TSTP Solution File: SEU258+1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU258+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 10:26:33 EDT 2022
% Result : Theorem 3.77s 4.09s
% Output : CNFRefutation 3.90s
% 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_subset,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
input ).
fof(t4_subset_0,plain,
! [A,B,C] :
( element(A,C)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(orientation,[status(thm)],[t4_subset]) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
input ).
fof(t3_subset_0,plain,
! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ),
inference(orientation,[status(thm)],[t3_subset]) ).
fof(t3_subset_1,plain,
! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) ),
inference(orientation,[status(thm)],[t3_subset]) ).
fof(t30_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(A,relation_field(C))
& in(B,relation_field(C)) ) ) ),
input ).
fof(t30_relat_1_0,plain,
! [A,B,C] :
( ~ relation(C)
| ( in(ordered_pair(A,B),C)
=> ( in(A,relation_field(C))
& in(B,relation_field(C)) ) ) ),
inference(orientation,[status(thm)],[t30_relat_1]) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
input ).
fof(t2_subset_0,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(orientation,[status(thm)],[t2_subset]) ).
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(t20_wellord1,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_field(relation_restriction(B,A)),relation_field(B))
& subset(relation_field(relation_restriction(B,A)),A) ) ),
input ).
fof(t20_wellord1_0,plain,
! [A,B] :
( ~ relation(B)
| ( subset(relation_field(relation_restriction(B,A)),relation_field(B))
& subset(relation_field(relation_restriction(B,A)),A) ) ),
inference(orientation,[status(thm)],[t20_wellord1]) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
input ).
fof(t1_subset_0,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(orientation,[status(thm)],[t1_subset]) ).
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(t16_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
input ).
fof(t16_wellord1_0,plain,
! [A,B,C] :
( ~ relation(C)
| ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
inference(orientation,[status(thm)],[t16_wellord1]) ).
fof(t106_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
input ).
fof(t106_zfmisc_1_0,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ ( in(A,C)
& in(B,D) ) ),
inference(orientation,[status(thm)],[t106_zfmisc_1]) ).
fof(t106_zfmisc_1_1,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) ),
inference(orientation,[status(thm)],[t106_zfmisc_1]) ).
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(l1_wellord1,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
input ).
fof(l1_wellord1_0,plain,
! [A] :
( ~ relation(A)
| ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
inference(orientation,[status(thm)],[l1_wellord1]) ).
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_m1_subset_1,axiom,
$true,
input ).
fof(dt_m1_subset_1_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_m1_subset_1]) ).
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_relat_1,axiom,
$true,
input ).
fof(dt_k3_relat_1_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k3_relat_1]) ).
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_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
input ).
fof(dt_k2_wellord1_0,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_restriction(A,B)) ),
inference(orientation,[status(thm)],[dt_k2_wellord1]) ).
fof(dt_k2_tarski,axiom,
$true,
input ).
fof(dt_k2_tarski_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k2_tarski]) ).
fof(dt_k2_relat_1,axiom,
$true,
input ).
fof(dt_k2_relat_1_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k2_relat_1]) ).
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(dt_k1_relat_1,axiom,
$true,
input ).
fof(dt_k1_relat_1_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k1_relat_1]) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
input ).
fof(d6_wellord1_0,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(orientation,[status(thm)],[d6_wellord1]) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
input ).
fof(d6_relat_1_0,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(orientation,[status(thm)],[d6_relat_1]) ).
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_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
input ).
fof(d4_wellord1_0,plain,
! [A] :
( ~ relation(A)
| ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
inference(orientation,[status(thm)],[d4_wellord1]) ).
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(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(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
input ).
fof(cc1_funct_1_0,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(orientation,[status(thm)],[cc1_funct_1]) ).
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,
! [A] :
( lhs_atom2(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A] :
( lhs_atom2(A)
| function(A) ),
inference(fold_definition,[status(thm)],[cc1_funct_1_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)
<=> ~ subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A,B] :
( lhs_atom8(B,A)
| ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[d3_tarski_1,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [B,A] :
( lhs_atom9(B,A)
<=> subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A,B] :
( lhs_atom9(B,A)
| ~ ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[d3_tarski_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [A] :
( lhs_atom10(A)
<=> ~ relation(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A] :
( lhs_atom10(A)
| ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ),
inference(fold_definition,[status(thm)],[d4_wellord1_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [B,A] :
( lhs_atom11(B,A)
<=> ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [A,B] :
( lhs_atom11(B,A)
| $false ),
inference(fold_definition,[status(thm)],[d5_tarski_0,def_lhs_atom11]) ).
fof(to_be_clausified_11,plain,
! [A] :
( lhs_atom10(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(fold_definition,[status(thm)],[d6_relat_1_0,def_lhs_atom10]) ).
fof(to_be_clausified_12,plain,
! [A] :
( lhs_atom10(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(fold_definition,[status(thm)],[d6_wellord1_0,def_lhs_atom10]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> $true ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_relat_1_0,def_lhs_atom12]) ).
fof(to_be_clausified_14,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_tarski_0,def_lhs_atom12]) ).
fof(to_be_clausified_15,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_xboole_0_0,def_lhs_atom12]) ).
fof(to_be_clausified_16,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_zfmisc_1_0,def_lhs_atom12]) ).
fof(to_be_clausified_17,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_relat_1_0,def_lhs_atom12]) ).
fof(to_be_clausified_18,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_tarski_0,def_lhs_atom12]) ).
fof(to_be_clausified_19,plain,
! [A,B] :
( lhs_atom10(A)
| relation(relation_restriction(A,B)) ),
inference(fold_definition,[status(thm)],[dt_k2_wellord1_0,def_lhs_atom10]) ).
fof(to_be_clausified_20,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_xboole_0_0,def_lhs_atom12]) ).
fof(to_be_clausified_21,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_zfmisc_1_0,def_lhs_atom12]) ).
fof(to_be_clausified_22,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k3_relat_1_0,def_lhs_atom12]) ).
fof(to_be_clausified_23,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k3_xboole_0_0,def_lhs_atom12]) ).
fof(to_be_clausified_24,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_k4_tarski_0,def_lhs_atom12]) ).
fof(to_be_clausified_25,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[dt_m1_subset_1_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [B,A] :
( lhs_atom14(B,A)
<=> ~ empty(ordered_pair(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [A,B] :
( lhs_atom14(B,A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_zfmisc_1_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [A] :
( lhs_atom15(A)
<=> empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [A,B] :
( lhs_atom15(A)
| ~ empty(set_union2(A,B)) ),
inference(fold_definition,[status(thm)],[fc2_xboole_0_0,def_lhs_atom15]) ).
fof(to_be_clausified_29,plain,
! [A,B] :
( lhs_atom15(A)
| ~ empty(set_union2(B,A)) ),
inference(fold_definition,[status(thm)],[fc3_xboole_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [A] :
( lhs_atom16(A)
<=> set_union2(A,A) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [A] :
( lhs_atom16(A)
| $false ),
inference(fold_definition,[status(thm)],[idempotence_k2_xboole_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [A] :
( lhs_atom17(A)
<=> set_intersection2(A,A) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [A] :
( lhs_atom17(A)
| $false ),
inference(fold_definition,[status(thm)],[idempotence_k3_xboole_0_0,def_lhs_atom17]) ).
fof(to_be_clausified_32,plain,
! [A] :
( lhs_atom10(A)
| ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
inference(fold_definition,[status(thm)],[l1_wellord1_0,def_lhs_atom10]) ).
fof(def_lhs_atom18,axiom,
! [A] :
( lhs_atom18(A)
<=> subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [A] :
( lhs_atom18(A)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [D,C,B,A] :
( lhs_atom19(D,C,B,A)
<=> ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [A,B,C,D] :
( lhs_atom19(D,C,B,A)
| ( in(A,C)
& in(B,D) ) ),
inference(fold_definition,[status(thm)],[t106_zfmisc_1_1,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [D,C,B,A] :
( lhs_atom20(D,C,B,A)
<=> in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [A,B,C,D] :
( lhs_atom20(D,C,B,A)
| ~ ( in(A,C)
& in(B,D) ) ),
inference(fold_definition,[status(thm)],[t106_zfmisc_1_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [C] :
( lhs_atom21(C)
<=> ~ relation(C) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [A,B,C] :
( lhs_atom21(C)
| ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
inference(fold_definition,[status(thm)],[t16_wellord1_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [A] :
( lhs_atom22(A)
<=> set_union2(A,empty_set) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [A] :
( lhs_atom22(A)
| $false ),
inference(fold_definition,[status(thm)],[t1_boole_0,def_lhs_atom22]) ).
fof(to_be_clausified_38,plain,
! [A,B] :
( lhs_atom1(B,A)
| element(A,B) ),
inference(fold_definition,[status(thm)],[t1_subset_0,def_lhs_atom1]) ).
fof(def_lhs_atom23,axiom,
! [B] :
( lhs_atom23(B)
<=> ~ relation(B) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [A,B] :
( lhs_atom23(B)
| ( subset(relation_field(relation_restriction(B,A)),relation_field(B))
& subset(relation_field(relation_restriction(B,A)),A) ) ),
inference(fold_definition,[status(thm)],[t20_wellord1_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [A] :
( lhs_atom24(A)
<=> set_intersection2(A,empty_set) = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [A] :
( lhs_atom24(A)
| $false ),
inference(fold_definition,[status(thm)],[t2_boole_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [B,A] :
( lhs_atom25(B,A)
<=> ~ element(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [A,B] :
( lhs_atom25(B,A)
| empty(B)
| in(A,B) ),
inference(fold_definition,[status(thm)],[t2_subset_0,def_lhs_atom25]) ).
fof(to_be_clausified_42,plain,
! [A,B,C] :
( lhs_atom21(C)
| ( in(ordered_pair(A,B),C)
=> ( in(A,relation_field(C))
& in(B,relation_field(C)) ) ) ),
inference(fold_definition,[status(thm)],[t30_relat_1_0,def_lhs_atom21]) ).
