( lhs_atom4(B,A)
| $false ),
inference(fold_definition,[status(thm)],[commutativity_k2_xboole_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [B,A] :
( lhs_atom5(B,A)
<=> set_intersection2(A,B) = set_intersection2(B,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [A,B] :
( lhs_atom5(B,A)
| $false ),
inference(fold_definition,[status(thm)],[commutativity_k3_xboole_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [B,A] :
( lhs_atom6(B,A)
<=> A != B ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [A,B] :
( lhs_atom6(B,A)
| ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[d10_xboole_0_1,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [B,A] :
( lhs_atom7(B,A)
<=> A = B ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A,B] :
( lhs_atom7(B,A)
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[d10_xboole_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [B,A] :
( lhs_atom8(B,A)
<=> B != singleton(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A,B] :
( lhs_atom8(B,A)
| ! [C] :
( in(C,B)
<=> C = A ) ),
inference(fold_definition,[status(thm)],[d1_tarski_1,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [B,A] :
( lhs_atom9(B,A)
<=> B = singleton(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A,B] :
( lhs_atom9(B,A)
| ~ ! [C] :
( in(C,B)
<=> C = A ) ),
inference(fold_definition,[status(thm)],[d1_tarski_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [A] :
( lhs_atom10(A)
<=> A != empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A] :
( lhs_atom10(A)
| ! [B] : ~ in(B,A) ),
inference(fold_definition,[status(thm)],[d1_xboole_0_1,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [A] :
( lhs_atom11(A)
<=> A = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [A] :
( lhs_atom11(A)
| ~ ! [B] : ~ in(B,A) ),
inference(fold_definition,[status(thm)],[d1_xboole_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [B,A] :
( lhs_atom12(B,A)
<=> B != powerset(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [A,B] :
( lhs_atom12(B,A)
| ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
inference(fold_definition,[status(thm)],[d1_zfmisc_1_1,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [B,A] :
( lhs_atom13(B,A)
<=> B = powerset(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [A,B] :
( lhs_atom13(B,A)
| ~ ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
inference(fold_definition,[status(thm)],[d1_zfmisc_1_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [C,B,A] :
( lhs_atom14(C,B,A)
<=> C != unordered_pair(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [A,B,C] :
( lhs_atom14(C,B,A)
| ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(fold_definition,[status(thm)],[d2_tarski_1,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [C,B,A] :
( lhs_atom15(C,B,A)
<=> C = unordered_pair(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [A,B,C] :
( lhs_atom15(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(fold_definition,[status(thm)],[d2_tarski_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [C,B,A] :
( lhs_atom16(C,B,A)
<=> C != set_union2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [A,B,C] :
( lhs_atom16(C,B,A)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d2_xboole_0_1,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [C,B,A] :
( lhs_atom17(C,B,A)
<=> C = set_union2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [A,B,C] :
( lhs_atom17(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d2_xboole_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [C,B,A] :
( lhs_atom18(C,B,A)
<=> C != cartesian_product2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [A,B,C] :
( lhs_atom18(C,B,A)
| ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
inference(fold_definition,[status(thm)],[d2_zfmisc_1_1,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [C,B,A] :
( lhs_atom19(C,B,A)
<=> C = cartesian_product2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [A,B,C] :
( lhs_atom19(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
inference(fold_definition,[status(thm)],[d2_zfmisc_1_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [B,A] :
( lhs_atom20(B,A)
<=> ~ subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [A,B] :
( lhs_atom20(B,A)
| ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[d3_tarski_1,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [B,A] :
( lhs_atom21(B,A)
<=> subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [A,B] :
( lhs_atom21(B,A)
| ~ ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[d3_tarski_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [C,B,A] :
( lhs_atom22(C,B,A)
<=> C != set_intersection2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [A,B,C] :
( lhs_atom22(C,B,A)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d3_xboole_0_1,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [C,B,A] :
( lhs_atom23(C,B,A)
<=> C = set_intersection2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [A,B,C] :
( lhs_atom23(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d3_xboole_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [B,A] :
( lhs_atom24(B,A)
<=> B != union(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [A,B] :
( lhs_atom24(B,A)
| ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(fold_definition,[status(thm)],[d4_tarski_1,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [B,A] :
( lhs_atom25(B,A)
<=> B = union(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [A,B] :
( lhs_atom25(B,A)
| ~ ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(fold_definition,[status(thm)],[d4_tarski_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [C,B,A] :
( lhs_atom26(C,B,A)
<=> C != set_difference(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [A,B,C] :
( lhs_atom26(C,B,A)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d4_xboole_0_1,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [C,B,A] :
( lhs_atom27(C,B,A)
<=> C = set_difference(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [A,B,C] :
( lhs_atom27(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d4_xboole_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [B,A] :
( lhs_atom28(B,A)
<=> ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [A,B] :
( lhs_atom28(B,A)
| $false ),
inference(fold_definition,[status(thm)],[d5_tarski_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [B,A] :
( lhs_atom29(B,A)
<=> ~ disjoint(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [A,B] :
( lhs_atom29(B,A)
| set_intersection2(A,B) = empty_set ),
inference(fold_definition,[status(thm)],[d7_xboole_0_1,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [B,A] :
( lhs_atom30(B,A)
<=> disjoint(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [A,B] :
( lhs_atom30(B,A)
| set_intersection2(A,B) != empty_set ),
inference(fold_definition,[status(thm)],[d7_xboole_0_0,def_lhs_atom30]) ).
fof(to_be_clausified_30,plain,
! [A,B] :
( lhs_atom2(B,A)
| ( subset(A,B)
& A != B ) ),
inference(fold_definition,[status(thm)],[d8_xboole_0_1,def_lhs_atom2]) ).
fof(def_lhs_atom31,axiom,
! [B,A] :
( lhs_atom31(B,A)
<=> proper_subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [A,B] :
( lhs_atom31(B,A)
| ~ ( subset(A,B)
& A != B ) ),
inference(fold_definition,[status(thm)],[d8_xboole_0_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
( lhs_atom32
<=> $true ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_tarski_0,def_lhs_atom32]) ).
fof(to_be_clausified_33,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_xboole_0_0,def_lhs_atom32]) ).
fof(to_be_clausified_34,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_zfmisc_1_0,def_lhs_atom32]) ).
fof(to_be_clausified_35,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_tarski_0,def_lhs_atom32]) ).
fof(to_be_clausified_36,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_xboole_0_0,def_lhs_atom32]) ).
fof(to_be_clausified_37,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_zfmisc_1_0,def_lhs_atom32]) ).
fof(to_be_clausified_38,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k3_tarski_0,def_lhs_atom32]) ).
fof(to_be_clausified_39,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k3_xboole_0_0,def_lhs_atom32]) ).
fof(to_be_clausified_40,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k4_tarski_0,def_lhs_atom32]) ).
fof(to_be_clausified_41,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[dt_k4_xboole_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
( lhs_atom33
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
( lhs_atom33
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [B,A] :
( lhs_atom34(B,A)
<=> ~ empty(ordered_pair(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [A,B] :
( lhs_atom34(B,A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_zfmisc_1_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [A] :
( lhs_atom35(A)
<=> empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [A,B] :
( lhs_atom35(A)
| ~ empty(set_union2(A,B)) ),
inference(fold_definition,[status(thm)],[fc2_xboole_0_0,def_lhs_atom35]) ).
fof(to_be_clausified_45,plain,
! [A,B] :
( lhs_atom35(A)
| ~ empty(set_union2(B,A)) ),
inference(fold_definition,[status(thm)],[fc3_xboole_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [A] :
( lhs_atom36(A)
<=> set_union2(A,A) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
! [A] :
( lhs_atom36(A)
| $false ),
inference(fold_definition,[status(thm)],[idempotence_k2_xboole_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [A] :
( lhs_atom37(A)
<=> set_intersection2(A,A) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
! [A] :
( lhs_atom37(A)
| $false ),
inference(fold_definition,[status(thm)],[idempotence_k3_xboole_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [A] :
( lhs_atom38(A)
<=> ~ proper_subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
! [A] :
( lhs_atom38(A)
| $false ),
inference(fold_definition,[status(thm)],[irreflexivity_r2_xboole_0_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [A] :
( lhs_atom39(A)
<=> subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
! [A] :
( lhs_atom39(A)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0,def_lhs_atom39]) ).
fof(to_be_clausified_50,plain,
! [A,B] :
( lhs_atom29(B,A)
| disjoint(B,A) ),
inference(fold_definition,[status(thm)],[symmetry_r1_xboole_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom40,axiom,
! [A] :
( lhs_atom40(A)
<=> set_union2(A,empty_set) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_51,plain,
! [A] :
( lhs_atom40(A)
| $false ),
inference(fold_definition,[status(thm)],[t1_boole_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [A] :
( lhs_atom41(A)
<=> set_intersection2(A,empty_set) = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_52,plain,
! [A] :
( lhs_atom41(A)
| $false ),
inference(fold_definition,[status(thm)],[t2_boole_0,def_lhs_atom41]) ).
fof(to_be_clausified_53,plain,
! [A,B] :
( lhs_atom7(B,A)
| ~ ! [C] :
( in(C,A)
<=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[t2_tarski_0,def_lhs_atom7]) ).
fof(def_lhs_atom42,axiom,
! [A] :
( lhs_atom42(A)
<=> set_difference(A,empty_set) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_54,plain,
! [A] :
( lhs_atom42(A)
| $false ),
inference(fold_definition,[status(thm)],[t3_boole_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [A] :
( lhs_atom43(A)
<=> set_difference(empty_set,A) = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_55,plain,
! [A] :
( lhs_atom43(A)
| $false ),
inference(fold_definition,[status(thm)],[t4_boole_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [A] :
( lhs_atom44(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_56,plain,
! [A] :
( lhs_atom44(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom44]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X1,X2] :
( lhs_atom18(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X2)
& in(X6,X1)
& X4 = ordered_pair(X5,X6) ) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_1,axiom,
! [X3,X1,X2] :
( lhs_atom23(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_2,axiom,
! [X3,X1,X2] :
( lhs_atom27(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_3,axiom,
! [X3,X1,X2] :
( lhs_atom19(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X2)
& in(X6,X1)
& X4 = ordered_pair(X5,X6) ) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_4,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_5,axiom,
! [X3,X1,X2] :
( lhs_atom15(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_6,axiom,
! [X1,X2] :
( lhs_atom25(X1,X2)
| ~ ! [X3] :
( in(X3,X1)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X2) ) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_7,axiom,
! [X1,X2] :
( lhs_atom24(X1,X2)
| ! [X3] :
( in(X3,X1)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X2) ) ) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_8,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
<=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_9,axiom,
! [X1,X2] :
( lhs_atom13(X1,X2)
| ~ ! [X3] :
( in(X3,X1)
<=> subset(X3,X2) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_10,axiom,
! [X3,X1,X2] :
( lhs_atom22(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_11,axiom,
! [X3,X1,X2] :
( lhs_atom26(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_12,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_13,axiom,
! [X1,X2] :
( lhs_atom9(X1,X2)
| ~ ! [X3] :
( in(X3,X1)
<=> X3 = X2 ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_14,axiom,
! [X3,X1,X2] :
( lhs_atom14(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_15,axiom,
! [X1,X2] :
( lhs_atom21(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_16,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_17,axiom,
! [X1,X2] :
( lhs_atom35(X2)
| ~ empty(set_union2(X1,X2)) ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_18,axiom,
! [X1,X2] :
( lhs_atom35(X2)
| ~ empty(set_union2(X2,X1)) ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_19,axiom,
! [X1,X2] :
( lhs_atom20(X1,X2)
| ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_20,axiom,
! [X1,X2] :
( lhs_atom12(X1,X2)
| ! [X3] :
( in(X3,X1)
<=> subset(X3,X2) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_21,axiom,
! [X1,X2] :
( lhs_atom31(X1,X2)
| ~ ( subset(X2,X1)
& X2 != X1 ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_22,axiom,
! [X1,X2] :
( lhs_atom8(X1,X2)
| ! [X3] :
( in(X3,X1)
<=> X3 = X2 ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_23,axiom,
! [X1,X2] :
( lhs_atom30(X1,X2)
| set_intersection2(X2,X1) != empty_set ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_24,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_25,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_26,axiom,
! [X1,X2] :
( lhs_atom29(X1,X2)
| disjoint(X1,X2) ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_27,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ( subset(X2,X1)
& X2 != X1 ) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_28,axiom,
! [X1,X2] :
( lhs_atom29(X1,X2)
| set_intersection2(X2,X1) = empty_set ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_29,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_30,axiom,
! [X2] :
( lhs_atom10(X2)
| ! [X1] : ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_31,axiom,
! [X2] :
( lhs_atom11(X2)
| ~ ! [X1] : ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_32,axiom,
! [X1,X2] :
( lhs_atom34(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_33,axiom,
! [X1,X2] :
( lhs_atom28(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_34,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_35,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_36,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_37,axiom,
! [X2] :
( lhs_atom44(X2)
| X2 = empty_set ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_38,axiom,
! [X2] :
( lhs_atom43(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_39,axiom,
! [X2] :
( lhs_atom42(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_40,axiom,
! [X2] :
( lhs_atom41(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_41,axiom,
! [X2] :
( lhs_atom40(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_42,axiom,
! [X2] :
( lhs_atom39(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_43,axiom,
! [X2] :
( lhs_atom38(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_44,axiom,
! [X2] :
( lhs_atom37(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_45,axiom,
! [X2] :
( lhs_atom36(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_46,axiom,
( lhs_atom33
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_47,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_48,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_49,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_50,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_51,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_52,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_53,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_54,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_55,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_56,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_57,axiom,
! [X3,X1,X2] :
( lhs_atom18(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X2)
& in(X6,X1)
& X4 = ordered_pair(X5,X6) ) ) ),
c_0_0 ).
