TSTP Solution File: SEU085+1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU085+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n021.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 10:24:50 EDT 2022
% Result : Theorem 0.32s 0.56s
% Output : CNFRefutation 0.32s
% 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(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
input ).
fof(t4_boole_0,plain,
! [A] :
( set_difference(empty_set,A) = empty_set
| $false ),
inference(orientation,[status(thm)],[t4_boole]) ).
fof(t3_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(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
input ).
fof(t3_boole_0,plain,
! [A] :
( set_difference(A,empty_set) = A
| $false ),
inference(orientation,[status(thm)],[t3_boole]) ).
fof(t36_xboole_1,axiom,
! [A,B] : subset(set_difference(A,B),A),
input ).
fof(t36_xboole_1_0,plain,
! [A,B] :
( subset(set_difference(A,B),A)
| $false ),
inference(orientation,[status(thm)],[t36_xboole_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(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(t13_finset_1,axiom,
! [A,B] :
( ( subset(A,B)
& finite(B) )
=> finite(A) ),
input ).
fof(t13_finset_1_0,plain,
! [A,B] :
( finite(A)
| ~ ( subset(A,B)
& finite(B) ) ),
inference(orientation,[status(thm)],[t13_finset_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(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
input ).
fof(rc3_finset_1_0,plain,
! [A] :
( empty(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
inference(orientation,[status(thm)],[rc3_finset_1]) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
input ).
fof(rc1_subset_1_0,plain,
! [A] :
( empty(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
inference(orientation,[status(thm)],[rc1_subset_1]) ).
fof(fc8_arytm_3,axiom,
~ empty(positive_rationals),
input ).
fof(fc8_arytm_3_0,plain,
( ~ empty(positive_rationals)
| $false ),
inference(orientation,[status(thm)],[fc8_arytm_3]) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
input ).
fof(fc4_relat_1_0,plain,
( empty(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc4_relat_1]) ).
fof(fc4_relat_1_1,plain,
( relation(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc4_relat_1]) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(set_difference(A,B)) ),
input ).
fof(fc3_relat_1_0,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ ( relation(A)
& relation(B) ) ),
inference(orientation,[status(thm)],[fc3_relat_1]) ).
fof(fc2_ordinal1,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
input ).
fof(fc2_ordinal1_0,plain,
( relation(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_1,plain,
( relation_empty_yielding(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_2,plain,
( function(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_3,plain,
( one_to_one(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_4,plain,
( empty(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_5,plain,
( epsilon_transitive(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_6,plain,
( epsilon_connected(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
fof(fc2_ordinal1_7,plain,
( ordinal(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc2_ordinal1]) ).
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(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
input ).
fof(fc1_subset_1_0,plain,
! [A] :
( ~ empty(powerset(A))
| $false ),
inference(orientation,[status(thm)],[fc1_subset_1]) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
input ).
fof(fc12_relat_1_0,plain,
( empty(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc12_relat_1]) ).
fof(fc12_relat_1_1,plain,
( relation(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc12_relat_1]) ).
fof(fc12_relat_1_2,plain,
( relation_empty_yielding(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc12_relat_1]) ).
fof(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
input ).
fof(fc12_finset_1_0,plain,
! [A,B] :
( ~ finite(A)
| finite(set_difference(A,B)) ),
inference(orientation,[status(thm)],[fc12_finset_1]) ).
fof(cc4_arytm_3,axiom,
! [A] :
( element(A,positive_rationals)
=> ( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A)
& natural(A) ) ) ),
input ).
fof(cc4_arytm_3_0,plain,
! [A] :
( ~ element(A,positive_rationals)
| ( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A)
& natural(A) ) ) ),
inference(orientation,[status(thm)],[cc4_arytm_3]) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
input ).
fof(cc3_ordinal1_0,plain,
! [A] :
( ~ empty(A)
| ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
inference(orientation,[status(thm)],[cc3_ordinal1]) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
input ).
fof(cc2_ordinal1_0,plain,
! [A] :
( ordinal(A)
| ~ ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(orientation,[status(thm)],[cc2_ordinal1]) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
input ).
fof(cc2_finset_1_0,plain,
! [A] :
( ~ finite(A)
| ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
inference(orientation,[status(thm)],[cc2_finset_1]) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
input ).
fof(cc1_relat_1_0,plain,
! [A] :
( ~ empty(A)
| relation(A) ),
inference(orientation,[status(thm)],[cc1_relat_1]) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
input ).
fof(cc1_ordinal1_0,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(orientation,[status(thm)],[cc1_ordinal1]) ).
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(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
input ).
fof(cc1_finset_1_0,plain,
! [A] :
( ~ empty(A)
| finite(A) ),
inference(orientation,[status(thm)],[cc1_finset_1]) ).
fof(cc1_arytm_3,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( element(B,A)
=> ( epsilon_transitive(B)
& epsilon_connected(B)
& ordinal(B) ) ) ),
input ).
fof(cc1_arytm_3_0,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( element(B,A)
=> ( epsilon_transitive(B)
& epsilon_connected(B)
& ordinal(B) ) ) ),
inference(orientation,[status(thm)],[cc1_arytm_3]) ).