fof(def_lhs_atom26,axiom,
! [B,A] :
( lhs_atom26(B,A)
<=> ~ element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [A,B] :
( lhs_atom26(B,A)
| subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_1,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [B,A] :
( lhs_atom27(B,A)
<=> element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [A,B] :
( lhs_atom27(B,A)
| ~ subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [C,A] :
( lhs_atom28(C,A)
<=> element(A,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [A,B,C] :
( lhs_atom28(C,A)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(fold_definition,[status(thm)],[t4_subset_0,def_lhs_atom28]) ).
fof(to_be_clausified_46,plain,
! [A] :
( lhs_atom2(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom2]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X4,X3,X1,X2] :
( lhs_atom20(X4,X3,X1,X2)
| ~ ( in(X2,X3)
& in(X1,X4) ) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_1,axiom,
! [X4,X3,X1,X2] :
( lhs_atom19(X4,X3,X1,X2)
| ( in(X2,X3)
& in(X1,X4) ) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_2,axiom,
! [X3,X1,X2] :
( lhs_atom21(X3)
| ( in(X2,relation_restriction(X3,X1))
<=> ( in(X2,X3)
& in(X2,cartesian_product2(X1,X1)) ) ) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_3,axiom,
! [X2] :
( lhs_atom10(X2)
| ( reflexive(X2)
<=> ! [X1] :
( in(X1,relation_field(X2))
=> in(ordered_pair(X1,X1),X2) ) ) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_4,axiom,
! [X3,X1,X2] :
( lhs_atom21(X3)
| ( in(ordered_pair(X2,X1),X3)
=> ( in(X2,relation_field(X3))
& in(X1,relation_field(X3)) ) ) ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_5,axiom,
! [X1,X2] :
( lhs_atom23(X1)
| ( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
& subset(relation_field(relation_restriction(X1,X2)),X2) ) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_6,axiom,
! [X1,X2] :
( lhs_atom9(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_7,axiom,
! [X3,X1,X2] :
( lhs_atom28(X3,X2)
| ~ ( in(X2,X1)
& element(X1,powerset(X3)) ) ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_8,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_9,axiom,
! [X2] :
( lhs_atom10(X2)
| ! [X1] : relation_restriction(X2,X1) = set_intersection2(X2,cartesian_product2(X1,X1)) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_10,axiom,
! [X1,X2] :
( lhs_atom15(X2)
| ~ empty(set_union2(X1,X2)) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_11,axiom,
! [X1,X2] :
( lhs_atom15(X2)
| ~ empty(set_union2(X2,X1)) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_12,axiom,
! [X1,X2] :
( lhs_atom8(X1,X2)
| ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_13,axiom,
! [X2] :
( lhs_atom10(X2)
| ( well_ordering(X2)
<=> ( reflexive(X2)
& transitive(X2)
& antisymmetric(X2)
& connected(X2)
& well_founded_relation(X2) ) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_14,axiom,
! [X1,X2] :
( lhs_atom27(X1,X2)
| ~ subset(X2,X1) ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_15,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_16,axiom,
! [X1,X2] :
( lhs_atom10(X2)
| relation(relation_restriction(X2,X1)) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_17,axiom,
! [X2] :
( lhs_atom10(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_18,axiom,
! [X1,X2] :
( lhs_atom25(X1,X2)
| empty(X1)
| in(X2,X1) ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_19,axiom,
! [X1,X2] :
( lhs_atom26(X1,X2)
| subset(X2,X1) ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_20,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| element(X2,X1) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_21,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_22,axiom,
! [X1,X2] :
( lhs_atom14(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_23,axiom,
! [X1,X2] :
( lhs_atom11(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_24,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_25,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_26,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_27,axiom,
! [X2] :
( lhs_atom2(X2)
| function(X2) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_28,axiom,
! [X2] :
( lhs_atom2(X2)
| X2 = empty_set ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_29,axiom,
! [X2] :
( lhs_atom24(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_30,axiom,
! [X2] :
( lhs_atom22(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_31,axiom,
! [X2] :
( lhs_atom18(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_32,axiom,
! [X2] :
( lhs_atom17(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_33,axiom,
! [X2] :
( lhs_atom16(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_34,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_35,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_36,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_37,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_38,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_39,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_40,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_41,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_42,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_43,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_44,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_45,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_46,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_47,axiom,
! [X4,X3,X1,X2] :
( lhs_atom20(X4,X3,X1,X2)
| ~ ( in(X2,X3)
& in(X1,X4) ) ),
c_0_0 ).
fof(c_0_48,axiom,
! [X4,X3,X1,X2] :
( lhs_atom19(X4,X3,X1,X2)
| ( in(X2,X3)
& in(X1,X4) ) ),
c_0_1 ).
fof(c_0_49,axiom,
! [X3,X1,X2] :
( lhs_atom21(X3)
| ( in(X2,relation_restriction(X3,X1))
<=> ( in(X2,X3)
& in(X2,cartesian_product2(X1,X1)) ) ) ),
c_0_2 ).
fof(c_0_50,axiom,
! [X2] :
( lhs_atom10(X2)
| ( reflexive(X2)
<=> ! [X1] :
( in(X1,relation_field(X2))
=> in(ordered_pair(X1,X1),X2) ) ) ),
c_0_3 ).
fof(c_0_51,axiom,
! [X3,X1,X2] :
( lhs_atom21(X3)
| ( in(ordered_pair(X2,X1),X3)
=> ( in(X2,relation_field(X3))
& in(X1,relation_field(X3)) ) ) ),
c_0_4 ).
fof(c_0_52,axiom,
! [X1,X2] :
( lhs_atom23(X1)
| ( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
& subset(relation_field(relation_restriction(X1,X2)),X2) ) ),
c_0_5 ).
fof(c_0_53,axiom,
! [X1,X2] :
( lhs_atom9(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_6 ).
fof(c_0_54,axiom,
! [X3,X1,X2] :
( lhs_atom28(X3,X2)
| ~ ( in(X2,X1)
& element(X1,powerset(X3)) ) ),
c_0_7 ).
fof(c_0_55,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_8 ).
fof(c_0_56,axiom,
! [X2] :
( lhs_atom10(X2)
| ! [X1] : relation_restriction(X2,X1) = set_intersection2(X2,cartesian_product2(X1,X1)) ),
c_0_9 ).
fof(c_0_57,plain,
! [X1,X2] :
( lhs_atom15(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_58,plain,
! [X1,X2] :
( lhs_atom15(X2)
| ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_59,axiom,
! [X1,X2] :
( lhs_atom8(X1,X2)
| ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_12 ).
fof(c_0_60,axiom,
! [X2] :
( lhs_atom10(X2)
| ( well_ordering(X2)
<=> ( reflexive(X2)
& transitive(X2)
& antisymmetric(X2)
& connected(X2)
& well_founded_relation(X2) ) ) ),
c_0_13 ).
fof(c_0_61,plain,
! [X1,X2] :
( lhs_atom27(X1,X2)
| ~ subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_62,plain,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_63,axiom,
! [X1,X2] :
( lhs_atom10(X2)
| relation(relation_restriction(X2,X1)) ),
c_0_16 ).
fof(c_0_64,axiom,
! [X2] :
( lhs_atom10(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
c_0_17 ).
fof(c_0_65,axiom,
! [X1,X2] :
( lhs_atom25(X1,X2)
| empty(X1)
| in(X2,X1) ),
c_0_18 ).
fof(c_0_66,axiom,
! [X1,X2] :
( lhs_atom26(X1,X2)
| subset(X2,X1) ),
c_0_19 ).
fof(c_0_67,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| element(X2,X1) ),
c_0_20 ).
fof(c_0_68,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_21 ).
fof(c_0_69,plain,
! [X1,X2] : lhs_atom14(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_70,plain,
! [X1,X2] : lhs_atom11(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_71,plain,
! [X1,X2] : lhs_atom5(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_72,plain,
! [X1,X2] : lhs_atom4(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_73,plain,
! [X1,X2] : lhs_atom3(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_74,axiom,
! [X2] :
( lhs_atom2(X2)
| function(X2) ),
c_0_27 ).
fof(c_0_75,axiom,
! [X2] :
( lhs_atom2(X2)
| X2 = empty_set ),
c_0_28 ).
fof(c_0_76,plain,
! [X2] : lhs_atom24(X2),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_77,plain,
! [X2] : lhs_atom22(X2),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_78,plain,
! [X2] : lhs_atom18(X2),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_79,plain,
! [X2] : lhs_atom17(X2),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_80,plain,
! [X2] : lhs_atom16(X2),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_81,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_82,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_83,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_84,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_85,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_86,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_87,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_88,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_89,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_90,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_91,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_92,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_93,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_94,plain,
! [X5,X6,X7,X8] :
( lhs_atom20(X5,X6,X7,X8)
| ~ in(X8,X6)
| ~ in(X7,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])]) ).
fof(c_0_95,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X6)
| lhs_atom19(X5,X6,X7,X8) )
& ( in(X7,X5)
| lhs_atom19(X5,X6,X7,X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
fof(c_0_96,plain,
! [X4,X5,X6,X7,X8] :
( ( in(X6,X4)
| ~ in(X6,relation_restriction(X4,X5))
| lhs_atom21(X4) )
& ( in(X6,cartesian_product2(X5,X5))
| ~ in(X6,relation_restriction(X4,X5))
| lhs_atom21(X4) )
& ( ~ in(X8,X4)
| ~ in(X8,cartesian_product2(X7,X7))
| in(X8,relation_restriction(X4,X7))
| lhs_atom21(X4) ) ),
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_97,plain,
! [X3,X4] :
( ( ~ reflexive(X3)
| ~ in(X4,relation_field(X3))
| in(ordered_pair(X4,X4),X3)
| lhs_atom10(X3) )
& ( in(esk2_1(X3),relation_field(X3))
| reflexive(X3)
| lhs_atom10(X3) )
& ( ~ in(ordered_pair(esk2_1(X3),esk2_1(X3)),X3)
| reflexive(X3)
| lhs_atom10(X3) ) ),
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_50])])])])]) ).
fof(c_0_98,plain,
! [X4,X5,X6] :
( ( in(X6,relation_field(X4))
| ~ in(ordered_pair(X6,X5),X4)
| lhs_atom21(X4) )
& ( in(X5,relation_field(X4))
| ~ in(ordered_pair(X6,X5),X4)
| lhs_atom21(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])])]) ).