fof(c_0_58,axiom,
! [X3,X1,X2] :
( lhs_atom23(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
c_0_1 ).
fof(c_0_59,plain,
! [X3,X1,X2] :
( lhs_atom27(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_60,axiom,
! [X3,X1,X2] :
( lhs_atom19(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X2)
& in(X6,X1)
& X4 = ordered_pair(X5,X6) ) ) ),
c_0_3 ).
fof(c_0_61,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
c_0_4 ).
fof(c_0_62,axiom,
! [X3,X1,X2] :
( lhs_atom15(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
c_0_5 ).
fof(c_0_63,axiom,
! [X1,X2] :
( lhs_atom25(X1,X2)
| ~ ! [X3] :
( in(X3,X1)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X2) ) ) ),
c_0_6 ).
fof(c_0_64,axiom,
! [X1,X2] :
( lhs_atom24(X1,X2)
| ! [X3] :
( in(X3,X1)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X2) ) ) ),
c_0_7 ).
fof(c_0_65,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
<=> in(X3,X1) ) ),
c_0_8 ).
fof(c_0_66,axiom,
! [X1,X2] :
( lhs_atom13(X1,X2)
| ~ ! [X3] :
( in(X3,X1)
<=> subset(X3,X2) ) ),
c_0_9 ).
fof(c_0_67,axiom,
! [X3,X1,X2] :
( lhs_atom22(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
c_0_10 ).
fof(c_0_68,plain,
! [X3,X1,X2] :
( lhs_atom26(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_69,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
c_0_12 ).
fof(c_0_70,axiom,
! [X1,X2] :
( lhs_atom9(X1,X2)
| ~ ! [X3] :
( in(X3,X1)
<=> X3 = X2 ) ),
c_0_13 ).
fof(c_0_71,axiom,
! [X3,X1,X2] :
( lhs_atom14(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
c_0_14 ).
fof(c_0_72,axiom,
! [X1,X2] :
( lhs_atom21(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_15 ).
fof(c_0_73,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_16 ).
fof(c_0_74,plain,
! [X1,X2] :
( lhs_atom35(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_75,plain,
! [X1,X2] :
( lhs_atom35(X2)
| ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_76,axiom,
! [X1,X2] :
( lhs_atom20(X1,X2)
| ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_19 ).
fof(c_0_77,axiom,
! [X1,X2] :
( lhs_atom12(X1,X2)
| ! [X3] :
( in(X3,X1)
<=> subset(X3,X2) ) ),
c_0_20 ).
fof(c_0_78,axiom,
! [X1,X2] :
( lhs_atom31(X1,X2)
| ~ ( subset(X2,X1)
& X2 != X1 ) ),
c_0_21 ).
fof(c_0_79,axiom,
! [X1,X2] :
( lhs_atom8(X1,X2)
| ! [X3] :
( in(X3,X1)
<=> X3 = X2 ) ),
c_0_22 ).
fof(c_0_80,plain,
! [X1,X2] :
( lhs_atom30(X1,X2)
| set_intersection2(X2,X1) != empty_set ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_81,plain,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_82,plain,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_83,axiom,
! [X1,X2] :
( lhs_atom29(X1,X2)
| disjoint(X1,X2) ),
c_0_26 ).
fof(c_0_84,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ( subset(X2,X1)
& X2 != X1 ) ),
c_0_27 ).
fof(c_0_85,axiom,
! [X1,X2] :
( lhs_atom29(X1,X2)
| set_intersection2(X2,X1) = empty_set ),
c_0_28 ).
fof(c_0_86,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_29 ).
fof(c_0_87,plain,
! [X2] :
( lhs_atom10(X2)
| ! [X1] : ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_88,plain,
! [X2] :
( lhs_atom11(X2)
| ~ ! [X1] : ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_89,plain,
! [X1,X2] : lhs_atom34(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_90,plain,
! [X1,X2] : lhs_atom28(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_91,plain,
! [X1,X2] : lhs_atom5(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_92,plain,
! [X1,X2] : lhs_atom4(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_93,plain,
! [X1,X2] : lhs_atom3(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_94,axiom,
! [X2] :
( lhs_atom44(X2)
| X2 = empty_set ),
c_0_37 ).
fof(c_0_95,plain,
! [X2] : lhs_atom43(X2),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_96,plain,
! [X2] : lhs_atom42(X2),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_97,plain,
! [X2] : lhs_atom41(X2),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_98,plain,
! [X2] : lhs_atom40(X2),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_99,plain,
! [X2] : lhs_atom39(X2),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_100,plain,
! [X2] : lhs_atom38(X2),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_101,plain,
! [X2] : lhs_atom37(X2),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_102,plain,
! [X2] : lhs_atom36(X2),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_103,plain,
lhs_atom33,
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_104,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_105,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_106,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_107,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_108,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_109,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_110,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_111,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_112,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_113,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_114,plain,
! [X7,X8,X9,X10,X13,X14,X15] :
( ( in(esk6_4(X7,X8,X9,X10),X9)
| ~ in(X10,X7)
| lhs_atom18(X7,X8,X9) )
& ( in(esk7_4(X7,X8,X9,X10),X8)
| ~ in(X10,X7)
| lhs_atom18(X7,X8,X9) )
& ( X10 = ordered_pair(esk6_4(X7,X8,X9,X10),esk7_4(X7,X8,X9,X10))
| ~ in(X10,X7)
| lhs_atom18(X7,X8,X9) )
& ( ~ in(X14,X9)
| ~ in(X15,X8)
| X13 != ordered_pair(X14,X15)
| in(X13,X7)
| lhs_atom18(X7,X8,X9) ) ),
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_115,plain,
! [X5,X6,X7] :
( ( ~ in(esk12_3(X5,X6,X7),X5)
| ~ in(esk12_3(X5,X6,X7),X7)
| ~ in(esk12_3(X5,X6,X7),X6)
| lhs_atom23(X5,X6,X7) )
& ( in(esk12_3(X5,X6,X7),X7)
| in(esk12_3(X5,X6,X7),X5)
| lhs_atom23(X5,X6,X7) )
& ( in(esk12_3(X5,X6,X7),X6)
| in(esk12_3(X5,X6,X7),X5)
| lhs_atom23(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
fof(c_0_116,plain,
! [X5,X6,X7] :
( ( ~ in(esk16_3(X5,X6,X7),X5)
| ~ in(esk16_3(X5,X6,X7),X7)
| in(esk16_3(X5,X6,X7),X6)
| lhs_atom27(X5,X6,X7) )
& ( in(esk16_3(X5,X6,X7),X7)
| in(esk16_3(X5,X6,X7),X5)
| lhs_atom27(X5,X6,X7) )
& ( ~ in(esk16_3(X5,X6,X7),X6)
| in(esk16_3(X5,X6,X7),X5)
| lhs_atom27(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
fof(c_0_117,plain,
! [X7,X8,X9,X11,X12] :
( ( ~ in(esk8_3(X7,X8,X9),X7)
| ~ in(X11,X9)
| ~ in(X12,X8)
| esk8_3(X7,X8,X9) != ordered_pair(X11,X12)
| lhs_atom19(X7,X8,X9) )
& ( in(esk9_3(X7,X8,X9),X9)
| in(esk8_3(X7,X8,X9),X7)
| lhs_atom19(X7,X8,X9) )
& ( in(esk10_3(X7,X8,X9),X8)
| in(esk8_3(X7,X8,X9),X7)
| lhs_atom19(X7,X8,X9) )
& ( esk8_3(X7,X8,X9) = ordered_pair(esk9_3(X7,X8,X9),esk10_3(X7,X8,X9))
| in(esk8_3(X7,X8,X9),X7)
| lhs_atom19(X7,X8,X9) ) ),
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_118,plain,
! [X5,X6,X7] :
( ( ~ in(esk5_3(X5,X6,X7),X7)
| ~ in(esk5_3(X5,X6,X7),X5)
| lhs_atom17(X5,X6,X7) )
& ( ~ in(esk5_3(X5,X6,X7),X6)
| ~ in(esk5_3(X5,X6,X7),X5)
| lhs_atom17(X5,X6,X7) )
& ( in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X6)
| lhs_atom17(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
fof(c_0_119,plain,
! [X5,X6,X7] :
( ( esk4_3(X5,X6,X7) != X7
| ~ in(esk4_3(X5,X6,X7),X5)
| lhs_atom15(X5,X6,X7) )
& ( esk4_3(X5,X6,X7) != X6
| ~ in(esk4_3(X5,X6,X7),X5)
| lhs_atom15(X5,X6,X7) )
& ( in(esk4_3(X5,X6,X7),X5)
| esk4_3(X5,X6,X7) = X7
| esk4_3(X5,X6,X7) = X6
| lhs_atom15(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
fof(c_0_120,plain,
! [X5,X6,X8] :
( ( ~ in(esk14_2(X5,X6),X5)
| ~ in(esk14_2(X5,X6),X8)
| ~ in(X8,X6)
| lhs_atom25(X5,X6) )
& ( in(esk14_2(X5,X6),esk15_2(X5,X6))
| in(esk14_2(X5,X6),X5)
| lhs_atom25(X5,X6) )
& ( in(esk15_2(X5,X6),X6)
| in(esk14_2(X5,X6),X5)
| lhs_atom25(X5,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_63])])])])]) ).
fof(c_0_121,plain,
! [X5,X6,X7,X9,X10] :
( ( in(X7,esk13_3(X5,X6,X7))
| ~ in(X7,X5)
| lhs_atom24(X5,X6) )
& ( in(esk13_3(X5,X6,X7),X6)
| ~ in(X7,X5)
| lhs_atom24(X5,X6) )
& ( ~ in(X9,X10)
| ~ in(X10,X6)
| in(X9,X5)
| lhs_atom24(X5,X6) ) ),
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_122,plain,
! [X4,X5] :
( ( ~ in(esk17_2(X4,X5),X5)
| ~ in(esk17_2(X4,X5),X4)
| lhs_atom7(X4,X5) )
& ( in(esk17_2(X4,X5),X5)
| in(esk17_2(X4,X5),X4)
| lhs_atom7(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
fof(c_0_123,plain,
! [X4,X5] :
( ( ~ in(esk3_2(X4,X5),X4)
| ~ subset(esk3_2(X4,X5),X5)
| lhs_atom13(X4,X5) )
& ( in(esk3_2(X4,X5),X4)
| subset(esk3_2(X4,X5),X5)
| lhs_atom13(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])]) ).
fof(c_0_124,plain,
! [X5,X6,X7,X8,X9] :
( ( in(X8,X7)
| ~ in(X8,X5)
| lhs_atom22(X5,X6,X7) )
& ( in(X8,X6)
| ~ in(X8,X5)
| lhs_atom22(X5,X6,X7) )
& ( ~ in(X9,X7)
| ~ in(X9,X6)
| in(X9,X5)
| lhs_atom22(X5,X6,X7) ) ),
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_67])])])])]) ).
fof(c_0_125,plain,
! [X5,X6,X7,X8,X9] :
( ( in(X8,X7)
| ~ in(X8,X5)
| lhs_atom26(X5,X6,X7) )
& ( ~ in(X8,X6)
| ~ in(X8,X5)
| lhs_atom26(X5,X6,X7) )
& ( ~ in(X9,X7)
| in(X9,X6)
| in(X9,X5)
| lhs_atom26(X5,X6,X7) ) ),
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_68])])])])]) ).
fof(c_0_126,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ in(X8,X5)
| in(X8,X7)
| in(X8,X6)
| lhs_atom16(X5,X6,X7) )
& ( ~ in(X9,X7)
| in(X9,X5)
| lhs_atom16(X5,X6,X7) )
& ( ~ in(X9,X6)
| in(X9,X5)
| lhs_atom16(X5,X6,X7) ) ),
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_127,plain,
! [X4,X5] :
( ( ~ in(esk1_2(X4,X5),X4)
| esk1_2(X4,X5) != X5
| lhs_atom9(X4,X5) )
& ( in(esk1_2(X4,X5),X4)
| esk1_2(X4,X5) = X5
| lhs_atom9(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])]) ).
fof(c_0_128,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ in(X8,X5)
| X8 = X7
| X8 = X6
| lhs_atom14(X5,X6,X7) )
& ( X9 != X7
| in(X9,X5)
| lhs_atom14(X5,X6,X7) )
& ( X9 != X6
| in(X9,X5)
| lhs_atom14(X5,X6,X7) ) ),
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_71])])])])]) ).