fof(c_0_99,plain,
! [X3,X4,X5] :
( ( subset(relation_field(relation_restriction(X3,X4)),relation_field(X3))
| lhs_atom23(X3) )
& ( subset(relation_field(relation_restriction(X3,X5)),X5)
| lhs_atom23(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_52])])])]) ).
fof(c_0_100,plain,
! [X4,X5] :
( ( in(esk1_2(X4,X5),X5)
| lhs_atom9(X4,X5) )
& ( ~ in(esk1_2(X4,X5),X4)
| lhs_atom9(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
fof(c_0_101,plain,
! [X4,X5,X6] :
( lhs_atom28(X4,X6)
| ~ in(X6,X5)
| ~ element(X5,powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
fof(c_0_102,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_55])]) ).
fof(c_0_103,plain,
! [X3,X4] :
( lhs_atom10(X3)
| relation_restriction(X3,X4) = set_intersection2(X3,cartesian_product2(X4,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_56])]) ).
fof(c_0_104,plain,
! [X3,X4] :
( lhs_atom15(X4)
| ~ empty(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[c_0_57]) ).
fof(c_0_105,plain,
! [X3,X4] :
( lhs_atom15(X4)
| ~ empty(set_union2(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_58]) ).
fof(c_0_106,plain,
! [X4,X5,X6] :
( lhs_atom8(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_59])])]) ).
fof(c_0_107,plain,
! [X3] :
( ( reflexive(X3)
| ~ well_ordering(X3)
| lhs_atom10(X3) )
& ( transitive(X3)
| ~ well_ordering(X3)
| lhs_atom10(X3) )
& ( antisymmetric(X3)
| ~ well_ordering(X3)
| lhs_atom10(X3) )
& ( connected(X3)
| ~ well_ordering(X3)
| lhs_atom10(X3) )
& ( well_founded_relation(X3)
| ~ well_ordering(X3)
| lhs_atom10(X3) )
& ( ~ reflexive(X3)
| ~ transitive(X3)
| ~ antisymmetric(X3)
| ~ connected(X3)
| ~ well_founded_relation(X3)
| well_ordering(X3)
| lhs_atom10(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
fof(c_0_108,plain,
! [X3,X4] :
( lhs_atom27(X3,X4)
| ~ subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_61]) ).
fof(c_0_109,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_62]) ).
fof(c_0_110,plain,
! [X3,X4] :
( lhs_atom10(X4)
| relation(relation_restriction(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_63]) ).
fof(c_0_111,plain,
! [X3] :
( lhs_atom10(X3)
| relation_field(X3) = set_union2(relation_dom(X3),relation_rng(X3)) ),
inference(variable_rename,[status(thm)],[c_0_64]) ).
fof(c_0_112,plain,
! [X3,X4] :
( lhs_atom25(X3,X4)
| empty(X3)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_113,plain,
! [X3,X4] :
( lhs_atom26(X3,X4)
| subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_114,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| element(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_67]) ).
fof(c_0_115,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_68])]) ).
fof(c_0_116,plain,
! [X3,X4] : lhs_atom14(X3,X4),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_117,plain,
! [X3,X4] : lhs_atom11(X3,X4),
inference(variable_rename,[status(thm)],[c_0_70]) ).
fof(c_0_118,plain,
! [X3,X4] : lhs_atom5(X3,X4),
inference(variable_rename,[status(thm)],[c_0_71]) ).
fof(c_0_119,plain,
! [X3,X4] : lhs_atom4(X3,X4),
inference(variable_rename,[status(thm)],[c_0_72]) ).
fof(c_0_120,plain,
! [X3,X4] : lhs_atom3(X3,X4),
inference(variable_rename,[status(thm)],[c_0_73]) ).
fof(c_0_121,plain,
! [X3] :
( lhs_atom2(X3)
| function(X3) ),
inference(variable_rename,[status(thm)],[c_0_74]) ).
fof(c_0_122,plain,
! [X3] :
( lhs_atom2(X3)
| X3 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_75]) ).
fof(c_0_123,plain,
! [X3] : lhs_atom24(X3),
inference(variable_rename,[status(thm)],[c_0_76]) ).
fof(c_0_124,plain,
! [X3] : lhs_atom22(X3),
inference(variable_rename,[status(thm)],[c_0_77]) ).
fof(c_0_125,plain,
! [X3] : lhs_atom18(X3),
inference(variable_rename,[status(thm)],[c_0_78]) ).
fof(c_0_126,plain,
! [X3] : lhs_atom17(X3),
inference(variable_rename,[status(thm)],[c_0_79]) ).
fof(c_0_127,plain,
! [X3] : lhs_atom16(X3),
inference(variable_rename,[status(thm)],[c_0_80]) ).
fof(c_0_128,plain,
lhs_atom13,
c_0_81 ).
fof(c_0_129,plain,
lhs_atom12,
c_0_82 ).
fof(c_0_130,plain,
lhs_atom12,
c_0_83 ).
fof(c_0_131,plain,
lhs_atom12,
c_0_84 ).
fof(c_0_132,plain,
lhs_atom12,
c_0_85 ).
fof(c_0_133,plain,
lhs_atom12,
c_0_86 ).
fof(c_0_134,plain,
lhs_atom12,
c_0_87 ).
fof(c_0_135,plain,
lhs_atom12,
c_0_88 ).
fof(c_0_136,plain,
lhs_atom12,
c_0_89 ).
fof(c_0_137,plain,
lhs_atom12,
c_0_90 ).
fof(c_0_138,plain,
lhs_atom12,
c_0_91 ).
fof(c_0_139,plain,
lhs_atom12,
c_0_92 ).
fof(c_0_140,plain,
lhs_atom12,
c_0_93 ).
cnf(c_0_141,plain,
( lhs_atom20(X2,X4,X1,X3)
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_142,plain,
( lhs_atom19(X1,X2,X3,X4)
| in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_143,plain,
( lhs_atom19(X1,X2,X3,X4)
| in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_144,plain,
( lhs_atom21(X1)
| in(X2,relation_restriction(X1,X3))
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_145,plain,
( lhs_atom10(X1)
| reflexive(X1)
| ~ in(ordered_pair(esk2_1(X1),esk2_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_146,plain,
( lhs_atom21(X1)
| in(X2,cartesian_product2(X3,X3))
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_147,plain,
( lhs_atom21(X1)
| in(X2,relation_field(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_148,plain,
( lhs_atom21(X1)
| in(X3,relation_field(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_149,plain,
( lhs_atom10(X1)
| in(ordered_pair(X2,X2),X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_150,plain,
( lhs_atom23(X1)
| subset(relation_field(relation_restriction(X1,X2)),relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_151,plain,
( lhs_atom21(X1)
| in(X2,X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_152,plain,
( lhs_atom9(X1,X2)
| ~ in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_153,plain,
( lhs_atom23(X1)
| subset(relation_field(relation_restriction(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_154,plain,
( lhs_atom28(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_155,plain,
( lhs_atom7(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_156,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| lhs_atom10(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_157,plain,
( lhs_atom9(X1,X2)
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_158,plain,
( lhs_atom15(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_159,plain,
( lhs_atom15(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_160,plain,
( in(X1,X2)
| lhs_atom8(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_161,plain,
( lhs_atom10(X1)
| well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_162,plain,
( lhs_atom27(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_163,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_164,plain,
( lhs_atom10(X1)
| reflexive(X1)
| in(esk2_1(X1),relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_165,plain,
( relation(relation_restriction(X1,X2))
| lhs_atom10(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_166,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| lhs_atom10(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_167,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom25(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_168,plain,
( subset(X1,X2)
| lhs_atom26(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_169,plain,
( element(X1,X2)
| lhs_atom1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_170,plain,
( lhs_atom6(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_171,plain,
( lhs_atom6(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_172,plain,
( lhs_atom10(X1)
| reflexive(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_173,plain,
( lhs_atom10(X1)
| transitive(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_174,plain,
( lhs_atom10(X1)
| antisymmetric(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_175,plain,
( lhs_atom10(X1)
| connected(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_176,plain,
( lhs_atom10(X1)
| well_founded_relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_177,plain,
lhs_atom14(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_178,plain,
lhs_atom11(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_179,plain,
lhs_atom5(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_180,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_181,plain,
lhs_atom3(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_182,plain,
( function(X1)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_183,plain,
( X1 = empty_set
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_184,plain,
lhs_atom24(X1),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_185,plain,
lhs_atom22(X1),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_186,plain,
lhs_atom18(X1),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_187,plain,
lhs_atom17(X1),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_188,plain,
lhs_atom16(X1),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_189,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_190,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_191,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_192,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_193,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_194,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_195,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_196,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_197,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_198,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_199,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_200,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_201,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_202,plain,
( lhs_atom20(X2,X4,X1,X3)
| ~ in(X1,X2)
| ~ in(X3,X4) ),
c_0_141,
[final] ).
cnf(c_0_203,plain,
( lhs_atom19(X1,X2,X3,X4)
| in(X4,X2) ),
c_0_142,
[final] ).
cnf(c_0_204,plain,
( lhs_atom19(X1,X2,X3,X4)
| in(X3,X1) ),
c_0_143,
[final] ).
cnf(c_0_205,plain,
( lhs_atom21(X1)
| in(X2,relation_restriction(X1,X3))
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
c_0_144,
[final] ).
cnf(c_0_206,plain,
( lhs_atom10(X1)
| reflexive(X1)
| ~ in(ordered_pair(esk2_1(X1),esk2_1(X1)),X1) ),
c_0_145,
[final] ).
cnf(c_0_207,plain,
( lhs_atom21(X1)
| in(X2,cartesian_product2(X3,X3))
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_146,
[final] ).
cnf(c_0_208,plain,
( lhs_atom21(X1)
| in(X2,relation_field(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_147,
[final] ).
cnf(c_0_209,plain,
( lhs_atom21(X1)
| in(X3,relation_field(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_148,
[final] ).
cnf(c_0_210,plain,
( lhs_atom10(X1)
| in(ordered_pair(X2,X2),X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
c_0_149,
[final] ).
cnf(c_0_211,plain,
( lhs_atom23(X1)
| subset(relation_field(relation_restriction(X1,X2)),relation_field(X1)) ),
c_0_150,
[final] ).
cnf(c_0_212,plain,
( lhs_atom21(X1)
| in(X2,X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
c_0_151,
[final] ).
cnf(c_0_213,plain,
( lhs_atom9(X1,X2)
| ~ in(esk1_2(X1,X2),X1) ),
c_0_152,
[final] ).
cnf(c_0_214,plain,
( lhs_atom23(X1)
| subset(relation_field(relation_restriction(X1,X2)),X2) ),
c_0_153,
[final] ).
cnf(c_0_215,plain,
( lhs_atom28(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
c_0_154,
[final] ).
cnf(c_0_216,plain,
( lhs_atom7(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_155,
[final] ).
cnf(c_0_217,plain,
( set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2)
| lhs_atom10(X1) ),
c_0_156,
[final] ).
cnf(c_0_218,plain,
( lhs_atom9(X1,X2)
| in(esk1_2(X1,X2),X2) ),
c_0_157,
[final] ).
cnf(c_0_219,plain,
( lhs_atom15(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_158,
[final] ).
cnf(c_0_220,plain,
( lhs_atom15(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_159,
[final] ).
cnf(c_0_221,plain,
( in(X1,X2)
| lhs_atom8(X2,X3)
| ~ in(X1,X3) ),
c_0_160,
[final] ).
cnf(c_0_222,plain,
( lhs_atom10(X1)
| well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
c_0_161,
[final] ).
cnf(c_0_223,plain,
( lhs_atom27(X2,X1)
| ~ subset(X1,X2) ),
c_0_162,
[final] ).
cnf(c_0_224,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
c_0_163,
[final] ).
cnf(c_0_225,plain,
( lhs_atom10(X1)
| reflexive(X1)
| in(esk2_1(X1),relation_field(X1)) ),
c_0_164,
[final] ).
cnf(c_0_226,plain,
( relation(relation_restriction(X1,X2))
| lhs_atom10(X1) ),
c_0_165,
[final] ).
cnf(c_0_227,plain,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| lhs_atom10(X1) ),
c_0_166,
[final] ).
cnf(c_0_228,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom25(X2,X1) ),
c_0_167,
[final] ).
cnf(c_0_229,plain,
( subset(X1,X2)
| lhs_atom26(X2,X1) ),
c_0_168,
[final] ).
cnf(c_0_230,plain,
( element(X1,X2)
| lhs_atom1(X2,X1) ),
c_0_169,
[final] ).
cnf(c_0_231,plain,
( lhs_atom6(X1,X2)
| subset(X2,X1) ),
c_0_170,
[final] ).
cnf(c_0_232,plain,
( lhs_atom6(X1,X2)
| subset(X1,X2) ),
c_0_171,
[final] ).
cnf(c_0_233,plain,
( lhs_atom10(X1)
| reflexive(X1)
| ~ well_ordering(X1) ),
c_0_172,
[final] ).
cnf(c_0_234,plain,
( lhs_atom10(X1)
| transitive(X1)
| ~ well_ordering(X1) ),
c_0_173,
[final] ).
cnf(c_0_235,plain,
( lhs_atom10(X1)
| antisymmetric(X1)
| ~ well_ordering(X1) ),
c_0_174,
[final] ).
cnf(c_0_236,plain,
( lhs_atom10(X1)
| connected(X1)
| ~ well_ordering(X1) ),
c_0_175,
[final] ).
cnf(c_0_237,plain,
( lhs_atom10(X1)
| well_founded_relation(X1)
| ~ well_ordering(X1) ),
c_0_176,
[final] ).
cnf(c_0_238,plain,
lhs_atom14(X1,X2),
c_0_177,
[final] ).
cnf(c_0_239,plain,
lhs_atom11(X1,X2),
c_0_178,
[final] ).
cnf(c_0_240,plain,
lhs_atom5(X1,X2),
c_0_179,
[final] ).
cnf(c_0_241,plain,
lhs_atom4(X1,X2),
c_0_180,
[final] ).
cnf(c_0_242,plain,
lhs_atom3(X1,X2),
c_0_181,
[final] ).
cnf(c_0_243,plain,
( function(X1)
| lhs_atom2(X1) ),
c_0_182,
[final] ).
cnf(c_0_244,plain,
( X1 = empty_set
| lhs_atom2(X1) ),
c_0_183,
[final] ).
cnf(c_0_245,plain,
lhs_atom24(X1),
c_0_184,
[final] ).
cnf(c_0_246,plain,
lhs_atom22(X1),
c_0_185,
[final] ).
cnf(c_0_247,plain,
lhs_atom18(X1),
c_0_186,
[final] ).
cnf(c_0_248,plain,
lhs_atom17(X1),
c_0_187,
[final] ).
cnf(c_0_249,plain,
lhs_atom16(X1),
c_0_188,
[final] ).
cnf(c_0_250,plain,
lhs_atom13,
c_0_189,
[final] ).
cnf(c_0_251,plain,
lhs_atom12,
c_0_190,
[final] ).
cnf(c_0_252,plain,
lhs_atom12,
c_0_191,
[final] ).
cnf(c_0_253,plain,
lhs_atom12,
c_0_192,
[final] ).
cnf(c_0_254,plain,
lhs_atom12,
c_0_193,
[final] ).
cnf(c_0_255,plain,
lhs_atom12,
c_0_194,
[final] ).
cnf(c_0_256,plain,
lhs_atom12,
c_0_195,
[final] ).
cnf(c_0_257,plain,
lhs_atom12,
c_0_196,
[final] ).
cnf(c_0_258,plain,
lhs_atom12,
c_0_197,
[final] ).
cnf(c_0_259,plain,
lhs_atom12,
c_0_198,
[final] ).
cnf(c_0_260,plain,
lhs_atom12,
c_0_199,
[final] ).
cnf(c_0_261,plain,
lhs_atom12,
c_0_200,
[final] ).
cnf(c_0_262,plain,
lhs_atom12,
c_0_201,
[final] ).
% End CNF derivation
cnf(c_0_202_0,axiom,
( in(ordered_pair(X3,X1),cartesian_product2(X4,X2))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_202,def_lhs_atom20]) ).
cnf(c_0_203_0,axiom,
( ~ in(ordered_pair(X4,X3),cartesian_product2(X2,X1))
| in(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_203,def_lhs_atom19]) ).
cnf(c_0_204_0,axiom,
( ~ in(ordered_pair(X4,X3),cartesian_product2(X2,X1))
| in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_204,def_lhs_atom19]) ).
cnf(c_0_205_0,axiom,
( ~ relation(X1)
| in(X2,relation_restriction(X1,X3))
| ~ in(X2,cartesian_product2(X3,X3))
| ~ in(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_205,def_lhs_atom21]) ).
cnf(c_0_206_0,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ in(ordered_pair(sk1_esk2_1(X1),sk1_esk2_1(X1)),X1) ),
inference(unfold_definition,[status(thm)],[c_0_206,def_lhs_atom10]) ).
cnf(c_0_207_0,axiom,
( ~ relation(X1)
| in(X2,cartesian_product2(X3,X3))
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_207,def_lhs_atom21]) ).
cnf(c_0_208_0,axiom,
( ~ relation(X1)
| in(X2,relation_field(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_208,def_lhs_atom21]) ).
cnf(c_0_209_0,axiom,
( ~ relation(X1)
| in(X3,relation_field(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_209,def_lhs_atom21]) ).
cnf(c_0_210_0,axiom,
( ~ relation(X1)
| in(ordered_pair(X2,X2),X1)
| ~ in(X2,relation_field(X1))
| ~ reflexive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_210,def_lhs_atom10]) ).
cnf(c_0_211_0,axiom,
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X2)),relation_field(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_211,def_lhs_atom23]) ).
cnf(c_0_212_0,axiom,
( ~ relation(X1)
| in(X2,X1)
| ~ in(X2,relation_restriction(X1,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_212,def_lhs_atom21]) ).
cnf(c_0_213_0,axiom,
( subset(X2,X1)
| ~ in(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_213,def_lhs_atom9]) ).
cnf(c_0_214_0,axiom,
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X2)),X2) ),
inference(unfold_definition,[status(thm)],[c_0_214,def_lhs_atom23]) ).
cnf(c_0_215_0,axiom,
( element(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_215,def_lhs_atom28]) ).
cnf(c_0_216_0,axiom,
( X2 = X1
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_216,def_lhs_atom7]) ).
cnf(c_0_217_0,axiom,
( ~ relation(X1)
| set_intersection2(X1,cartesian_product2(X2,X2)) = relation_restriction(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_217,def_lhs_atom10]) ).
cnf(c_0_218_0,axiom,
( subset(X2,X1)
| in(sk1_esk1_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_218,def_lhs_atom9]) ).
cnf(c_0_219_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_219,def_lhs_atom15]) ).
cnf(c_0_220_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_220,def_lhs_atom15]) ).
cnf(c_0_221_0,axiom,
( ~ subset(X3,X2)
| in(X1,X2)
| ~ in(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_221,def_lhs_atom8]) ).
cnf(c_0_222_0,axiom,
( ~ relation(X1)
| well_ordering(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_222,def_lhs_atom10]) ).
cnf(c_0_223_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_223,def_lhs_atom27]) ).
cnf(c_0_224_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_224,def_lhs_atom1]) ).
cnf(c_0_225_0,axiom,
( ~ relation(X1)
| reflexive(X1)
| in(sk1_esk2_1(X1),relation_field(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_225,def_lhs_atom10]) ).
cnf(c_0_226_0,axiom,
( ~ relation(X1)
| relation(relation_restriction(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_226,def_lhs_atom10]) ).
cnf(c_0_227_0,axiom,
( ~ relation(X1)
| set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1) ),
inference(unfold_definition,[status(thm)],[c_0_227,def_lhs_atom10]) ).
cnf(c_0_228_0,axiom,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(unfold_definition,[status(thm)],[c_0_228,def_lhs_atom25]) ).
cnf(c_0_229_0,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_229,def_lhs_atom26]) ).
cnf(c_0_230_0,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_230,def_lhs_atom1]) ).
cnf(c_0_231_0,axiom,
( X2 != X1
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_231,def_lhs_atom6]) ).
cnf(c_0_232_0,axiom,
( X2 != X1
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_232,def_lhs_atom6]) ).