fof(c_0_129,plain,
! [X4,X5] :
( ( in(esk11_2(X4,X5),X5)
| lhs_atom21(X4,X5) )
& ( ~ in(esk11_2(X4,X5),X4)
| lhs_atom21(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])]) ).
fof(c_0_130,plain,
! [X3,X4] :
( lhs_atom7(X3,X4)
| ~ subset(X4,X3)
| ~ subset(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])]) ).
fof(c_0_131,plain,
! [X3,X4] :
( lhs_atom35(X4)
| ~ empty(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[c_0_74]) ).
fof(c_0_132,plain,
! [X3,X4] :
( lhs_atom35(X4)
| ~ empty(set_union2(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_75]) ).
fof(c_0_133,plain,
! [X4,X5,X6] :
( lhs_atom20(X4,X5)
| ~ in(X6,X5)
| in(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
fof(c_0_134,plain,
! [X4,X5,X6,X7] :
( ( ~ in(X6,X4)
| subset(X6,X5)
| lhs_atom12(X4,X5) )
& ( ~ subset(X7,X5)
| in(X7,X4)
| lhs_atom12(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_77])])])])]) ).
fof(c_0_135,plain,
! [X3,X4] :
( lhs_atom31(X3,X4)
| ~ subset(X4,X3)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])]) ).
fof(c_0_136,plain,
! [X4,X5,X6,X7] :
( ( ~ in(X6,X4)
| X6 = X5
| lhs_atom8(X4,X5) )
& ( X7 != X5
| in(X7,X4)
| lhs_atom8(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_79])])])])]) ).
fof(c_0_137,plain,
! [X3,X4] :
( lhs_atom30(X3,X4)
| set_intersection2(X4,X3) != empty_set ),
inference(variable_rename,[status(thm)],[c_0_80]) ).
fof(c_0_138,plain,
! [X3,X4] :
( lhs_atom2(X3,X4)
| ~ proper_subset(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_81]) ).
fof(c_0_139,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_82]) ).
fof(c_0_140,plain,
! [X3,X4] :
( lhs_atom29(X3,X4)
| disjoint(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_83]) ).
fof(c_0_141,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom2(X3,X4) )
& ( X4 != X3
| lhs_atom2(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_84])]) ).
fof(c_0_142,plain,
! [X3,X4] :
( lhs_atom29(X3,X4)
| set_intersection2(X4,X3) = empty_set ),
inference(variable_rename,[status(thm)],[c_0_85]) ).
fof(c_0_143,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom6(X3,X4) )
& ( subset(X3,X4)
| lhs_atom6(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_86])]) ).
fof(c_0_144,plain,
! [X3,X4] :
( lhs_atom10(X3)
| ~ in(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_87])]) ).
fof(c_0_145,plain,
! [X3] :
( lhs_atom11(X3)
| in(esk2_1(X3),X3) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])]) ).
fof(c_0_146,plain,
! [X3,X4] : lhs_atom34(X3,X4),
inference(variable_rename,[status(thm)],[c_0_89]) ).
fof(c_0_147,plain,
! [X3,X4] : lhs_atom28(X3,X4),
inference(variable_rename,[status(thm)],[c_0_90]) ).
fof(c_0_148,plain,
! [X3,X4] : lhs_atom5(X3,X4),
inference(variable_rename,[status(thm)],[c_0_91]) ).
fof(c_0_149,plain,
! [X3,X4] : lhs_atom4(X3,X4),
inference(variable_rename,[status(thm)],[c_0_92]) ).
fof(c_0_150,plain,
! [X3,X4] : lhs_atom3(X3,X4),
inference(variable_rename,[status(thm)],[c_0_93]) ).
fof(c_0_151,plain,
! [X3] :
( lhs_atom44(X3)
| X3 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_94]) ).
fof(c_0_152,plain,
! [X3] : lhs_atom43(X3),
inference(variable_rename,[status(thm)],[c_0_95]) ).
fof(c_0_153,plain,
! [X3] : lhs_atom42(X3),
inference(variable_rename,[status(thm)],[c_0_96]) ).
fof(c_0_154,plain,
! [X3] : lhs_atom41(X3),
inference(variable_rename,[status(thm)],[c_0_97]) ).
fof(c_0_155,plain,
! [X3] : lhs_atom40(X3),
inference(variable_rename,[status(thm)],[c_0_98]) ).
fof(c_0_156,plain,
! [X3] : lhs_atom39(X3),
inference(variable_rename,[status(thm)],[c_0_99]) ).
fof(c_0_157,plain,
! [X3] : lhs_atom38(X3),
inference(variable_rename,[status(thm)],[c_0_100]) ).
fof(c_0_158,plain,
! [X3] : lhs_atom37(X3),
inference(variable_rename,[status(thm)],[c_0_101]) ).
fof(c_0_159,plain,
! [X3] : lhs_atom36(X3),
inference(variable_rename,[status(thm)],[c_0_102]) ).
fof(c_0_160,plain,
lhs_atom33,
c_0_103 ).
fof(c_0_161,plain,
lhs_atom32,
c_0_104 ).
fof(c_0_162,plain,
lhs_atom32,
c_0_105 ).
fof(c_0_163,plain,
lhs_atom32,
c_0_106 ).
fof(c_0_164,plain,
lhs_atom32,
c_0_107 ).
fof(c_0_165,plain,
lhs_atom32,
c_0_108 ).
fof(c_0_166,plain,
lhs_atom32,
c_0_109 ).
fof(c_0_167,plain,
lhs_atom32,
c_0_110 ).
fof(c_0_168,plain,
lhs_atom32,
c_0_111 ).
fof(c_0_169,plain,
lhs_atom32,
c_0_112 ).
fof(c_0_170,plain,
lhs_atom32,
c_0_113 ).
cnf(c_0_171,plain,
( lhs_atom18(X1,X2,X3)
| X4 = ordered_pair(esk6_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4))
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_172,plain,
( lhs_atom23(X1,X2,X3)
| ~ in(esk12_3(X1,X2,X3),X2)
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(esk12_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_173,plain,
( lhs_atom18(X1,X2,X3)
| in(esk6_4(X1,X2,X3,X4),X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_174,plain,
( lhs_atom18(X1,X2,X3)
| in(esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_175,plain,
( lhs_atom27(X1,X2,X3)
| in(esk16_3(X1,X2,X3),X2)
| ~ in(esk16_3(X1,X2,X3),X3)
| ~ in(esk16_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_176,plain,
( lhs_atom19(X1,X2,X3)
| in(esk8_3(X1,X2,X3),X1)
| esk8_3(X1,X2,X3) = ordered_pair(esk9_3(X1,X2,X3),esk10_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_177,plain,
( lhs_atom17(X1,X2,X3)
| ~ in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_178,plain,
( lhs_atom17(X1,X2,X3)
| ~ in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_179,plain,
( lhs_atom17(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X2)
| in(esk5_3(X1,X2,X3),X3)
| in(esk5_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_180,plain,
( lhs_atom19(X1,X2,X3)
| esk8_3(X1,X2,X3) != ordered_pair(X4,X5)
| ~ in(X5,X2)
| ~ in(X4,X3)
| ~ in(esk8_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_181,plain,
( lhs_atom27(X1,X2,X3)
| in(esk16_3(X1,X2,X3),X1)
| ~ in(esk16_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_182,plain,
( lhs_atom15(X1,X2,X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| esk4_3(X1,X2,X3) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_183,plain,
( lhs_atom15(X1,X2,X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| esk4_3(X1,X2,X3) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_184,plain,
( lhs_atom27(X1,X2,X3)
| in(esk16_3(X1,X2,X3),X1)
| in(esk16_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_185,plain,
( lhs_atom23(X1,X2,X3)
| in(esk12_3(X1,X2,X3),X1)
| in(esk12_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_186,plain,
( lhs_atom23(X1,X2,X3)
| in(esk12_3(X1,X2,X3),X1)
| in(esk12_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_187,plain,
( lhs_atom19(X1,X2,X3)
| in(esk8_3(X1,X2,X3),X1)
| in(esk9_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_188,plain,
( lhs_atom19(X1,X2,X3)
| in(esk8_3(X1,X2,X3),X1)
| in(esk10_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_189,plain,
( lhs_atom15(X1,X2,X3)
| esk4_3(X1,X2,X3) = X2
| esk4_3(X1,X2,X3) = X3
| in(esk4_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_190,plain,
( lhs_atom25(X1,X2)
| ~ in(X3,X2)
| ~ in(esk14_2(X1,X2),X3)
| ~ in(esk14_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_191,plain,
( lhs_atom24(X1,X2)
| in(X3,esk13_3(X1,X2,X3))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_192,plain,
( lhs_atom24(X1,X2)
| in(esk13_3(X1,X2,X3),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_193,plain,
( lhs_atom7(X1,X2)
| ~ in(esk17_2(X1,X2),X1)
| ~ in(esk17_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_194,plain,
( lhs_atom13(X1,X2)
| ~ subset(esk3_2(X1,X2),X2)
| ~ in(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_195,plain,
( lhs_atom18(X1,X2,X3)
| in(X4,X1)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X2)
| ~ in(X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_196,plain,
( lhs_atom25(X1,X2)
| in(esk14_2(X1,X2),X1)
| in(esk14_2(X1,X2),esk15_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_197,plain,
( lhs_atom22(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_198,plain,
( lhs_atom26(X1,X2,X3)
| in(X4,X1)
| in(X4,X2)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_199,plain,
( lhs_atom16(X1,X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_200,plain,
( lhs_atom9(X1,X2)
| esk1_2(X1,X2) != X2
| ~ in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_201,plain,
( lhs_atom26(X1,X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_202,plain,
( lhs_atom7(X1,X2)
| in(esk17_2(X1,X2),X1)
| in(esk17_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_203,plain,
( lhs_atom25(X1,X2)
| in(esk14_2(X1,X2),X1)
| in(esk15_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_204,plain,
( lhs_atom13(X1,X2)
| subset(esk3_2(X1,X2),X2)
| in(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_205,plain,
( lhs_atom26(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_206,plain,
( lhs_atom22(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_207,plain,
( lhs_atom22(X1,X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_208,plain,
( lhs_atom16(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_209,plain,
( lhs_atom16(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_210,plain,
( lhs_atom14(X1,X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_211,plain,
( lhs_atom21(X1,X2)
| ~ in(esk11_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_212,plain,
( lhs_atom24(X1,X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_213,plain,
( lhs_atom14(X1,X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_214,plain,
( lhs_atom14(X1,X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_215,plain,
( lhs_atom9(X1,X2)
| esk1_2(X1,X2) = X2
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_216,plain,
( lhs_atom7(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_217,plain,
( lhs_atom21(X1,X2)
| in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_218,plain,
( lhs_atom35(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_219,plain,
( lhs_atom35(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_220,plain,
( in(X1,X2)
| lhs_atom20(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_221,plain,
( lhs_atom12(X1,X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_222,plain,
( lhs_atom12(X1,X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_223,plain,
( X1 = X2
| lhs_atom31(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_224,plain,
( lhs_atom8(X1,X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_225,plain,
( lhs_atom30(X2,X1)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_226,plain,
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_227,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_228,plain,
( lhs_atom8(X1,X2)
| in(X3,X1)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_229,plain,
( disjoint(X1,X2)
| lhs_atom29(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_230,plain,
( lhs_atom2(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_231,plain,
( set_intersection2(X1,X2) = empty_set
| lhs_atom29(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_232,plain,
( lhs_atom6(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_233,plain,
( lhs_atom6(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_234,plain,
( lhs_atom10(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_235,plain,
( in(esk2_1(X1),X1)
| lhs_atom11(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_236,plain,
( lhs_atom2(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_237,plain,
lhs_atom34(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_238,plain,
lhs_atom28(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_239,plain,
lhs_atom5(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_240,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_241,plain,
lhs_atom3(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_242,plain,
( X1 = empty_set
| lhs_atom44(X1) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_243,plain,
lhs_atom43(X1),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_244,plain,
lhs_atom42(X1),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_245,plain,
lhs_atom41(X1),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_246,plain,
lhs_atom40(X1),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
cnf(c_0_247,plain,
lhs_atom39(X1),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_248,plain,
lhs_atom38(X1),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_249,plain,
lhs_atom37(X1),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_250,plain,
lhs_atom36(X1),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_251,plain,
lhs_atom33,
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_252,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_253,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_254,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_255,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_256,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_165]) ).
cnf(c_0_257,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_258,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_259,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_260,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_261,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_262,plain,
( lhs_atom18(X1,X2,X3)
| ordered_pair(esk6_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4)) = X4
| ~ in(X4,X1) ),
c_0_171,
[final] ).
cnf(c_0_263,plain,
( lhs_atom23(X1,X2,X3)
| ~ in(esk12_3(X1,X2,X3),X2)
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(esk12_3(X1,X2,X3),X1) ),
c_0_172,
[final] ).
cnf(c_0_264,plain,
( lhs_atom18(X1,X2,X3)
| in(esk6_4(X1,X2,X3,X4),X3)
| ~ in(X4,X1) ),
c_0_173,
[final] ).