cnf(c_0_233_0,axiom,
( ~ relation(X1)
| reflexive(X1)
| ~ well_ordering(X1) ),
inference(unfold_definition,[status(thm)],[c_0_233,def_lhs_atom10]) ).
cnf(c_0_234_0,axiom,
( ~ relation(X1)
| transitive(X1)
| ~ well_ordering(X1) ),
inference(unfold_definition,[status(thm)],[c_0_234,def_lhs_atom10]) ).
cnf(c_0_235_0,axiom,
( ~ relation(X1)
| antisymmetric(X1)
| ~ well_ordering(X1) ),
inference(unfold_definition,[status(thm)],[c_0_235,def_lhs_atom10]) ).
cnf(c_0_236_0,axiom,
( ~ relation(X1)
| connected(X1)
| ~ well_ordering(X1) ),
inference(unfold_definition,[status(thm)],[c_0_236,def_lhs_atom10]) ).
cnf(c_0_237_0,axiom,
( ~ relation(X1)
| well_founded_relation(X1)
| ~ well_ordering(X1) ),
inference(unfold_definition,[status(thm)],[c_0_237,def_lhs_atom10]) ).
cnf(c_0_243_0,axiom,
( ~ empty(X1)
| function(X1) ),
inference(unfold_definition,[status(thm)],[c_0_243,def_lhs_atom2]) ).
cnf(c_0_244_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_244,def_lhs_atom2]) ).
cnf(c_0_238_0,axiom,
~ empty(ordered_pair(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_238,def_lhs_atom14]) ).
cnf(c_0_239_0,axiom,
ordered_pair(X2,X1) = unordered_pair(unordered_pair(X2,X1),singleton(X2)),
inference(unfold_definition,[status(thm)],[c_0_239,def_lhs_atom11]) ).
cnf(c_0_240_0,axiom,
set_intersection2(X2,X1) = set_intersection2(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_240,def_lhs_atom5]) ).
cnf(c_0_241_0,axiom,
set_union2(X2,X1) = set_union2(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_241,def_lhs_atom4]) ).
cnf(c_0_242_0,axiom,
unordered_pair(X2,X1) = unordered_pair(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_242,def_lhs_atom3]) ).
cnf(c_0_245_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(unfold_definition,[status(thm)],[c_0_245,def_lhs_atom24]) ).
cnf(c_0_246_0,axiom,
set_union2(X1,empty_set) = X1,
inference(unfold_definition,[status(thm)],[c_0_246,def_lhs_atom22]) ).
cnf(c_0_247_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_247,def_lhs_atom18]) ).
cnf(c_0_248_0,axiom,
set_intersection2(X1,X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_248,def_lhs_atom17]) ).
cnf(c_0_249_0,axiom,
set_union2(X1,X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_249,def_lhs_atom16]) ).
cnf(c_0_250_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_250,def_lhs_atom13]) ).
cnf(c_0_251_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_251,def_lhs_atom12]) ).
cnf(c_0_252_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_252,def_lhs_atom12]) ).
cnf(c_0_253_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_253,def_lhs_atom12]) ).
cnf(c_0_254_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_254,def_lhs_atom12]) ).
cnf(c_0_255_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_255,def_lhs_atom12]) ).
cnf(c_0_256_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_256,def_lhs_atom12]) ).
cnf(c_0_257_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_257,def_lhs_atom12]) ).
cnf(c_0_258_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_258,def_lhs_atom12]) ).
cnf(c_0_259_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_259,def_lhs_atom12]) ).
cnf(c_0_260_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_260,def_lhs_atom12]) ).
cnf(c_0_261_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_261,def_lhs_atom12]) ).
cnf(c_0_262_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_262,def_lhs_atom12]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_1_002,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_2_003,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_3_004,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_4_005,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_5_006,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_6_007,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_7_008,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_8_009,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_9_010,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_10_011,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_0 ).
fof(c_0_11_012,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_1 ).
fof(c_0_12_013,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_2 ).
fof(c_0_13_014,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_3 ).
fof(c_0_14_015,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_4 ).
fof(c_0_15_016,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_16_017,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_6 ).
fof(c_0_17_018,axiom,
? [X1] : empty(X1),
c_0_7 ).
fof(c_0_18_019,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_8 ).
fof(c_0_19_020,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_9 ).
fof(c_0_20_021,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_21_022,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_22_023,plain,
! [X2] :
( ( relation(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) )
& ( function(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) )
& ( one_to_one(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_23_024,plain,
! [X3] : element(esk6_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
fof(c_0_24_025,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_14])])])]) ).
fof(c_0_25_026,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_15])]) ).
fof(c_0_26_027,plain,
( relation(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
fof(c_0_27_028,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
fof(c_0_28_029,plain,
( relation(esk3_0)
& empty(esk3_0)
& function(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_18])]) ).
fof(c_0_29_030,plain,
( relation(esk1_0)
& function(esk1_0)
& one_to_one(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
cnf(c_0_30_031,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31_032,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32_033,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33_034,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34_035,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35_036,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36_037,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37_038,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38_039,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39_040,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_40_041,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41_042,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_42_043,plain,
empty(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_43_044,plain,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_44_045,plain,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_45_046,plain,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_46_047,plain,
one_to_one(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_47_048,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_30,
[final] ).
cnf(c_0_48_049,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_31,
[final] ).
cnf(c_0_49_050,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_32,
[final] ).
cnf(c_0_50_051,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_33,
[final] ).
cnf(c_0_51_052,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_34,
[final] ).
cnf(c_0_52_053,plain,
element(esk6_1(X1),X1),
c_0_35,
[final] ).
cnf(c_0_53_054,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_36,
[final] ).
cnf(c_0_54_055,plain,
~ empty(esk2_0),
c_0_37,
[final] ).
cnf(c_0_55_056,plain,
relation(esk5_0),
c_0_38,
[final] ).
cnf(c_0_56_057,plain,
function(esk5_0),
c_0_39,
[final] ).
cnf(c_0_57_058,plain,
empty(esk4_0),
c_0_40,
[final] ).
cnf(c_0_58_059,plain,
relation(esk3_0),
c_0_41,
[final] ).
cnf(c_0_59_060,plain,
empty(esk3_0),
c_0_42,
[final] ).
cnf(c_0_60_061,plain,
function(esk3_0),
c_0_43,
[final] ).
cnf(c_0_61_062,plain,
relation(esk1_0),
c_0_44,
[final] ).
cnf(c_0_62_063,plain,
function(esk1_0),
c_0_45,
[final] ).
cnf(c_0_63_064,plain,
one_to_one(esk1_0),
c_0_46,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_47_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_47_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_47]) ).
cnf(c_0_48_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_48_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_48]) ).
cnf(c_0_49_0,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_49_1,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_49_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_49_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_49]) ).
cnf(c_0_50_0,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_50_1,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_50_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_50_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_50]) ).
cnf(c_0_51_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_51_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_51]) ).
cnf(c_0_53_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_53_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_53_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_53]) ).
cnf(c_0_54_0,axiom,
~ empty(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_54]) ).
cnf(c_0_52_0,axiom,
element(sk2_esk6_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_52]) ).
cnf(c_0_55_0,axiom,
relation(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_56_0,axiom,
function(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_57_0,axiom,
empty(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_58_0,axiom,
relation(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_58]) ).
cnf(c_0_59_0,axiom,
empty(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_59]) ).
cnf(c_0_60_0,axiom,
function(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_61_0,axiom,
relation(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_61]) ).
cnf(c_0_62_0,axiom,
function(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_62]) ).
cnf(c_0_63_0,axiom,
one_to_one(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_63]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_065,conjecture,
! [X1,X2] :
( relation(X2)
=> ( ( well_ordering(X2)
& subset(X1,relation_field(X2)) )
=> relation_field(relation_restriction(X2,X1)) = X1 ) ),
file('<stdin>',t39_wellord1) ).
fof(c_0_1_066,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( ( well_ordering(X2)
& subset(X1,relation_field(X2)) )
=> relation_field(relation_restriction(X2,X1)) = X1 ) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_067,negated_conjecture,
( relation(esk2_0)
& well_ordering(esk2_0)
& subset(esk1_0,relation_field(esk2_0))
& relation_field(relation_restriction(esk2_0,esk1_0)) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_068,negated_conjecture,
relation_field(relation_restriction(esk2_0,esk1_0)) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_069,negated_conjecture,
subset(esk1_0,relation_field(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_070,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_071,negated_conjecture,
well_ordering(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7_072,negated_conjecture,
relation_field(relation_restriction(esk2_0,esk1_0)) != esk1_0,
c_0_3,
[final] ).
cnf(c_0_8_073,negated_conjecture,
subset(esk1_0,relation_field(esk2_0)),
c_0_4,
[final] ).
cnf(c_0_9_074,negated_conjecture,
relation(esk2_0),
c_0_5,
[final] ).
cnf(c_0_10_075,negated_conjecture,
well_ordering(esk2_0),
c_0_6,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_67,plain,
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_226_0) ).
cnf(c_233,plain,
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(copy,[status(esa)],[c_67]) ).
cnf(c_11676,plain,
( relation(relation_restriction(sk3_esk2_0,X0))
| ~ relation(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_233]) ).
cnf(c_66299,plain,
( relation(relation_restriction(sk3_esk2_0,sk3_esk1_0))
| ~ relation(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_11676]) ).
cnf(c_84,plain,
( ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_209_0) ).
cnf(c_250,plain,
( ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(copy,[status(esa)],[c_84]) ).
cnf(c_11781,plain,
( ~ in(ordered_pair(X0,X1),relation_restriction(sk3_esk2_0,X2))
| in(X1,relation_field(relation_restriction(sk3_esk2_0,X2)))
| ~ relation(relation_restriction(sk3_esk2_0,X2)) ),
inference(instantiation,[status(thm)],[c_250]) ).
cnf(c_46496,plain,
( ~ in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),relation_restriction(sk3_esk2_0,sk3_esk1_0))
| in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)))
| ~ relation(relation_restriction(sk3_esk2_0,sk3_esk1_0)) ),
inference(instantiation,[status(thm)],[c_11781]) ).