cnf(c_0_265,plain,
( lhs_atom18(X1,X2,X3)
| in(esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X1) ),
c_0_174,
[final] ).
cnf(c_0_266,plain,
( lhs_atom27(X1,X2,X3)
| in(esk16_3(X1,X2,X3),X2)
| ~ in(esk16_3(X1,X2,X3),X3)
| ~ in(esk16_3(X1,X2,X3),X1) ),
c_0_175,
[final] ).
cnf(c_0_267,plain,
( lhs_atom19(X1,X2,X3)
| in(esk8_3(X1,X2,X3),X1)
| ordered_pair(esk9_3(X1,X2,X3),esk10_3(X1,X2,X3)) = esk8_3(X1,X2,X3) ),
c_0_176,
[final] ).
cnf(c_0_268,plain,
( lhs_atom17(X1,X2,X3)
| ~ in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X3) ),
c_0_177,
[final] ).
cnf(c_0_269,plain,
( lhs_atom17(X1,X2,X3)
| ~ in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X2) ),
c_0_178,
[final] ).
cnf(c_0_270,plain,
( lhs_atom17(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X2)
| in(esk5_3(X1,X2,X3),X3)
| in(esk5_3(X1,X2,X3),X1) ),
c_0_179,
[final] ).
cnf(c_0_271,plain,
( lhs_atom19(X1,X2,X3)
| esk8_3(X1,X2,X3) != ordered_pair(X4,X5)
| ~ in(X5,X2)
| ~ in(X4,X3)
| ~ in(esk8_3(X1,X2,X3),X1) ),
c_0_180,
[final] ).
cnf(c_0_272,plain,
( lhs_atom27(X1,X2,X3)
| in(esk16_3(X1,X2,X3),X1)
| ~ in(esk16_3(X1,X2,X3),X2) ),
c_0_181,
[final] ).
cnf(c_0_273,plain,
( lhs_atom15(X1,X2,X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| esk4_3(X1,X2,X3) != X3 ),
c_0_182,
[final] ).
cnf(c_0_274,plain,
( lhs_atom15(X1,X2,X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| esk4_3(X1,X2,X3) != X2 ),
c_0_183,
[final] ).
cnf(c_0_275,plain,
( lhs_atom27(X1,X2,X3)
| in(esk16_3(X1,X2,X3),X1)
| in(esk16_3(X1,X2,X3),X3) ),
c_0_184,
[final] ).
cnf(c_0_276,plain,
( lhs_atom23(X1,X2,X3)
| in(esk12_3(X1,X2,X3),X1)
| in(esk12_3(X1,X2,X3),X3) ),
c_0_185,
[final] ).
cnf(c_0_277,plain,
( lhs_atom23(X1,X2,X3)
| in(esk12_3(X1,X2,X3),X1)
| in(esk12_3(X1,X2,X3),X2) ),
c_0_186,
[final] ).
cnf(c_0_278,plain,
( lhs_atom19(X1,X2,X3)
| in(esk8_3(X1,X2,X3),X1)
| in(esk9_3(X1,X2,X3),X3) ),
c_0_187,
[final] ).
cnf(c_0_279,plain,
( lhs_atom19(X1,X2,X3)
| in(esk8_3(X1,X2,X3),X1)
| in(esk10_3(X1,X2,X3),X2) ),
c_0_188,
[final] ).
cnf(c_0_280,plain,
( lhs_atom15(X1,X2,X3)
| esk4_3(X1,X2,X3) = X2
| esk4_3(X1,X2,X3) = X3
| in(esk4_3(X1,X2,X3),X1) ),
c_0_189,
[final] ).
cnf(c_0_281,plain,
( lhs_atom25(X1,X2)
| ~ in(X3,X2)
| ~ in(esk14_2(X1,X2),X3)
| ~ in(esk14_2(X1,X2),X1) ),
c_0_190,
[final] ).
cnf(c_0_282,plain,
( lhs_atom24(X1,X2)
| in(X3,esk13_3(X1,X2,X3))
| ~ in(X3,X1) ),
c_0_191,
[final] ).
cnf(c_0_283,plain,
( lhs_atom24(X1,X2)
| in(esk13_3(X1,X2,X3),X2)
| ~ in(X3,X1) ),
c_0_192,
[final] ).
cnf(c_0_284,plain,
( lhs_atom7(X1,X2)
| ~ in(esk17_2(X1,X2),X1)
| ~ in(esk17_2(X1,X2),X2) ),
c_0_193,
[final] ).
cnf(c_0_285,plain,
( lhs_atom13(X1,X2)
| ~ subset(esk3_2(X1,X2),X2)
| ~ in(esk3_2(X1,X2),X1) ),
c_0_194,
[final] ).
cnf(c_0_286,plain,
( lhs_atom18(X1,X2,X3)
| in(X4,X1)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X2)
| ~ in(X5,X3) ),
c_0_195,
[final] ).
cnf(c_0_287,plain,
( lhs_atom25(X1,X2)
| in(esk14_2(X1,X2),X1)
| in(esk14_2(X1,X2),esk15_2(X1,X2)) ),
c_0_196,
[final] ).
cnf(c_0_288,plain,
( lhs_atom22(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X3) ),
c_0_197,
[final] ).
cnf(c_0_289,plain,
( lhs_atom26(X1,X2,X3)
| in(X4,X1)
| in(X4,X2)
| ~ in(X4,X3) ),
c_0_198,
[final] ).
cnf(c_0_290,plain,
( lhs_atom16(X1,X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
c_0_199,
[final] ).
cnf(c_0_291,plain,
( lhs_atom9(X1,X2)
| esk1_2(X1,X2) != X2
| ~ in(esk1_2(X1,X2),X1) ),
c_0_200,
[final] ).
cnf(c_0_292,plain,
( lhs_atom26(X1,X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) ),
c_0_201,
[final] ).
cnf(c_0_293,plain,
( lhs_atom7(X1,X2)
| in(esk17_2(X1,X2),X1)
| in(esk17_2(X1,X2),X2) ),
c_0_202,
[final] ).
cnf(c_0_294,plain,
( lhs_atom25(X1,X2)
| in(esk14_2(X1,X2),X1)
| in(esk15_2(X1,X2),X2) ),
c_0_203,
[final] ).
cnf(c_0_295,plain,
( lhs_atom13(X1,X2)
| subset(esk3_2(X1,X2),X2)
| in(esk3_2(X1,X2),X1) ),
c_0_204,
[final] ).
cnf(c_0_296,plain,
( lhs_atom26(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
c_0_205,
[final] ).
cnf(c_0_297,plain,
( lhs_atom22(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
c_0_206,
[final] ).
cnf(c_0_298,plain,
( lhs_atom22(X1,X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
c_0_207,
[final] ).
cnf(c_0_299,plain,
( lhs_atom16(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
c_0_208,
[final] ).
cnf(c_0_300,plain,
( lhs_atom16(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
c_0_209,
[final] ).
cnf(c_0_301,plain,
( lhs_atom14(X1,X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
c_0_210,
[final] ).
cnf(c_0_302,plain,
( lhs_atom21(X1,X2)
| ~ in(esk11_2(X1,X2),X1) ),
c_0_211,
[final] ).
cnf(c_0_303,plain,
( lhs_atom24(X1,X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_212,
[final] ).
cnf(c_0_304,plain,
( lhs_atom14(X1,X2,X3)
| in(X4,X1)
| X4 != X3 ),
c_0_213,
[final] ).
cnf(c_0_305,plain,
( lhs_atom14(X1,X2,X3)
| in(X4,X1)
| X4 != X2 ),
c_0_214,
[final] ).
cnf(c_0_306,plain,
( lhs_atom9(X1,X2)
| esk1_2(X1,X2) = X2
| in(esk1_2(X1,X2),X1) ),
c_0_215,
[final] ).
cnf(c_0_307,plain,
( lhs_atom7(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_216,
[final] ).
cnf(c_0_308,plain,
( lhs_atom21(X1,X2)
| in(esk11_2(X1,X2),X2) ),
c_0_217,
[final] ).
cnf(c_0_309,plain,
( lhs_atom35(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_218,
[final] ).
cnf(c_0_310,plain,
( lhs_atom35(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_219,
[final] ).
cnf(c_0_311,plain,
( in(X1,X2)
| lhs_atom20(X2,X3)
| ~ in(X1,X3) ),
c_0_220,
[final] ).
cnf(c_0_312,plain,
( lhs_atom12(X1,X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
c_0_221,
[final] ).
cnf(c_0_313,plain,
( lhs_atom12(X1,X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
c_0_222,
[final] ).
cnf(c_0_314,plain,
( X1 = X2
| lhs_atom31(X2,X1)
| ~ subset(X1,X2) ),
c_0_223,
[final] ).
cnf(c_0_315,plain,
( lhs_atom8(X1,X2)
| X3 = X2
| ~ in(X3,X1) ),
c_0_224,
[final] ).
cnf(c_0_316,plain,
( lhs_atom30(X2,X1)
| set_intersection2(X1,X2) != empty_set ),
c_0_225,
[final] ).
cnf(c_0_317,plain,
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_226,
[final] ).
cnf(c_0_318,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
c_0_227,
[final] ).
cnf(c_0_319,plain,
( lhs_atom8(X1,X2)
| in(X3,X1)
| X3 != X2 ),
c_0_228,
[final] ).
cnf(c_0_320,plain,
( disjoint(X1,X2)
| lhs_atom29(X1,X2) ),
c_0_229,
[final] ).
cnf(c_0_321,plain,
( lhs_atom2(X1,X2)
| subset(X2,X1) ),
c_0_230,
[final] ).
cnf(c_0_322,plain,
( set_intersection2(X1,X2) = empty_set
| lhs_atom29(X2,X1) ),
c_0_231,
[final] ).
cnf(c_0_323,plain,
( lhs_atom6(X1,X2)
| subset(X2,X1) ),
c_0_232,
[final] ).
cnf(c_0_324,plain,
( lhs_atom6(X1,X2)
| subset(X1,X2) ),
c_0_233,
[final] ).
cnf(c_0_325,plain,
( lhs_atom10(X2)
| ~ in(X1,X2) ),
c_0_234,
[final] ).
cnf(c_0_326,plain,
( in(esk2_1(X1),X1)
| lhs_atom11(X1) ),
c_0_235,
[final] ).
cnf(c_0_327,plain,
( lhs_atom2(X1,X2)
| X2 != X1 ),
c_0_236,
[final] ).
cnf(c_0_328,plain,
lhs_atom34(X1,X2),
c_0_237,
[final] ).
cnf(c_0_329,plain,
lhs_atom28(X1,X2),
c_0_238,
[final] ).
cnf(c_0_330,plain,
lhs_atom5(X1,X2),
c_0_239,
[final] ).
cnf(c_0_331,plain,
lhs_atom4(X1,X2),
c_0_240,
[final] ).
cnf(c_0_332,plain,
lhs_atom3(X1,X2),
c_0_241,
[final] ).
cnf(c_0_333,plain,
( X1 = empty_set
| lhs_atom44(X1) ),
c_0_242,
[final] ).
cnf(c_0_334,plain,
lhs_atom43(X1),
c_0_243,
[final] ).
cnf(c_0_335,plain,
lhs_atom42(X1),
c_0_244,
[final] ).
cnf(c_0_336,plain,
lhs_atom41(X1),
c_0_245,
[final] ).
cnf(c_0_337,plain,
lhs_atom40(X1),
c_0_246,
[final] ).
cnf(c_0_338,plain,
lhs_atom39(X1),
c_0_247,
[final] ).
cnf(c_0_339,plain,
lhs_atom38(X1),
c_0_248,
[final] ).
cnf(c_0_340,plain,
lhs_atom37(X1),
c_0_249,
[final] ).
cnf(c_0_341,plain,
lhs_atom36(X1),
c_0_250,
[final] ).
cnf(c_0_342,plain,
lhs_atom33,
c_0_251,
[final] ).
cnf(c_0_343,plain,
lhs_atom32,
c_0_252,
[final] ).
cnf(c_0_344,plain,
lhs_atom32,
c_0_253,
[final] ).
cnf(c_0_345,plain,
lhs_atom32,
c_0_254,
[final] ).
cnf(c_0_346,plain,
lhs_atom32,
c_0_255,
[final] ).
cnf(c_0_347,plain,
lhs_atom32,
c_0_256,
[final] ).
cnf(c_0_348,plain,
lhs_atom32,
c_0_257,
[final] ).
cnf(c_0_349,plain,
lhs_atom32,
c_0_258,
[final] ).
cnf(c_0_350,plain,
lhs_atom32,
c_0_259,
[final] ).
cnf(c_0_351,plain,
lhs_atom32,
c_0_260,
[final] ).
cnf(c_0_352,plain,
lhs_atom32,
c_0_261,
[final] ).