cnf(c_88,plain,
( ~ in(X0,X1)
| ~ in(X0,cartesian_product2(X2,X2))
| in(X0,relation_restriction(X1,X2))
| ~ relation(X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_205_0) ).
cnf(c_254,plain,
( ~ in(X0,X1)
| ~ in(X0,cartesian_product2(X2,X2))
| in(X0,relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(copy,[status(esa)],[c_88]) ).
cnf(c_11887,plain,
( in(X0,relation_restriction(sk3_esk2_0,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,sk3_esk2_0)
| ~ relation(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_254]) ).
cnf(c_27960,plain,
( in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),relation_restriction(sk3_esk2_0,X0))
| ~ in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),cartesian_product2(X0,X0))
| ~ in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),sk3_esk2_0)
| ~ relation(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_11887]) ).
cnf(c_43989,plain,
( in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),relation_restriction(sk3_esk2_0,sk3_esk1_0))
| ~ in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),cartesian_product2(sk3_esk1_0,sk3_esk1_0))
| ~ in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),sk3_esk2_0)
| ~ relation(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_27960]) ).
cnf(c_91,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_202_0) ).
cnf(c_257,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ),
inference(copy,[status(esa)],[c_91]) ).
cnf(c_26818,plain,
( in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),X0),cartesian_product2(sk3_esk1_0,X1))
| ~ in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0)
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_257]) ).
cnf(c_27256,plain,
( in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),cartesian_product2(sk3_esk1_0,sk3_esk1_0))
| ~ in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_26818]) ).
cnf(c_83,plain,
( ~ reflexive(X0)
| ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0)
| ~ relation(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_210_0) ).
cnf(c_249,plain,
( ~ reflexive(X0)
| ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0)
| ~ relation(X0) ),
inference(copy,[status(esa)],[c_83]) ).
cnf(c_11863,plain,
( in(ordered_pair(X0,X0),sk3_esk2_0)
| ~ in(X0,relation_field(sk3_esk2_0))
| ~ relation(sk3_esk2_0)
| ~ reflexive(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_249]) ).
cnf(c_27215,plain,
( in(ordered_pair(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)),sk3_esk2_0)
| ~ in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),relation_field(sk3_esk2_0))
| ~ relation(sk3_esk2_0)
| ~ reflexive(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_11863]) ).
cnf(c_72,plain,
( ~ in(X0,X1)
| in(X0,X2)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_221_0) ).
cnf(c_238,plain,
( ~ in(X0,X1)
| in(X0,X2)
| ~ subset(X1,X2) ),
inference(copy,[status(esa)],[c_72]) ).
cnf(c_12130,plain,
( ~ in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0)
| in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),X0)
| ~ subset(sk3_esk1_0,X0) ),
inference(instantiation,[status(thm)],[c_238]) ).
cnf(c_26739,plain,
( in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),relation_field(sk3_esk2_0))
| ~ in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0)
| ~ subset(sk3_esk1_0,relation_field(sk3_esk2_0)) ),
inference(instantiation,[status(thm)],[c_12130]) ).
cnf(c_80,plain,
( ~ in(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_213_0) ).
cnf(c_246,plain,
( ~ in(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
inference(copy,[status(esa)],[c_80]) ).
cnf(c_11900,plain,
( ~ in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)))
| subset(sk3_esk1_0,relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0))) ),
inference(instantiation,[status(thm)],[c_246]) ).
cnf(c_75,plain,
( in(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_218_0) ).
cnf(c_241,plain,
( in(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
inference(copy,[status(esa)],[c_75]) ).
cnf(c_11901,plain,
( in(sk1_esk1_2(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0)
| subset(sk3_esk1_0,relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0))) ),
inference(instantiation,[status(thm)],[c_241]) ).
cnf(c_79,plain,
( subset(relation_field(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_214_0) ).
cnf(c_245,plain,
( subset(relation_field(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(copy,[status(esa)],[c_79]) ).
cnf(c_11711,plain,
( ~ relation(sk3_esk2_0)
| subset(relation_field(relation_restriction(sk3_esk2_0,X0)),X0) ),
inference(instantiation,[status(thm)],[c_245]) ).
cnf(c_11783,plain,
( ~ relation(sk3_esk2_0)
| subset(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_11711]) ).
cnf(c_77,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_216_0) ).
cnf(c_243,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(copy,[status(esa)],[c_77]) ).
cnf(c_11733,plain,
( ~ subset(relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)),sk3_esk1_0)
| ~ subset(sk3_esk1_0,relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)))
| relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)) = sk3_esk1_0 ),
inference(instantiation,[status(thm)],[c_243]) ).
cnf(c_60,plain,
( ~ well_ordering(X0)
| reflexive(X0)
| ~ relation(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_233_0) ).
cnf(c_226,plain,
( ~ well_ordering(X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(copy,[status(esa)],[c_60]) ).
cnf(c_11669,plain,
( ~ relation(sk3_esk2_0)
| ~ well_ordering(sk3_esk2_0)
| reflexive(sk3_esk2_0) ),
inference(instantiation,[status(thm)],[c_226]) ).
cnf(c_92,negated_conjecture,
relation_field(relation_restriction(sk3_esk2_0,sk3_esk1_0)) != sk3_esk1_0,
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_7) ).
cnf(c_93,negated_conjecture,
subset(sk3_esk1_0,relation_field(sk3_esk2_0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_8) ).
cnf(c_94,negated_conjecture,
relation(sk3_esk2_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_9) ).
cnf(c_95,negated_conjecture,
well_ordering(sk3_esk2_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p',c_0_10) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_66299,c_46496,c_43989,c_27256,c_27215,c_26739,c_11900,c_11901,c_11783,c_11733,c_11669,c_92,c_93,c_94,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU258+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 11:36:54 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running in mono-core mode
% 0.19/0.41 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.41 % FOF problem with conjecture
% 0.19/0.41 % 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_e897d8.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_a58f51.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_3d39d8 | grep -v "SZS"
% 0.19/0.44
% 0.19/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.44
% 0.19/0.44 %
% 0.19/0.44 % ------ iProver source info
% 0.19/0.44
% 0.19/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.44 % git: non_committed_changes: true
% 0.19/0.44 % git: last_make_outside_of_git: true
% 0.19/0.44
% 0.19/0.44 %
% 0.19/0.44 % ------ Input Options
% 0.19/0.44
% 0.19/0.44 % --out_options all
% 0.19/0.44 % --tptp_safe_out true
% 0.19/0.44 % --problem_path ""
% 0.19/0.44 % --include_path ""
% 0.19/0.44 % --clausifier .//eprover
% 0.19/0.44 % --clausifier_options --tstp-format
% 0.19/0.44 % --stdin false
% 0.19/0.44 % --dbg_backtrace false
% 0.19/0.44 % --dbg_dump_prop_clauses false
% 0.19/0.44 % --dbg_dump_prop_clauses_file -
% 0.19/0.44 % --dbg_out_stat false
% 0.19/0.44
% 0.19/0.44 % ------ General Options
% 0.19/0.44
% 0.19/0.44 % --fof false
% 0.19/0.44 % --time_out_real 150.
% 0.19/0.44 % --time_out_prep_mult 0.2
% 0.19/0.44 % --time_out_virtual -1.
% 0.19/0.44 % --schedule none
% 0.19/0.44 % --ground_splitting input
% 0.19/0.44 % --splitting_nvd 16