% End CNF derivation
cnf(c_0_262_0,axiom,
( X1 != cartesian_product2(X3,X2)
| ordered_pair(sk1_esk6_4(X1,X2,X3,X4),sk1_esk7_4(X1,X2,X3,X4)) = X4
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_262,def_lhs_atom18]) ).
cnf(c_0_263_0,axiom,
( X1 = set_intersection2(X3,X2)
| ~ in(sk1_esk12_3(X1,X2,X3),X2)
| ~ in(sk1_esk12_3(X1,X2,X3),X3)
| ~ in(sk1_esk12_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_263,def_lhs_atom23]) ).
cnf(c_0_264_0,axiom,
( X1 != cartesian_product2(X3,X2)
| in(sk1_esk6_4(X1,X2,X3,X4),X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_264,def_lhs_atom18]) ).
cnf(c_0_265_0,axiom,
( X1 != cartesian_product2(X3,X2)
| in(sk1_esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_265,def_lhs_atom18]) ).
cnf(c_0_266_0,axiom,
( X1 = set_difference(X3,X2)
| in(sk1_esk16_3(X1,X2,X3),X2)
| ~ in(sk1_esk16_3(X1,X2,X3),X3)
| ~ in(sk1_esk16_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_266,def_lhs_atom27]) ).
cnf(c_0_267_0,axiom,
( X1 = cartesian_product2(X3,X2)
| in(sk1_esk8_3(X1,X2,X3),X1)
| ordered_pair(sk1_esk9_3(X1,X2,X3),sk1_esk10_3(X1,X2,X3)) = sk1_esk8_3(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_267,def_lhs_atom19]) ).
cnf(c_0_268_0,axiom,
( X1 = set_union2(X3,X2)
| ~ in(sk1_esk5_3(X1,X2,X3),X1)
| ~ in(sk1_esk5_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_268,def_lhs_atom17]) ).
cnf(c_0_269_0,axiom,
( X1 = set_union2(X3,X2)
| ~ in(sk1_esk5_3(X1,X2,X3),X1)
| ~ in(sk1_esk5_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_269,def_lhs_atom17]) ).
cnf(c_0_270_0,axiom,
( X1 = set_union2(X3,X2)
| in(sk1_esk5_3(X1,X2,X3),X2)
| in(sk1_esk5_3(X1,X2,X3),X3)
| in(sk1_esk5_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_270,def_lhs_atom17]) ).
cnf(c_0_271_0,axiom,
( X1 = cartesian_product2(X3,X2)
| sk1_esk8_3(X1,X2,X3) != ordered_pair(X4,X5)
| ~ in(X5,X2)
| ~ in(X4,X3)
| ~ in(sk1_esk8_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_271,def_lhs_atom19]) ).
cnf(c_0_272_0,axiom,
( X1 = set_difference(X3,X2)
| in(sk1_esk16_3(X1,X2,X3),X1)
| ~ in(sk1_esk16_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_272,def_lhs_atom27]) ).
cnf(c_0_273_0,axiom,
( X1 = unordered_pair(X3,X2)
| ~ in(sk1_esk4_3(X1,X2,X3),X1)
| sk1_esk4_3(X1,X2,X3) != X3 ),
inference(unfold_definition,[status(thm)],[c_0_273,def_lhs_atom15]) ).
cnf(c_0_274_0,axiom,
( X1 = unordered_pair(X3,X2)
| ~ in(sk1_esk4_3(X1,X2,X3),X1)
| sk1_esk4_3(X1,X2,X3) != X2 ),
inference(unfold_definition,[status(thm)],[c_0_274,def_lhs_atom15]) ).
cnf(c_0_275_0,axiom,
( X1 = set_difference(X3,X2)
| in(sk1_esk16_3(X1,X2,X3),X1)
| in(sk1_esk16_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_275,def_lhs_atom27]) ).
cnf(c_0_276_0,axiom,
( X1 = set_intersection2(X3,X2)
| in(sk1_esk12_3(X1,X2,X3),X1)
| in(sk1_esk12_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_276,def_lhs_atom23]) ).
cnf(c_0_277_0,axiom,
( X1 = set_intersection2(X3,X2)
| in(sk1_esk12_3(X1,X2,X3),X1)
| in(sk1_esk12_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_277,def_lhs_atom23]) ).
cnf(c_0_278_0,axiom,
( X1 = cartesian_product2(X3,X2)
| in(sk1_esk8_3(X1,X2,X3),X1)
| in(sk1_esk9_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_278,def_lhs_atom19]) ).
cnf(c_0_279_0,axiom,
( X1 = cartesian_product2(X3,X2)
| in(sk1_esk8_3(X1,X2,X3),X1)
| in(sk1_esk10_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_279,def_lhs_atom19]) ).
cnf(c_0_280_0,axiom,
( X1 = unordered_pair(X3,X2)
| sk1_esk4_3(X1,X2,X3) = X2
| sk1_esk4_3(X1,X2,X3) = X3
| in(sk1_esk4_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_280,def_lhs_atom15]) ).
cnf(c_0_281_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk14_2(X1,X2),X3)
| ~ in(sk1_esk14_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_281,def_lhs_atom25]) ).
cnf(c_0_282_0,axiom,
( X1 != union(X2)
| in(X3,sk1_esk13_3(X1,X2,X3))
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_282,def_lhs_atom24]) ).
cnf(c_0_283_0,axiom,
( X1 != union(X2)
| in(sk1_esk13_3(X1,X2,X3),X2)
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_283,def_lhs_atom24]) ).
cnf(c_0_284_0,axiom,
( X2 = X1
| ~ in(sk1_esk17_2(X1,X2),X1)
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_284,def_lhs_atom7]) ).
cnf(c_0_285_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk3_2(X1,X2),X2)
| ~ in(sk1_esk3_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_285,def_lhs_atom13]) ).
cnf(c_0_286_0,axiom,
( X1 != cartesian_product2(X3,X2)
| in(X4,X1)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X2)
| ~ in(X5,X3) ),
inference(unfold_definition,[status(thm)],[c_0_286,def_lhs_atom18]) ).
cnf(c_0_287_0,axiom,
( X1 = union(X2)
| in(sk1_esk14_2(X1,X2),X1)
| in(sk1_esk14_2(X1,X2),sk1_esk15_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_287,def_lhs_atom25]) ).
cnf(c_0_288_0,axiom,
( X1 != set_intersection2(X3,X2)
| in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_288,def_lhs_atom22]) ).
cnf(c_0_289_0,axiom,
( X1 != set_difference(X3,X2)
| in(X4,X1)
| in(X4,X2)
| ~ in(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_289,def_lhs_atom26]) ).
cnf(c_0_290_0,axiom,
( X1 != set_union2(X3,X2)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_290,def_lhs_atom16]) ).
cnf(c_0_291_0,axiom,
( X1 = singleton(X2)
| sk1_esk1_2(X1,X2) != X2
| ~ in(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_291,def_lhs_atom9]) ).
cnf(c_0_292_0,axiom,
( X1 != set_difference(X3,X2)
| ~ in(X4,X1)
| ~ in(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_292,def_lhs_atom26]) ).
cnf(c_0_293_0,axiom,
( X2 = X1
| in(sk1_esk17_2(X1,X2),X1)
| in(sk1_esk17_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_293,def_lhs_atom7]) ).
cnf(c_0_294_0,axiom,
( X1 = union(X2)
| in(sk1_esk14_2(X1,X2),X1)
| in(sk1_esk15_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_294,def_lhs_atom25]) ).
cnf(c_0_295_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk3_2(X1,X2),X2)
| in(sk1_esk3_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_295,def_lhs_atom13]) ).
cnf(c_0_296_0,axiom,
( X1 != set_difference(X3,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_296,def_lhs_atom26]) ).
cnf(c_0_297_0,axiom,
( X1 != set_intersection2(X3,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_297,def_lhs_atom22]) ).
cnf(c_0_298_0,axiom,
( X1 != set_intersection2(X3,X2)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_298,def_lhs_atom22]) ).
cnf(c_0_299_0,axiom,
( X1 != set_union2(X3,X2)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_299,def_lhs_atom16]) ).
cnf(c_0_300_0,axiom,
( X1 != set_union2(X3,X2)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_300,def_lhs_atom16]) ).
cnf(c_0_301_0,axiom,
( X1 != unordered_pair(X3,X2)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_301,def_lhs_atom14]) ).
cnf(c_0_302_0,axiom,
( subset(X2,X1)
| ~ in(sk1_esk11_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_302,def_lhs_atom21]) ).
cnf(c_0_303_0,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_303,def_lhs_atom24]) ).
cnf(c_0_304_0,axiom,
( X1 != unordered_pair(X3,X2)
| in(X4,X1)
| X4 != X3 ),
inference(unfold_definition,[status(thm)],[c_0_304,def_lhs_atom14]) ).
cnf(c_0_305_0,axiom,
( X1 != unordered_pair(X3,X2)
| in(X4,X1)
| X4 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_305,def_lhs_atom14]) ).
cnf(c_0_306_0,axiom,
( X1 = singleton(X2)
| sk1_esk1_2(X1,X2) = X2
| in(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_306,def_lhs_atom9]) ).
cnf(c_0_307_0,axiom,
( X2 = X1
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_307,def_lhs_atom7]) ).
cnf(c_0_308_0,axiom,
( subset(X2,X1)
| in(sk1_esk11_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_308,def_lhs_atom21]) ).
cnf(c_0_309_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_309,def_lhs_atom35]) ).
cnf(c_0_310_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_310,def_lhs_atom35]) ).
cnf(c_0_311_0,axiom,
( ~ subset(X3,X2)
| in(X1,X2)
| ~ in(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_311,def_lhs_atom20]) ).
cnf(c_0_312_0,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_312,def_lhs_atom12]) ).
cnf(c_0_313_0,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_313,def_lhs_atom12]) ).
cnf(c_0_314_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_314,def_lhs_atom31]) ).
cnf(c_0_315_0,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_315,def_lhs_atom8]) ).
cnf(c_0_316_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(unfold_definition,[status(thm)],[c_0_316,def_lhs_atom30]) ).
cnf(c_0_317_0,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_317,def_lhs_atom2]) ).
cnf(c_0_318_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_318,def_lhs_atom1]) ).
cnf(c_0_319_0,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_319,def_lhs_atom8]) ).
cnf(c_0_320_0,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_320,def_lhs_atom29]) ).
cnf(c_0_321_0,axiom,
( ~ proper_subset(X2,X1)
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_321,def_lhs_atom2]) ).
cnf(c_0_322_0,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_322,def_lhs_atom29]) ).
cnf(c_0_323_0,axiom,
( X2 != X1
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_323,def_lhs_atom6]) ).
cnf(c_0_324_0,axiom,
( X2 != X1
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_324,def_lhs_atom6]) ).
cnf(c_0_325_0,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_325,def_lhs_atom10]) ).
cnf(c_0_326_0,axiom,
( X1 = empty_set
| in(sk1_esk2_1(X1),X1) ),
inference(unfold_definition,[status(thm)],[c_0_326,def_lhs_atom11]) ).
cnf(c_0_327_0,axiom,
( ~ proper_subset(X2,X1)
| X2 != X1 ),
inference(unfold_definition,[status(thm)],[c_0_327,def_lhs_atom2]) ).
cnf(c_0_333_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_333,def_lhs_atom44]) ).
cnf(c_0_328_0,axiom,
~ empty(ordered_pair(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_328,def_lhs_atom34]) ).
cnf(c_0_329_0,axiom,
ordered_pair(X2,X1) = unordered_pair(unordered_pair(X2,X1),singleton(X2)),
inference(unfold_definition,[status(thm)],[c_0_329,def_lhs_atom28]) ).
cnf(c_0_330_0,axiom,
set_intersection2(X2,X1) = set_intersection2(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_330,def_lhs_atom5]) ).
cnf(c_0_331_0,axiom,
set_union2(X2,X1) = set_union2(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_331,def_lhs_atom4]) ).
cnf(c_0_332_0,axiom,
unordered_pair(X2,X1) = unordered_pair(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_332,def_lhs_atom3]) ).
cnf(c_0_334_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(unfold_definition,[status(thm)],[c_0_334,def_lhs_atom43]) ).
cnf(c_0_335_0,axiom,
set_difference(X1,empty_set) = X1,
inference(unfold_definition,[status(thm)],[c_0_335,def_lhs_atom42]) ).
cnf(c_0_336_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(unfold_definition,[status(thm)],[c_0_336,def_lhs_atom41]) ).
cnf(c_0_337_0,axiom,
set_union2(X1,empty_set) = X1,
inference(unfold_definition,[status(thm)],[c_0_337,def_lhs_atom40]) ).
cnf(c_0_338_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_338,def_lhs_atom39]) ).
cnf(c_0_339_0,axiom,
~ proper_subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_339,def_lhs_atom38]) ).
cnf(c_0_340_0,axiom,
set_intersection2(X1,X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_340,def_lhs_atom37]) ).
cnf(c_0_341_0,axiom,
set_union2(X1,X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_341,def_lhs_atom36]) ).
cnf(c_0_342_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_342,def_lhs_atom33]) ).
cnf(c_0_343_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_343,def_lhs_atom32]) ).
cnf(c_0_344_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_344,def_lhs_atom32]) ).
cnf(c_0_345_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_345,def_lhs_atom32]) ).
cnf(c_0_346_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_346,def_lhs_atom32]) ).