% 0.19/0.44 % --non_eq_to_eq false
% 0.19/0.44 % --prep_gs_sim true
% 0.19/0.44 % --prep_unflatten false
% 0.19/0.44 % --prep_res_sim true
% 0.19/0.44 % --prep_upred true
% 0.19/0.44 % --res_sim_input true
% 0.19/0.44 % --clause_weak_htbl true
% 0.19/0.44 % --gc_record_bc_elim false
% 0.19/0.44 % --symbol_type_check false
% 0.19/0.44 % --clausify_out false
% 0.19/0.44 % --large_theory_mode false
% 0.19/0.44 % --prep_sem_filter none
% 0.19/0.44 % --prep_sem_filter_out false
% 0.19/0.44 % --preprocessed_out false
% 0.19/0.44 % --sub_typing false
% 0.19/0.44 % --brand_transform false
% 0.19/0.44 % --pure_diseq_elim true
% 0.19/0.44 % --min_unsat_core false
% 0.19/0.44 % --pred_elim true
% 0.19/0.44 % --add_important_lit false
% 0.19/0.44 % --soft_assumptions false
% 0.19/0.44 % --reset_solvers false
% 0.19/0.44 % --bc_imp_inh []
% 0.19/0.44 % --conj_cone_tolerance 1.5
% 0.19/0.44 % --prolific_symb_bound 500
% 0.19/0.44 % --lt_threshold 2000
% 0.19/0.44
% 0.19/0.44 % ------ SAT Options
% 0.19/0.44
% 0.19/0.44 % --sat_mode false
% 0.19/0.44 % --sat_fm_restart_options ""
% 0.19/0.44 % --sat_gr_def false
% 0.19/0.44 % --sat_epr_types true
% 0.19/0.44 % --sat_non_cyclic_types false
% 0.19/0.44 % --sat_finite_models false
% 0.19/0.44 % --sat_fm_lemmas false
% 0.19/0.44 % --sat_fm_prep false
% 0.19/0.44 % --sat_fm_uc_incr true
% 0.19/0.44 % --sat_out_model small
% 0.19/0.44 % --sat_out_clauses false
% 0.19/0.44
% 0.19/0.44 % ------ QBF Options
% 0.19/0.44
% 0.19/0.44 % --qbf_mode false
% 0.19/0.44 % --qbf_elim_univ true
% 0.19/0.44 % --qbf_sk_in true
% 0.19/0.44 % --qbf_pred_elim true
% 0.19/0.44 % --qbf_split 32
% 0.19/0.44
% 0.19/0.44 % ------ BMC1 Options
% 0.19/0.44
% 0.19/0.44 % --bmc1_incremental false
% 0.19/0.44 % --bmc1_axioms reachable_all
% 0.19/0.44 % --bmc1_min_bound 0
% 0.19/0.44 % --bmc1_max_bound -1
% 0.19/0.44 % --bmc1_max_bound_default -1
% 0.19/0.44 % --bmc1_symbol_reachability true
% 0.19/0.44 % --bmc1_property_lemmas false
% 0.19/0.44 % --bmc1_k_induction false
% 0.19/0.44 % --bmc1_non_equiv_states false
% 0.19/0.44 % --bmc1_deadlock false
% 0.19/0.44 % --bmc1_ucm false
% 0.19/0.44 % --bmc1_add_unsat_core none
% 0.19/0.44 % --bmc1_unsat_core_children false
% 0.19/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.44 % --bmc1_out_stat full
% 0.19/0.44 % --bmc1_ground_init false
% 0.19/0.44 % --bmc1_pre_inst_next_state false
% 0.19/0.44 % --bmc1_pre_inst_state false
% 0.19/0.44 % --bmc1_pre_inst_reach_state false
% 0.19/0.44 % --bmc1_out_unsat_core false
% 0.19/0.44 % --bmc1_aig_witness_out false
% 0.19/0.44 % --bmc1_verbose false
% 0.19/0.44 % --bmc1_dump_clauses_tptp false
% 0.46/0.78 % --bmc1_dump_unsat_core_tptp false
% 0.46/0.78 % --bmc1_dump_file -
% 0.46/0.78 % --bmc1_ucm_expand_uc_limit 128
% 0.46/0.78 % --bmc1_ucm_n_expand_iterations 6
% 0.46/0.78 % --bmc1_ucm_extend_mode 1
% 0.46/0.78 % --bmc1_ucm_init_mode 2
% 0.46/0.78 % --bmc1_ucm_cone_mode none
% 0.46/0.78 % --bmc1_ucm_reduced_relation_type 0
% 0.46/0.78 % --bmc1_ucm_relax_model 4
% 0.46/0.78 % --bmc1_ucm_full_tr_after_sat true
% 0.46/0.78 % --bmc1_ucm_expand_neg_assumptions false
% 0.46/0.78 % --bmc1_ucm_layered_model none
% 0.46/0.78 % --bmc1_ucm_max_lemma_size 10
% 0.46/0.78
% 0.46/0.78 % ------ AIG Options
% 0.46/0.78
% 0.46/0.78 % --aig_mode false
% 0.46/0.78
% 0.46/0.78 % ------ Instantiation Options
% 0.46/0.78
% 0.46/0.78 % --instantiation_flag true
% 0.46/0.78 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.46/0.78 % --inst_solver_per_active 750
% 0.46/0.78 % --inst_solver_calls_frac 0.5
% 0.46/0.78 % --inst_passive_queue_type priority_queues
% 0.46/0.78 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.46/0.78 % --inst_passive_queues_freq [25;2]
% 0.46/0.78 % --inst_dismatching true
% 0.46/0.78 % --inst_eager_unprocessed_to_passive true
% 0.46/0.78 % --inst_prop_sim_given true
% 0.46/0.78 % --inst_prop_sim_new false
% 0.46/0.78 % --inst_orphan_elimination true
% 0.46/0.78 % --inst_learning_loop_flag true
% 0.46/0.78 % --inst_learning_start 3000
% 0.46/0.78 % --inst_learning_factor 2
% 0.46/0.78 % --inst_start_prop_sim_after_learn 3
% 0.46/0.78 % --inst_sel_renew solver
% 0.46/0.78 % --inst_lit_activity_flag true
% 0.46/0.78 % --inst_out_proof true
% 0.46/0.78
% 0.46/0.78 % ------ Resolution Options
% 0.46/0.78
% 0.46/0.78 % --resolution_flag true
% 0.46/0.78 % --res_lit_sel kbo_max
% 0.46/0.78 % --res_to_prop_solver none
% 0.46/0.78 % --res_prop_simpl_new false
% 0.46/0.78 % --res_prop_simpl_given false
% 0.46/0.78 % --res_passive_queue_type priority_queues
% 0.46/0.78 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.46/0.78 % --res_passive_queues_freq [15;5]
% 0.46/0.78 % --res_forward_subs full
% 0.46/0.78 % --res_backward_subs full
% 0.46/0.78 % --res_forward_subs_resolution true
% 0.46/0.78 % --res_backward_subs_resolution true
% 0.46/0.78 % --res_orphan_elimination false
% 0.46/0.78 % --res_time_limit 1000.
% 0.46/0.78 % --res_out_proof true
% 0.46/0.78 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e897d8.s
% 0.46/0.78 % --modulo true
% 0.46/0.78
% 0.46/0.78 % ------ Combination Options
% 0.46/0.78
% 0.46/0.78 % --comb_res_mult 1000
% 0.46/0.78 % --comb_inst_mult 300
% 0.46/0.78 % ------
% 0.46/0.78
% 0.46/0.78 % ------ Parsing...% successful
% 0.46/0.78
% 0.46/0.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.46/0.78
% 0.46/0.78 % ------ Proving...
% 0.46/0.78 % ------ Problem Properties
% 0.46/0.78
% 0.46/0.78 %
% 0.46/0.78 % EPR false
% 0.46/0.78 % Horn false
% 0.46/0.78 % Has equality true
% 0.46/0.78
% 0.46/0.78 % % ------ Input Options Time Limit: Unbounded
% 0.46/0.78
% 0.46/0.78
% 0.46/0.78 Compiling...
% 0.46/0.78 Loading plugin: done.
% 0.46/0.78 Compiling...
% 0.46/0.78 Loading plugin: done.
% 0.46/0.78 Compiling...
% 0.46/0.78 Loading plugin: done.
% 0.46/0.78 % % ------ Current options:
% 0.46/0.78
% 0.46/0.78 % ------ Input Options
% 0.46/0.78
% 0.46/0.78 % --out_options all
% 0.46/0.78 % --tptp_safe_out true
% 0.46/0.78 % --problem_path ""
% 0.46/0.78 % --include_path ""
% 0.46/0.78 % --clausifier .//eprover
% 0.46/0.78 % --clausifier_options --tstp-format
% 0.46/0.78 % --stdin false
% 0.46/0.78 % --dbg_backtrace false
% 0.46/0.78 % --dbg_dump_prop_clauses false
% 0.46/0.78 % --dbg_dump_prop_clauses_file -
% 0.46/0.78 % --dbg_out_stat false
% 0.46/0.78
% 0.46/0.78 % ------ General Options
% 0.46/0.78
% 0.46/0.78 % --fof false
% 0.46/0.78 % --time_out_real 150.
% 0.46/0.78 % --time_out_prep_mult 0.2
% 0.46/0.78 % --time_out_virtual -1.
% 0.46/0.78 % --schedule none
% 0.46/0.78 % --ground_splitting input
% 0.46/0.78 % --splitting_nvd 16
% 0.46/0.78 % --non_eq_to_eq false
% 0.46/0.78 % --prep_gs_sim true
% 0.46/0.78 % --prep_unflatten false
% 0.46/0.78 % --prep_res_sim true
% 0.46/0.78 % --prep_upred true
% 0.46/0.78 % --res_sim_input true
% 0.46/0.78 % --clause_weak_htbl true
% 0.46/0.78 % --gc_record_bc_elim false
% 0.46/0.78 % --symbol_type_check false
% 0.46/0.78 % --clausify_out false
% 0.46/0.78 % --large_theory_mode false
% 0.46/0.78 % --prep_sem_filter none
% 0.46/0.78 % --prep_sem_filter_out false
% 0.46/0.78 % --preprocessed_out false
% 0.46/0.78 % --sub_typing false
% 0.46/0.78 % --brand_transform false
% 0.46/0.78 % --pure_diseq_elim true
% 0.46/0.78 % --min_unsat_core false
% 0.46/0.78 % --pred_elim true
% 0.46/0.78 % --add_important_lit false
% 0.46/0.78 % --soft_assumptions false
% 0.46/0.78 % --reset_solvers false
% 0.46/0.78 % --bc_imp_inh []
% 0.46/0.78 % --conj_cone_tolerance 1.5
% 0.46/0.78 % --prolific_symb_bound 500
% 0.46/0.78 % --lt_threshold 2000
% 0.46/0.78
% 0.46/0.78 % ------ SAT Options
% 0.46/0.78
% 0.46/0.78 % --sat_mode false
% 0.46/0.78 % --sat_fm_restart_options ""
% 0.46/0.78 % --sat_gr_def false
% 0.46/0.78 % --sat_epr_types true
% 0.46/0.78 % --sat_non_cyclic_types false
% 0.46/0.78 % --sat_finite_models false
% 0.46/0.78 % --sat_fm_lemmas false
% 0.46/0.78 % --sat_fm_prep false
% 0.46/0.78 % --sat_fm_uc_incr true
% 0.46/0.78 % --sat_out_model small
% 0.46/0.78 % --sat_out_clauses false
% 0.46/0.78
% 0.46/0.78 % ------ QBF Options
% 0.46/0.78
% 0.46/0.78 % --qbf_mode false
% 0.46/0.78 % --qbf_elim_univ true
% 0.46/0.78 % --qbf_sk_in true
% 0.46/0.78 % --qbf_pred_elim true
% 0.46/0.78 % --qbf_split 32
% 0.46/0.78
% 0.46/0.78 % ------ BMC1 Options
% 0.46/0.78
% 0.46/0.78 % --bmc1_incremental false
% 0.46/0.78 % --bmc1_axioms reachable_all
% 0.46/0.78 % --bmc1_min_bound 0
% 0.46/0.78 % --bmc1_max_bound -1
% 0.46/0.78 % --bmc1_max_bound_default -1
% 0.46/0.78 % --bmc1_symbol_reachability true
% 0.46/0.78 % --bmc1_property_lemmas false
% 0.46/0.78 % --bmc1_k_induction false
% 0.46/0.78 % --bmc1_non_equiv_states false
% 0.46/0.78 % --bmc1_deadlock false
% 0.46/0.78 % --bmc1_ucm false
% 0.46/0.78 % --bmc1_add_unsat_core none
% 0.46/0.78 % --bmc1_unsat_core_children false
% 0.46/0.78 % --bmc1_unsat_core_extrapolate_axioms false
% 0.46/0.78 % --bmc1_out_stat full
% 0.46/0.78 % --bmc1_ground_init false
% 0.46/0.78 % --bmc1_pre_inst_next_state false
% 0.46/0.78 % --bmc1_pre_inst_state false
% 0.46/0.78 % --bmc1_pre_inst_reach_state false
% 0.46/0.78 % --bmc1_out_unsat_core false
% 0.46/0.78 % --bmc1_aig_witness_out false
% 0.46/0.78 % --bmc1_verbose false
% 0.46/0.78 % --bmc1_dump_clauses_tptp false
% 0.46/0.78 % --bmc1_dump_unsat_core_tptp false
% 0.46/0.78 % --bmc1_dump_file -
% 0.46/0.78 % --bmc1_ucm_expand_uc_limit 128
% 0.46/0.78 % --bmc1_ucm_n_expand_iterations 6
% 0.46/0.78 % --bmc1_ucm_extend_mode 1
% 0.46/0.78 % --bmc1_ucm_init_mode 2
% 0.46/0.78 % --bmc1_ucm_cone_mode none
% 0.46/0.78 % --bmc1_ucm_reduced_relation_type 0
% 0.46/0.78 % --bmc1_ucm_relax_model 4
% 0.46/0.78 % --bmc1_ucm_full_tr_after_sat true
% 0.46/0.78 % --bmc1_ucm_expand_neg_assumptions false
% 0.46/0.78 % --bmc1_ucm_layered_model none
% 0.46/0.78 % --bmc1_ucm_max_lemma_size 10
% 0.46/0.78
% 0.46/0.78 % ------ AIG Options
% 0.46/0.78
% 0.46/0.78 % --aig_mode false
% 0.46/0.78
% 0.46/0.78 % ------ Instantiation Options
% 0.46/0.78
% 0.46/0.78 % --instantiation_flag true
% 0.46/0.78 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.46/0.78 % --inst_solver_per_active 750
% 0.46/0.78 % --inst_solver_calls_frac 0.5
% 0.46/0.78 % --inst_passive_queue_type priority_queues
% 0.46/0.78 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.46/0.78 % --inst_passive_queues_freq [25;2]
% 0.46/0.78 % --inst_dismatching true
% 3.77/4.09 % --inst_eager_unprocessed_to_passive true
% 3.77/4.09 % --inst_prop_sim_given true
% 3.77/4.09 % --inst_prop_sim_new false
% 3.77/4.09 % --inst_orphan_elimination true
% 3.77/4.09 % --inst_learning_loop_flag true
% 3.77/4.09 % --inst_learning_start 3000
% 3.77/4.09 % --inst_learning_factor 2
% 3.77/4.09 % --inst_start_prop_sim_after_learn 3
% 3.77/4.09 % --inst_sel_renew solver
% 3.77/4.09 % --inst_lit_activity_flag true
% 3.77/4.09 % --inst_out_proof true
% 3.77/4.09
% 3.77/4.09 % ------ Resolution Options
% 3.77/4.09
% 3.77/4.09 % --resolution_flag true
% 3.77/4.09 % --res_lit_sel kbo_max
% 3.77/4.09 % --res_to_prop_solver none
% 3.77/4.09 % --res_prop_simpl_new false
% 3.77/4.09 % --res_prop_simpl_given false
% 3.77/4.09 % --res_passive_queue_type priority_queues
% 3.77/4.09 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.77/4.09 % --res_passive_queues_freq [15;5]
% 3.77/4.09 % --res_forward_subs full
% 3.77/4.09 % --res_backward_subs full
% 3.77/4.09 % --res_forward_subs_resolution true
% 3.77/4.09 % --res_backward_subs_resolution true
% 3.77/4.09 % --res_orphan_elimination false
% 3.77/4.09 % --res_time_limit 1000.
% 3.77/4.09 % --res_out_proof true
% 3.77/4.09 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e897d8.s
% 3.77/4.09 % --modulo true
% 3.77/4.09
% 3.77/4.09 % ------ Combination Options
% 3.77/4.09
% 3.77/4.09 % --comb_res_mult 1000
% 3.77/4.09 % --comb_inst_mult 300
% 3.77/4.09 % ------
% 3.77/4.09
% 3.77/4.09
% 3.77/4.09
% 3.77/4.09 % ------ Proving...
% 3.77/4.09 %
% 3.77/4.09
% 3.77/4.09
% 3.77/4.09 % ------ Statistics
% 3.77/4.09
% 3.77/4.09 % ------ General
% 3.77/4.09
% 3.77/4.09 % num_of_input_clauses: 96
% 3.77/4.09 % num_of_input_neg_conjectures: 4
% 3.77/4.09 % num_of_splits: 0
% 3.77/4.09 % num_of_split_atoms: 0
% 3.77/4.09 % num_of_sem_filtered_clauses: 0
% 3.77/4.09 % num_of_subtypes: 0
% 3.77/4.09 % monotx_restored_types: 0
% 3.77/4.09 % sat_num_of_epr_types: 0
% 3.77/4.09 % sat_num_of_non_cyclic_types: 0
% 3.77/4.09 % sat_guarded_non_collapsed_types: 0
% 3.77/4.09 % is_epr: 0
% 3.77/4.09 % is_horn: 0
% 3.77/4.09 % has_eq: 1
% 3.77/4.09 % num_pure_diseq_elim: 0
% 3.77/4.09 % simp_replaced_by: 0
% 3.77/4.09 % res_preprocessed: 8
% 3.77/4.09 % prep_upred: 0
% 3.77/4.09 % prep_unflattend: 0
% 3.77/4.09 % pred_elim_cands: 0
% 3.77/4.09 % pred_elim: 0
% 3.77/4.09 % pred_elim_cl: 0
% 3.77/4.09 % pred_elim_cycles: 0
% 3.77/4.09 % forced_gc_time: 0
% 3.77/4.09 % gc_basic_clause_elim: 0
% 3.77/4.09 % parsing_time: 0.002
% 3.77/4.09 % sem_filter_time: 0.
% 3.77/4.09 % pred_elim_time: 0.
% 3.77/4.09 % out_proof_time: 0.002
% 3.77/4.09 % monotx_time: 0.
% 3.77/4.09 % subtype_inf_time: 0.
% 3.77/4.09 % unif_index_cands_time: 0.018
% 3.77/4.09 % unif_index_add_time: 0.019
% 3.77/4.09 % total_time: 3.663
% 3.77/4.09 % num_of_symbols: 60
% 3.77/4.09 % num_of_terms: 80337
% 3.77/4.09
% 3.77/4.09 % ------ Propositional Solver
% 3.77/4.09
% 3.77/4.09 % prop_solver_calls: 13
% 3.77/4.09 % prop_fast_solver_calls: 12
% 3.77/4.09 % prop_num_of_clauses: 9229
% 3.77/4.09 % prop_preprocess_simplified: 9508
% 3.77/4.09 % prop_fo_subsumed: 0
% 3.77/4.09 % prop_solver_time: 0.003
% 3.77/4.09 % prop_fast_solver_time: 0.
% 3.77/4.09 % prop_unsat_core_time: 0.001
% 3.77/4.09
% 3.77/4.09 % ------ QBF
% 3.77/4.09
% 3.77/4.09 % qbf_q_res: 0
% 3.77/4.09 % qbf_num_tautologies: 0
% 3.77/4.09 % qbf_prep_cycles: 0
% 3.77/4.09
% 3.77/4.09 % ------ BMC1
% 3.77/4.09
% 3.77/4.09 % bmc1_current_bound: -1
% 3.77/4.09 % bmc1_last_solved_bound: -1
% 3.77/4.09 % bmc1_unsat_core_size: -1
% 3.77/4.09 % bmc1_unsat_core_parents_size: -1
% 3.77/4.09 % bmc1_merge_next_fun: 0
% 3.77/4.09 % bmc1_unsat_core_clauses_time: 0.
% 3.77/4.09
% 3.77/4.09 % ------ Instantiation
% 3.77/4.09
% 3.77/4.09 % inst_num_of_clauses: 6241
% 3.77/4.09 % inst_num_in_passive: 4632
% 3.77/4.09 % inst_num_in_active: 1077
% 3.77/4.09 % inst_num_in_unprocessed: 515
% 3.77/4.09 % inst_num_of_loops: 1153
% 3.77/4.09 % inst_num_of_learning_restarts: 0
% 3.77/4.09 % inst_num_moves_active_passive: 59
% 3.77/4.09 % inst_lit_activity: 3772
% 3.77/4.09 % inst_lit_activity_moves: 0
% 3.77/4.09 % inst_num_tautologies: 15
% 3.77/4.09 % inst_num_prop_implied: 0
% 3.77/4.09 % inst_num_existing_simplified: 0
% 3.77/4.09 % inst_num_eq_res_simplified: 0
% 3.77/4.09 % inst_num_child_elim: 0
% 3.77/4.09 % inst_num_of_dismatching_blockings: 338
% 3.77/4.09 % inst_num_of_non_proper_insts: 3624
% 3.77/4.09 % inst_num_of_duplicates: 1106
% 3.77/4.09 % inst_inst_num_from_inst_to_res: 0
% 3.77/4.09 % inst_dismatching_checking_time: 0.069
% 3.77/4.09
% 3.77/4.09 % ------ Resolution
% 3.77/4.09
% 3.77/4.09 % res_num_of_clauses: 17686
% 3.77/4.09 % res_num_in_passive: 13858
% 3.77/4.09 % res_num_in_active: 3783
% 3.77/4.09 % res_num_of_loops: 4000
% 3.77/4.09 % res_forward_subset_subsumed: 961
% 3.77/4.09 % res_backward_subset_subsumed: 1
% 3.77/4.09 % res_forward_subsumed: 257
% 3.77/4.09 % res_backward_subsumed: 8
% 3.77/4.09 % res_forward_subsumption_resolution: 162
% 3.77/4.09 % res_backward_subsumption_resolution: 3
% 3.77/4.09 % res_clause_to_clause_subsumption: 64876
% 3.77/4.09 % res_orphan_elimination: 0
% 3.77/4.09 % res_tautology_del: 472
% 3.77/4.09 % res_num_eq_res_simplified: 0
% 3.77/4.09 % res_num_sel_changes: 0
% 3.77/4.09 % res_moves_from_active_to_pass: 0
% 3.77/4.09
% 3.77/4.09 % Status Unsatisfiable
% 3.77/4.09 % SZS status Theorem
% 3.77/4.09 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------