cnf(c_0_347_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_347,def_lhs_atom32]) ).
cnf(c_0_348_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_348,def_lhs_atom32]) ).
cnf(c_0_349_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_349,def_lhs_atom32]) ).
cnf(c_0_350_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_350,def_lhs_atom32]) ).
cnf(c_0_351_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_351,def_lhs_atom32]) ).
cnf(c_0_352_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_352,def_lhs_atom32]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_1_002,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_2_003,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_3_004,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_4_005,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_0 ).
fof(c_0_5_006,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_1 ).
fof(c_0_6_007,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_7_008,axiom,
? [X1] : empty(X1),
c_0_3 ).
fof(c_0_8_009,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_9_010,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_5])])])]) ).
fof(c_0_10_011,plain,
~ empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_11_012,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
cnf(c_0_12_013,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_014,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14_015,plain,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15_016,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16_017,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_12,
[final] ).
cnf(c_0_17_018,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_13,
[final] ).
cnf(c_0_18_019,plain,
~ empty(esk1_0),
c_0_14,
[final] ).
cnf(c_0_19_020,plain,
empty(esk2_0),
c_0_15,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_16_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_16_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_17_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_18_0,axiom,
~ empty(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_18]) ).
cnf(c_0_19_0,axiom,
empty(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_19]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_021,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_1_022,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_2_023,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_3_024,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_4_025,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_5_026,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_6_027,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_7_028,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_8_029,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_9_030,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_10_031,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_11_032,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_12_033,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_13_034,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_14_035,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_15_036,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_16_037,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_17_038,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_18_039,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_19_040,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_20_041,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_21_042,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_22_043,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_23_044,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_24_045,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_25_046,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_26_047,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_27_048,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_28_049,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_29_050,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_30_051,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_31_052,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_32_053,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_33_054,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_34_055,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_35_056,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_36_057,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_37_058,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_38_059,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_39_060,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_40_061,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_41_062,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_42_063,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_43_064,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_44_065,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_1 ).
fof(c_0_45_066,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_2 ).
fof(c_0_46_067,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_3 ).
fof(c_0_47_068,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_4]) ).
fof(c_0_48_069,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_5 ).
fof(c_0_49_070,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_6 ).
fof(c_0_50_071,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_7 ).
fof(c_0_51_072,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_8]) ).
fof(c_0_52_073,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_9 ).
fof(c_0_53_074,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_10 ).
fof(c_0_54_075,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_11 ).
fof(c_0_55_076,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_12 ).
fof(c_0_56_077,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_13 ).
fof(c_0_57_078,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_14 ).
fof(c_0_58_079,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_15 ).
fof(c_0_59_080,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_16 ).
fof(c_0_60_081,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_17 ).
fof(c_0_61_082,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_18 ).
fof(c_0_62_083,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_19 ).
fof(c_0_63_084,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_20 ).
fof(c_0_64_085,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_21 ).
fof(c_0_65_086,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_22 ).
fof(c_0_66_087,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_23 ).
fof(c_0_67_088,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_24 ).
fof(c_0_68_089,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_25 ).
fof(c_0_69_090,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_26 ).
fof(c_0_70_091,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_27 ).
fof(c_0_71_092,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_28 ).
fof(c_0_72_093,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_29 ).
fof(c_0_73_094,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_30 ).
fof(c_0_74_095,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_31 ).
fof(c_0_75_096,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_32 ).
fof(c_0_76_097,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_33 ).
fof(c_0_77_098,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_78_099,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_35 ).
fof(c_0_79_100,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_36 ).
fof(c_0_80_101,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[c_0_37]) ).
fof(c_0_81_102,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_38 ).
fof(c_0_82_103,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_39 ).
fof(c_0_83_104,lemma,
! [X1] : subset(empty_set,X1),
c_0_40 ).
fof(c_0_84_105,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_41 ).
fof(c_0_85_106,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_42 ).
fof(c_0_86_107,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_43])])])])]) ).
fof(c_0_87_108,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_44])])])]) ).
fof(c_0_88_109,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_45])])])]) ).
fof(c_0_89_110,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_46])])])]) ).
fof(c_0_90_111,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk4_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_47])])])])]) ).
fof(c_0_91_112,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_48])]) ).
fof(c_0_92_113,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_49])])])])]) ).
fof(c_0_93_114,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_50])]) ).
fof(c_0_94_115,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk1_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk1_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_51])])])])])]) ).
fof(c_0_95_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_52])]) ).
fof(c_0_96_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_53])]) ).
fof(c_0_97_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_54])]) ).
fof(c_0_98_119,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])]) ).
fof(c_0_99_120,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_56]) ).
fof(c_0_100_121,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_57]) ).
fof(c_0_101_122,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_58]) ).
fof(c_0_102_123,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_59])]) ).
fof(c_0_103_124,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_60])])])]) ).
fof(c_0_104_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_61])])])]) ).
fof(c_0_105_126,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_62])])]) ).
fof(c_0_106_127,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])]) ).
fof(c_0_107_128,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])]) ).
fof(c_0_108_129,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])]) ).
fof(c_0_109_130,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])]) ).
fof(c_0_110_131,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_67]) ).
fof(c_0_111_132,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_112_133,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_113_134,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_70])])])])]) ).
fof(c_0_114_135,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_71])])])])]) ).
fof(c_0_115_136,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_72])])])]) ).
fof(c_0_116_137,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])]) ).
fof(c_0_117_138,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])]) ).
fof(c_0_118_139,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_75])])])]) ).
fof(c_0_119_140,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_76])])])]) ).
fof(c_0_120_141,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])]) ).
fof(c_0_121_142,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])]) ).
fof(c_0_122_143,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_79])])])]) ).
fof(c_0_123_144,negated_conjecture,
( in(esk2_0,esk3_0)
& set_union2(singleton(esk2_0),esk3_0) != esk3_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])]) ).
fof(c_0_124_145,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])]) ).
fof(c_0_125_146,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_82]) ).
fof(c_0_126_147,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_83]) ).
fof(c_0_127_148,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_84]) ).
fof(c_0_128_149,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_85 ).
cnf(c_0_129_150,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_130_151,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_131_152,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_132_153,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_133_154,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_134_155,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_135_156,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_136_157,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_137_158,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_138_159,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_139_160,lemma,
( in(esk4_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_140_161,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_141_162,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_142_163,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_143_164,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_144_165,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_145_166,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_146_167,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_147_168,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_148_169,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_149_170,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_150_171,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_151_172,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_152_173,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_153_174,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_154_175,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_155_176,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_156_177,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_157_178,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_158_179,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_159_180,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_160_181,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_161_182,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_162_183,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_163_184,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_164_185,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_165_186,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_166_187,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_167_188,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_168_189,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_169_190,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_170_191,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_171_192,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_172_193,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_173_194,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_174_195,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_175_196,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_176_197,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_177_198,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_178_199,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_179_200,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_180_201,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_181_202,negated_conjecture,
set_union2(singleton(esk2_0),esk3_0) != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_182_203,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_183_204,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_184_205,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_185_206,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_186_207,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_187_208,negated_conjecture,
in(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_188_209,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_189_210,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_190_211,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_129,
[final] ).
cnf(c_0_191_212,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_130,
[final] ).
cnf(c_0_192_213,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_131,
[final] ).
cnf(c_0_193_214,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_132,
[final] ).
cnf(c_0_194_215,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_133,
[final] ).
cnf(c_0_195_216,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_134,
[final] ).
cnf(c_0_196_217,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_135,
[final] ).
cnf(c_0_197_218,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_136,
[final] ).
cnf(c_0_198_219,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_137,
[final] ).
cnf(c_0_199_220,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_138,
[final] ).
cnf(c_0_200_221,lemma,
( in(esk4_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_139,
[final] ).
cnf(c_0_201_222,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_140,
[final] ).
cnf(c_0_202_223,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_141,
[final] ).
cnf(c_0_203_224,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_142,
[final] ).
cnf(c_0_204_225,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_143,
[final] ).
cnf(c_0_205_226,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_144,
[final] ).
cnf(c_0_206_227,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_145,
[final] ).
cnf(c_0_207_228,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_146,
[final] ).
cnf(c_0_208_229,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X1) ),
c_0_147,
[final] ).
cnf(c_0_209_230,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X2) ),
c_0_148,
[final] ).
cnf(c_0_210_231,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_149,
[final] ).
cnf(c_0_211_232,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_150,
[final] ).
cnf(c_0_212_233,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_151,
[final] ).
cnf(c_0_213_234,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_152,
[final] ).
cnf(c_0_214_235,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_153,
[final] ).
cnf(c_0_215_236,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_154,
[final] ).
cnf(c_0_216_237,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_155,
[final] ).
cnf(c_0_217_238,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_156,
[final] ).
cnf(c_0_218_239,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_157,
[final] ).
cnf(c_0_219_240,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_158,
[final] ).
cnf(c_0_220_241,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_159,
[final] ).
cnf(c_0_221_242,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_160,
[final] ).
cnf(c_0_222_243,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_161,
[final] ).
cnf(c_0_223_244,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_162,
[final] ).
cnf(c_0_224_245,lemma,
subset(X1,set_union2(X1,X2)),
c_0_163,
[final] ).
cnf(c_0_225_246,lemma,
subset(set_difference(X1,X2),X1),
c_0_164,
[final] ).
cnf(c_0_226_247,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_165,
[final] ).
cnf(c_0_227_248,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_166,
[final] ).
cnf(c_0_228_249,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_167,
[final] ).
cnf(c_0_229_250,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_168,
[final] ).
cnf(c_0_230_251,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_169,
[final] ).
cnf(c_0_231_252,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_170,
[final] ).
cnf(c_0_232_253,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_171,
[final] ).
cnf(c_0_233_254,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_172,
[final] ).
cnf(c_0_234_255,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_173,
[final] ).
cnf(c_0_235_256,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_174,
[final] ).
cnf(c_0_236_257,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_175,
[final] ).
cnf(c_0_237_258,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_176,
[final] ).
cnf(c_0_238_259,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_177,
[final] ).
cnf(c_0_239_260,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_178,
[final] ).
cnf(c_0_240_261,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_179,
[final] ).
cnf(c_0_241_262,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_180,
[final] ).
cnf(c_0_242_263,negated_conjecture,
set_union2(singleton(esk2_0),esk3_0) != esk3_0,
c_0_181,
[final] ).
cnf(c_0_243_264,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_182,
[final] ).
cnf(c_0_244_265,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_183,
[final] ).
cnf(c_0_245_266,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_184,
[final] ).
cnf(c_0_246_267,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_185,
[final] ).
cnf(c_0_247_268,lemma,
subset(empty_set,X1),
c_0_186,
[final] ).
cnf(c_0_248_269,negated_conjecture,
in(esk2_0,esk3_0),
c_0_187,
[final] ).
cnf(c_0_249_270,lemma,
singleton(X1) != empty_set,
c_0_188,
[final] ).
cnf(c_0_250_271,lemma,
singleton(empty_set) = powerset(empty_set),
c_0_189,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_134,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c4ef8.p',c_0_232) ).
cnf(c_320,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_134]) ).
cnf(c_407,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_320]) ).
cnf(c_448,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_407]) ).
cnf(c_529,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_448]) ).
cnf(c_969,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_529]) ).
cnf(c_147,negated_conjecture,
set_union2(singleton(sk3_esk2_0),sk3_esk3_0) != sk3_esk3_0,
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c4ef8.p',c_0_242) ).
cnf(c_366,negated_conjecture,
set_union2(singleton(sk3_esk2_0),sk3_esk3_0) != sk3_esk3_0,
inference(copy,[status(esa)],[c_147]) ).
cnf(c_416,negated_conjecture,
set_union2(singleton(sk3_esk2_0),sk3_esk3_0) != sk3_esk3_0,
inference(copy,[status(esa)],[c_366]) ).
cnf(c_439,negated_conjecture,
set_union2(singleton(sk3_esk2_0),sk3_esk3_0) != sk3_esk3_0,
inference(copy,[status(esa)],[c_416]) ).
cnf(c_485,negated_conjecture,
set_union2(singleton(sk3_esk2_0),sk3_esk3_0) != sk3_esk3_0,
inference(copy,[status(esa)],[c_439]) ).
cnf(c_881,negated_conjecture,
set_union2(singleton(sk3_esk2_0),sk3_esk3_0) != sk3_esk3_0,
inference(copy,[status(esa)],[c_485]) ).
cnf(c_1972,plain,
~ subset(singleton(sk3_esk2_0),sk3_esk3_0),
inference(resolution,[status(thm)],[c_969,c_881]) ).
cnf(c_1973,plain,
~ subset(singleton(sk3_esk2_0),sk3_esk3_0),
inference(rewriting,[status(thm)],[c_1972]) ).
cnf(c_126,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c4ef8.p',c_0_221) ).
cnf(c_304,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(copy,[status(esa)],[c_126]) ).
cnf(c_401,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(copy,[status(esa)],[c_304]) ).
cnf(c_454,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(copy,[status(esa)],[c_401]) ).
cnf(c_523,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(copy,[status(esa)],[c_454]) ).
cnf(c_957,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(copy,[status(esa)],[c_523]) ).
cnf(c_1998,plain,
~ in(sk3_esk2_0,sk3_esk3_0),
inference(resolution,[status(thm)],[c_1973,c_957]) ).
cnf(c_1999,plain,
~ in(sk3_esk2_0,sk3_esk3_0),
inference(rewriting,[status(thm)],[c_1998]) ).
cnf(c_157,negated_conjecture,
in(sk3_esk2_0,sk3_esk3_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_1c4ef8.p',c_0_248) ).
cnf(c_368,negated_conjecture,
in(sk3_esk2_0,sk3_esk3_0),
inference(copy,[status(esa)],[c_157]) ).
cnf(c_426,negated_conjecture,
in(sk3_esk2_0,sk3_esk3_0),
inference(copy,[status(esa)],[c_368]) ).
cnf(c_429,negated_conjecture,
in(sk3_esk2_0,sk3_esk3_0),
inference(copy,[status(esa)],[c_426]) ).
cnf(c_495,negated_conjecture,
in(sk3_esk2_0,sk3_esk3_0),
inference(copy,[status(esa)],[c_429]) ).
cnf(c_901,negated_conjecture,
in(sk3_esk2_0,sk3_esk3_0),
inference(copy,[status(esa)],[c_495]) ).
cnf(c_2001,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1999,c_901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU161+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : iprover_modulo %s %d
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 01:52:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Running in mono-core mode
% 0.20/0.41 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.41 % FOF problem with conjecture
% 0.20/0.41 % 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_422213.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_1c4ef8.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_51c5ba | grep -v "SZS"
% 0.20/0.44
% 0.20/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ iProver source info
% 0.20/0.44
% 0.20/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.44 % git: non_committed_changes: true
% 0.20/0.44 % git: last_make_outside_of_git: true
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ Input Options
% 0.20/0.44
% 0.20/0.44 % --out_options all
% 0.20/0.44 % --tptp_safe_out true
% 0.20/0.44 % --problem_path ""
% 0.20/0.44 % --include_path ""
% 0.20/0.44 % --clausifier .//eprover
% 0.20/0.44 % --clausifier_options --tstp-format
% 0.20/0.44 % --stdin false
% 0.20/0.44 % --dbg_backtrace false
% 0.20/0.44 % --dbg_dump_prop_clauses false
% 0.20/0.44 % --dbg_dump_prop_clauses_file -
% 0.20/0.44 % --dbg_out_stat false
% 0.20/0.44
% 0.20/0.44 % ------ General Options
% 0.20/0.44
% 0.20/0.44 % --fof false
% 0.20/0.44 % --time_out_real 150.
% 0.20/0.44 % --time_out_prep_mult 0.2
% 0.20/0.44 % --time_out_virtual -1.
% 0.20/0.44 % --schedule none
% 0.20/0.44 % --ground_splitting input
% 0.20/0.44 % --splitting_nvd 16
% 0.20/0.44 % --non_eq_to_eq false
% 0.20/0.44 % --prep_gs_sim true
% 0.20/0.44 % --prep_unflatten false
% 0.20/0.44 % --prep_res_sim true
% 0.20/0.44 % --prep_upred true
% 0.20/0.44 % --res_sim_input true
% 0.20/0.44 % --clause_weak_htbl true
% 0.20/0.44 % --gc_record_bc_elim false
% 0.20/0.44 % --symbol_type_check false
% 0.20/0.44 % --clausify_out false
% 0.20/0.44 % --large_theory_mode false
% 0.20/0.44 % --prep_sem_filter none
% 0.20/0.44 % --prep_sem_filter_out false
% 0.20/0.44 % --preprocessed_out false
% 0.20/0.44 % --sub_typing false
% 0.20/0.44 % --brand_transform false
% 0.20/0.44 % --pure_diseq_elim true
% 0.20/0.44 % --min_unsat_core false
% 0.20/0.44 % --pred_elim true
% 0.20/0.44 % --add_important_lit false
% 0.20/0.44 % --soft_assumptions false
% 0.20/0.44 % --reset_solvers false
% 0.20/0.44 % --bc_imp_inh []
% 0.20/0.44 % --conj_cone_tolerance 1.5
% 0.20/0.44 % --prolific_symb_bound 500
% 0.20/0.44 % --lt_threshold 2000
% 0.20/0.44
% 0.20/0.44 % ------ SAT Options
% 0.20/0.44
% 0.20/0.44 % --sat_mode false
% 0.20/0.44 % --sat_fm_restart_options ""
% 0.20/0.44 % --sat_gr_def false
% 0.20/0.44 % --sat_epr_types true
% 0.20/0.44 % --sat_non_cyclic_types false
% 0.20/0.44 % --sat_finite_models false
% 0.20/0.44 % --sat_fm_lemmas false
% 0.20/0.44 % --sat_fm_prep false
% 0.20/0.44 % --sat_fm_uc_incr true
% 0.20/0.44 % --sat_out_model small
% 0.20/0.44 % --sat_out_clauses false
% 0.20/0.44
% 0.20/0.44 % ------ QBF Options
% 0.20/0.44
% 0.20/0.44 % --qbf_mode false
% 0.20/0.44 % --qbf_elim_univ true
% 0.20/0.44 % --qbf_sk_in true
% 0.20/0.44 % --qbf_pred_elim true
% 0.20/0.44 % --qbf_split 32
% 0.20/0.44
% 0.20/0.44 % ------ BMC1 Options
% 0.20/0.44
% 0.20/0.44 % --bmc1_incremental false
% 0.20/0.44 % --bmc1_axioms reachable_all
% 0.20/0.44 % --bmc1_min_bound 0
% 0.20/0.44 % --bmc1_max_bound -1
% 0.20/0.44 % --bmc1_max_bound_default -1
% 0.20/0.44 % --bmc1_symbol_reachability true
% 0.20/0.44 % --bmc1_property_lemmas false
% 0.20/0.44 % --bmc1_k_induction false
% 0.20/0.44 % --bmc1_non_equiv_states false
% 0.20/0.44 % --bmc1_deadlock false
% 0.20/0.44 % --bmc1_ucm false
% 0.20/0.44 % --bmc1_add_unsat_core none
% 0.20/0.44 % --bmc1_unsat_core_children false
% 0.20/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.44 % --bmc1_out_stat full
% 0.20/0.44 % --bmc1_ground_init false
% 0.20/0.44 % --bmc1_pre_inst_next_state false
% 0.20/0.44 % --bmc1_pre_inst_state false
% 0.20/0.44 % --bmc1_pre_inst_reach_state false
% 0.20/0.44 % --bmc1_out_unsat_core false
% 0.20/0.44 % --bmc1_aig_witness_out false
% 0.20/0.44 % --bmc1_verbose false
% 0.20/0.44 % --bmc1_dump_clauses_tptp false
% 0.47/0.74 % --bmc1_dump_unsat_core_tptp false
% 0.47/0.74 % --bmc1_dump_file -
% 0.47/0.74 % --bmc1_ucm_expand_uc_limit 128
% 0.47/0.74 % --bmc1_ucm_n_expand_iterations 6
% 0.47/0.74 % --bmc1_ucm_extend_mode 1
% 0.47/0.74 % --bmc1_ucm_init_mode 2
% 0.47/0.74 % --bmc1_ucm_cone_mode none
% 0.47/0.74 % --bmc1_ucm_reduced_relation_type 0
% 0.47/0.74 % --bmc1_ucm_relax_model 4
% 0.47/0.74 % --bmc1_ucm_full_tr_after_sat true
% 0.47/0.74 % --bmc1_ucm_expand_neg_assumptions false
% 0.47/0.74 % --bmc1_ucm_layered_model none
% 0.47/0.74 % --bmc1_ucm_max_lemma_size 10
% 0.47/0.74
% 0.47/0.74 % ------ AIG Options
% 0.47/0.74
% 0.47/0.74 % --aig_mode false
% 0.47/0.74
% 0.47/0.74 % ------ Instantiation Options
% 0.47/0.74
% 0.47/0.74 % --instantiation_flag true
% 0.47/0.74 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.47/0.74 % --inst_solver_per_active 750
% 0.47/0.74 % --inst_solver_calls_frac 0.5
% 0.47/0.74 % --inst_passive_queue_type priority_queues
% 0.47/0.74 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.47/0.74 % --inst_passive_queues_freq [25;2]
% 0.47/0.74 % --inst_dismatching true
% 0.47/0.74 % --inst_eager_unprocessed_to_passive true
% 0.47/0.74 % --inst_prop_sim_given true
% 0.47/0.74 % --inst_prop_sim_new false
% 0.47/0.74 % --inst_orphan_elimination true
% 0.47/0.74 % --inst_learning_loop_flag true
% 0.47/0.74 % --inst_learning_start 3000
% 0.47/0.74 % --inst_learning_factor 2
% 0.47/0.74 % --inst_start_prop_sim_after_learn 3
% 0.47/0.74 % --inst_sel_renew solver
% 0.47/0.74 % --inst_lit_activity_flag true
% 0.47/0.74 % --inst_out_proof true
% 0.47/0.74
% 0.47/0.74 % ------ Resolution Options
% 0.47/0.74
% 0.47/0.74 % --resolution_flag true
% 0.47/0.74 % --res_lit_sel kbo_max
% 0.47/0.74 % --res_to_prop_solver none
% 0.47/0.74 % --res_prop_simpl_new false
% 0.47/0.74 % --res_prop_simpl_given false
% 0.47/0.74 % --res_passive_queue_type priority_queues
% 0.47/0.74 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.47/0.74 % --res_passive_queues_freq [15;5]
% 0.47/0.74 % --res_forward_subs full
% 0.47/0.74 % --res_backward_subs full
% 0.47/0.74 % --res_forward_subs_resolution true
% 0.47/0.74 % --res_backward_subs_resolution true
% 0.47/0.74 % --res_orphan_elimination false
% 0.47/0.74 % --res_time_limit 1000.
% 0.47/0.74 % --res_out_proof true
% 0.47/0.74 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_422213.s
% 0.47/0.74 % --modulo true
% 0.47/0.74
% 0.47/0.74 % ------ Combination Options
% 0.47/0.74
% 0.47/0.74 % --comb_res_mult 1000
% 0.47/0.74 % --comb_inst_mult 300
% 0.47/0.74 % ------
% 0.47/0.74
% 0.47/0.74 % ------ Parsing...% successful
% 0.47/0.74
% 0.47/0.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe_e snvd_s sp: 0 0s snvd_e %
% 0.47/0.74
% 0.47/0.74 % ------ Proving...
% 0.47/0.74 % ------ Problem Properties
% 0.47/0.74
% 0.47/0.74 %
% 0.47/0.74 % EPR false
% 0.47/0.74 % Horn false
% 0.47/0.74 % Has equality true
% 0.47/0.74
% 0.47/0.74 % % ------ Input Options Time Limit: Unbounded
% 0.47/0.74
% 0.47/0.74
% 0.47/0.74 Compiling...
% 0.47/0.74 Loading plugin: done.
% 0.47/0.74 Compiling...
% 0.47/0.74 Loading plugin: done.
% 0.47/0.74 Compiling...
% 0.47/0.74 Loading plugin: done.
% 0.47/0.74 % % ------ Current options:
% 0.47/0.74
% 0.47/0.74 % ------ Input Options
% 0.47/0.74
% 0.47/0.74 % --out_options all
% 0.47/0.74 % --tptp_safe_out true
% 0.47/0.74 % --problem_path ""
% 0.47/0.74 % --include_path ""
% 0.47/0.74 % --clausifier .//eprover
% 0.47/0.74 % --clausifier_options --tstp-format
% 0.47/0.74 % --stdin false
% 0.47/0.74 % --dbg_backtrace false
% 0.47/0.74 % --dbg_dump_prop_clauses false
% 0.47/0.74 % --dbg_dump_prop_clauses_file -
% 0.47/0.74 % --dbg_out_stat false
% 0.47/0.74
% 0.47/0.74 % ------ General Options
% 0.47/0.74
% 0.47/0.74 % --fof false
% 0.47/0.74 % --time_out_real 150.
% 0.47/0.74 % --time_out_prep_mult 0.2
% 0.47/0.74 % --time_out_virtual -1.
% 0.47/0.74 % --schedule none
% 0.47/0.74 % --ground_splitting input
% 0.47/0.74 % --splitting_nvd 16
% 0.47/0.74 % --non_eq_to_eq false
% 0.47/0.74 % --prep_gs_sim true
% 0.47/0.74 % --prep_unflatten false
% 0.47/0.74 % --prep_res_sim true
% 0.47/0.74 % --prep_upred true
% 0.47/0.74 % --res_sim_input true
% 0.47/0.74 % --clause_weak_htbl true
% 0.47/0.74 % --gc_record_bc_elim false
% 0.47/0.74 % --symbol_type_check false
% 0.47/0.74 % --clausify_out false
% 0.47/0.74 % --large_theory_mode false
% 0.47/0.74 % --prep_sem_filter none
% 0.47/0.74 % --prep_sem_filter_out false
% 0.47/0.74 % --preprocessed_out false
% 0.47/0.74 % --sub_typing false
% 0.47/0.74 % --brand_transform false
% 0.47/0.74 % --pure_diseq_elim true
% 0.47/0.74 % --min_unsat_core false
% 0.47/0.74 % --pred_elim true
% 0.47/0.74 % --add_important_lit false
% 0.47/0.74 % --soft_assumptions false
% 0.47/0.74 % --reset_solvers false
% 0.47/0.74 % --bc_imp_inh []
% 0.47/0.74 % --conj_cone_tolerance 1.5
% 0.47/0.74 % --prolific_symb_bound 500
% 0.47/0.74 % --lt_threshold 2000
% 0.47/0.74
% 0.47/0.74 % ------ SAT Options
% 0.47/0.74
% 0.47/0.74 % --sat_mode false
% 0.47/0.74 % --sat_fm_restart_options ""
% 0.47/0.74 % --sat_gr_def false
% 0.47/0.74 % --sat_epr_types true
% 0.47/0.74 % --sat_non_cyclic_types false
% 0.47/0.74 % --sat_finite_models false
% 0.47/0.74 % --sat_fm_lemmas false
% 0.47/0.74 % --sat_fm_prep false
% 0.47/0.74 % --sat_fm_uc_incr true
% 0.47/0.74 % --sat_out_model small
% 0.47/0.74 % --sat_out_clauses false
% 0.47/0.74
% 0.47/0.74 % ------ QBF Options
% 0.47/0.74
% 0.47/0.74 % --qbf_mode false
% 0.47/0.74 % --qbf_elim_univ true
% 0.47/0.74 % --qbf_sk_in true
% 0.47/0.74 % --qbf_pred_elim true
% 0.47/0.74 % --qbf_split 32
% 0.47/0.74
% 0.47/0.74 % ------ BMC1 Options
% 0.47/0.74
% 0.47/0.74 % --bmc1_incremental false
% 0.47/0.74 % --bmc1_axioms reachable_all
% 0.47/0.74 % --bmc1_min_bound 0
% 0.47/0.74 % --bmc1_max_bound -1
% 0.47/0.74 % --bmc1_max_bound_default -1
% 0.47/0.74 % --bmc1_symbol_reachability true
% 0.47/0.74 % --bmc1_property_lemmas false
% 0.47/0.74 % --bmc1_k_induction false
% 0.47/0.74 % --bmc1_non_equiv_states false
% 0.47/0.74 % --bmc1_deadlock false
% 0.47/0.74 % --bmc1_ucm false
% 0.47/0.74 % --bmc1_add_unsat_core none
% 0.47/0.74 % --bmc1_unsat_core_children false
% 0.47/0.74 % --bmc1_unsat_core_extrapolate_axioms false
% 0.47/0.74 % --bmc1_out_stat full
% 0.47/0.74 % --bmc1_ground_init false
% 0.47/0.74 % --bmc1_pre_inst_next_state false
% 0.47/0.74 % --bmc1_pre_inst_state false
% 0.47/0.74 % --bmc1_pre_inst_reach_state false
% 0.47/0.74 % --bmc1_out_unsat_core false
% 0.47/0.74 % --bmc1_aig_witness_out false
% 0.47/0.74 % --bmc1_verbose false
% 0.47/0.74 % --bmc1_dump_clauses_tptp false
% 0.47/0.74 % --bmc1_dump_unsat_core_tptp false
% 0.47/0.74 % --bmc1_dump_file -
% 0.47/0.74 % --bmc1_ucm_expand_uc_limit 128
% 0.47/0.74 % --bmc1_ucm_n_expand_iterations 6
% 0.47/0.74 % --bmc1_ucm_extend_mode 1
% 0.47/0.74 % --bmc1_ucm_init_mode 2
% 0.47/0.74 % --bmc1_ucm_cone_mode none
% 0.47/0.74 % --bmc1_ucm_reduced_relation_type 0
% 0.47/0.74 % --bmc1_ucm_relax_model 4
% 0.47/0.74 % --bmc1_ucm_full_tr_after_sat true
% 0.47/0.74 % --bmc1_ucm_expand_neg_assumptions false
% 0.47/0.74 % --bmc1_ucm_layered_model none
% 0.47/0.74 % --bmc1_ucm_max_lemma_size 10
% 0.47/0.74
% 0.47/0.74 % ------ AIG Options
% 0.47/0.74
% 0.47/0.74 % --aig_mode false
% 0.47/0.74
% 0.47/0.74 % ------ Instantiation Options
% 0.47/0.74
% 0.47/0.74 % --instantiation_flag true
% 0.47/0.74 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.47/0.74 % --inst_solver_per_active 750
% 0.47/0.74 % --inst_solver_calls_frac 0.5
% 0.47/0.74 % --inst_passive_queue_type priority_queues
% 0.47/0.74 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.47/0.74 % --inst_passive_queues_freq [25;2]
% 0.58/0.78 % --inst_dismatching true
% 0.58/0.78 % --inst_eager_unprocessed_to_passive true
% 0.58/0.78 % --inst_prop_sim_given true
% 0.58/0.78 % --inst_prop_sim_new false
% 0.58/0.78 % --inst_orphan_elimination true
% 0.58/0.78 % --inst_learning_loop_flag true
% 0.58/0.78 % --inst_learning_start 3000
% 0.58/0.78 % --inst_learning_factor 2
% 0.58/0.78 % --inst_start_prop_sim_after_learn 3
% 0.58/0.78 % --inst_sel_renew solver
% 0.58/0.78 % --inst_lit_activity_flag true
% 0.58/0.78 % --inst_out_proof true
% 0.58/0.78
% 0.58/0.78 % ------ Resolution Options
% 0.58/0.78
% 0.58/0.78 % --resolution_flag true
% 0.58/0.78 % --res_lit_sel kbo_max
% 0.58/0.78 % --res_to_prop_solver none
% 0.58/0.78 % --res_prop_simpl_new false
% 0.58/0.78 % --res_prop_simpl_given false
% 0.58/0.78 % --res_passive_queue_type priority_queues
% 0.58/0.78 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.58/0.78 % --res_passive_queues_freq [15;5]
% 0.58/0.78 % --res_forward_subs full
% 0.58/0.78 % --res_backward_subs full
% 0.58/0.78 % --res_forward_subs_resolution true
% 0.58/0.78 % --res_backward_subs_resolution true
% 0.58/0.78 % --res_orphan_elimination false
% 0.58/0.78 % --res_time_limit 1000.
% 0.58/0.78 % --res_out_proof true
% 0.58/0.78 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_422213.s
% 0.58/0.78 % --modulo true
% 0.58/0.78
% 0.58/0.78 % ------ Combination Options
% 0.58/0.78
% 0.58/0.78 % --comb_res_mult 1000
% 0.58/0.78 % --comb_inst_mult 300
% 0.58/0.78 % ------
% 0.58/0.78
% 0.58/0.78
% 0.58/0.78
% 0.58/0.78 % ------ Proving...
% 0.58/0.78 %
% 0.58/0.78
% 0.58/0.78
% 0.58/0.78 % Resolution empty clause
% 0.58/0.78
% 0.58/0.78 % ------ Statistics
% 0.58/0.78
% 0.58/0.78 % ------ General
% 0.58/0.78
% 0.58/0.78 % num_of_input_clauses: 159
% 0.58/0.78 % num_of_input_neg_conjectures: 2
% 0.58/0.78 % num_of_splits: 0
% 0.58/0.78 % num_of_split_atoms: 0
% 0.58/0.78 % num_of_sem_filtered_clauses: 0
% 0.58/0.78 % num_of_subtypes: 0
% 0.58/0.78 % monotx_restored_types: 0
% 0.58/0.78 % sat_num_of_epr_types: 0
% 0.58/0.78 % sat_num_of_non_cyclic_types: 0
% 0.58/0.78 % sat_guarded_non_collapsed_types: 0
% 0.58/0.78 % is_epr: 0
% 0.58/0.78 % is_horn: 0
% 0.58/0.78 % has_eq: 1
% 0.58/0.78 % num_pure_diseq_elim: 0
% 0.58/0.78 % simp_replaced_by: 0
% 0.58/0.78 % res_preprocessed: 63
% 0.58/0.78 % prep_upred: 0
% 0.58/0.78 % prep_unflattend: 0
% 0.58/0.78 % pred_elim_cands: 3
% 0.58/0.78 % pred_elim: 1
% 0.58/0.78 % pred_elim_cl: 1
% 0.58/0.78 % pred_elim_cycles: 2
% 0.58/0.78 % forced_gc_time: 0
% 0.58/0.78 % gc_basic_clause_elim: 0
% 0.58/0.78 % parsing_time: 0.006
% 0.58/0.78 % sem_filter_time: 0.
% 0.58/0.78 % pred_elim_time: 0.
% 0.58/0.78 % out_proof_time: 0.
% 0.58/0.78 % monotx_time: 0.
% 0.58/0.78 % subtype_inf_time: 0.
% 0.58/0.78 % unif_index_cands_time: 0.
% 0.58/0.78 % unif_index_add_time: 0.
% 0.58/0.78 % total_time: 0.359
% 0.58/0.78 % num_of_symbols: 63
% 0.58/0.78 % num_of_terms: 1701
% 0.58/0.78
% 0.58/0.78 % ------ Propositional Solver
% 0.58/0.78
% 0.58/0.78 % prop_solver_calls: 1
% 0.58/0.78 % prop_fast_solver_calls: 229
% 0.58/0.78 % prop_num_of_clauses: 230
% 0.58/0.78 % prop_preprocess_simplified: 917
% 0.58/0.78 % prop_fo_subsumed: 0
% 0.58/0.78 % prop_solver_time: 0.
% 0.58/0.78 % prop_fast_solver_time: 0.
% 0.58/0.78 % prop_unsat_core_time: 0.
% 0.58/0.78
% 0.58/0.78 % ------ QBF
% 0.58/0.78
% 0.58/0.78 % qbf_q_res: 0
% 0.58/0.78 % qbf_num_tautologies: 0
% 0.58/0.78 % qbf_prep_cycles: 0
% 0.58/0.78
% 0.58/0.78 % ------ BMC1
% 0.58/0.78
% 0.58/0.78 % bmc1_current_bound: -1
% 0.58/0.78 % bmc1_last_solved_bound: -1
% 0.58/0.78 % bmc1_unsat_core_size: -1
% 0.58/0.78 % bmc1_unsat_core_parents_size: -1
% 0.58/0.78 % bmc1_merge_next_fun: 0
% 0.58/0.78 % bmc1_unsat_core_clauses_time: 0.
% 0.58/0.78
% 0.58/0.78 % ------ Instantiation
% 0.58/0.78
% 0.58/0.78 % inst_num_of_clauses: 142
% 0.58/0.78 % inst_num_in_passive: 0
% 0.58/0.78 % inst_num_in_active: 0
% 0.58/0.78 % inst_num_in_unprocessed: 151
% 0.58/0.78 % inst_num_of_loops: 0
% 0.58/0.78 % inst_num_of_learning_restarts: 0
% 0.58/0.78 % inst_num_moves_active_passive: 0
% 0.58/0.78 % inst_lit_activity: 0
% 0.58/0.78 % inst_lit_activity_moves: 0
% 0.58/0.78 % inst_num_tautologies: 0
% 0.58/0.78 % inst_num_prop_implied: 0
% 0.58/0.78 % inst_num_existing_simplified: 0
% 0.58/0.78 % inst_num_eq_res_simplified: 0
% 0.58/0.78 % inst_num_child_elim: 0
% 0.58/0.78 % inst_num_of_dismatching_blockings: 0
% 0.58/0.78 % inst_num_of_non_proper_insts: 0
% 0.58/0.78 % inst_num_of_duplicates: 0
% 0.58/0.78 % inst_inst_num_from_inst_to_res: 0
% 0.58/0.78 % inst_dismatching_checking_time: 0.
% 0.58/0.78
% 0.58/0.78 % ------ Resolution
% 0.58/0.78
% 0.58/0.78 % res_num_of_clauses: 515
% 0.58/0.78 % res_num_in_passive: 281
% 0.58/0.78 % res_num_in_active: 200
% 0.58/0.78 % res_num_of_loops: 122
% 0.58/0.78 % res_forward_subset_subsumed: 17
% 0.58/0.78 % res_backward_subset_subsumed: 0
% 0.58/0.78 % res_forward_subsumed: 1
% 0.58/0.78 % res_backward_subsumed: 0
% 0.58/0.78 % res_forward_subsumption_resolution: 2
% 0.58/0.78 % res_backward_subsumption_resolution: 0
% 0.58/0.78 % res_clause_to_clause_subsumption: 1639
% 0.58/0.78 % res_orphan_elimination: 0
% 0.58/0.78 % res_tautology_del: 6
% 0.58/0.78 % res_num_eq_res_simplified: 0
% 0.58/0.78 % res_num_sel_changes: 0
% 0.58/0.78 % res_moves_from_active_to_pass: 0
% 0.58/0.78
% 0.58/0.78 % Status Unsatisfiable
% 0.58/0.78 % SZS status Theorem
% 0.58/0.78 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------