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)
<=> ~ ordinal(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A] :
( lhs_atom2(A)
| ! [B] :
( element(B,A)
=> ( epsilon_transitive(B)
& epsilon_connected(B)
& ordinal(B) ) ) ),
inference(fold_definition,[status(thm)],[cc1_arytm_3_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [A] :
( lhs_atom3(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A] :
( lhs_atom3(A)
| finite(A) ),
inference(fold_definition,[status(thm)],[cc1_finset_1_0,def_lhs_atom3]) ).
fof(to_be_clausified_3,plain,
! [A] :
( lhs_atom3(A)
| function(A) ),
inference(fold_definition,[status(thm)],[cc1_funct_1_0,def_lhs_atom3]) ).
fof(to_be_clausified_4,plain,
! [A] :
( lhs_atom2(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[cc1_ordinal1_0,def_lhs_atom2]) ).
fof(to_be_clausified_5,plain,
! [A] :
( lhs_atom3(A)
| relation(A) ),
inference(fold_definition,[status(thm)],[cc1_relat_1_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [A] :
( lhs_atom4(A)
<=> ~ finite(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A] :
( lhs_atom4(A)
| ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
inference(fold_definition,[status(thm)],[cc2_finset_1_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [A] :
( lhs_atom5(A)
<=> ordinal(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A] :
( lhs_atom5(A)
| ~ ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[cc2_ordinal1_0,def_lhs_atom5]) ).
fof(to_be_clausified_8,plain,
! [A] :
( lhs_atom3(A)
| ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
inference(fold_definition,[status(thm)],[cc3_ordinal1_0,def_lhs_atom3]) ).
fof(def_lhs_atom6,axiom,
! [A] :
( lhs_atom6(A)
<=> ~ element(A,positive_rationals) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A] :
( lhs_atom6(A)
| ( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A)
& natural(A) ) ) ),
inference(fold_definition,[status(thm)],[cc4_arytm_3_0,def_lhs_atom6]) ).
fof(to_be_clausified_10,plain,
! [A,B] :
( lhs_atom4(A)
| finite(set_difference(A,B)) ),
inference(fold_definition,[status(thm)],[fc12_finset_1_0,def_lhs_atom4]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> relation_empty_yielding(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_2,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> relation(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_1,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [A] :
( lhs_atom10(A)
<=> ~ empty(powerset(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [A] :
( lhs_atom10(A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_subset_1_0,def_lhs_atom10]) ).
fof(to_be_clausified_15,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> ordinal(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_7,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> epsilon_connected(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_6,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> epsilon_transitive(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_5,def_lhs_atom13]) ).
fof(to_be_clausified_19,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_4,def_lhs_atom9]) ).
fof(def_lhs_atom14,axiom,
( lhs_atom14
<=> one_to_one(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
( lhs_atom14
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_3,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> function(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_2,def_lhs_atom15]) ).
fof(to_be_clausified_22,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_1,def_lhs_atom7]) ).
fof(to_be_clausified_23,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_0,def_lhs_atom8]) ).
fof(def_lhs_atom16,axiom,
! [B,A] :
( lhs_atom16(B,A)
<=> relation(set_difference(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [A,B] :
( lhs_atom16(B,A)
| ~ ( relation(A)
& relation(B) ) ),
inference(fold_definition,[status(thm)],[fc3_relat_1_0,def_lhs_atom16]) ).
fof(to_be_clausified_25,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc4_relat_1_1,def_lhs_atom8]) ).
fof(to_be_clausified_26,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[fc4_relat_1_0,def_lhs_atom9]) ).
fof(def_lhs_atom17,axiom,
( lhs_atom17
<=> ~ empty(positive_rationals) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
( lhs_atom17
| $false ),
inference(fold_definition,[status(thm)],[fc8_arytm_3_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [A] :
( lhs_atom18(A)
<=> empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [A] :
( lhs_atom18(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
inference(fold_definition,[status(thm)],[rc1_subset_1_0,def_lhs_atom18]) ).
fof(to_be_clausified_29,plain,
! [A] :
( lhs_atom18(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
inference(fold_definition,[status(thm)],[rc3_finset_1_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [A] :
( lhs_atom19(A)
<=> subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [A] :
( lhs_atom19(A)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [A] :
( lhs_atom20(A)
<=> finite(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [A,B] :
( lhs_atom20(A)
| ~ ( subset(A,B)
& finite(B) ) ),
inference(fold_definition,[status(thm)],[t13_finset_1_0,def_lhs_atom20]) ).
fof(to_be_clausified_32,plain,
! [A,B] :
( lhs_atom1(B,A)
| element(A,B) ),
inference(fold_definition,[status(thm)],[t1_subset_0,def_lhs_atom1]) ).
fof(def_lhs_atom21,axiom,
! [B,A] :
( lhs_atom21(B,A)
<=> ~ element(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [A,B] :
( lhs_atom21(B,A)
| empty(B)
| in(A,B) ),
inference(fold_definition,[status(thm)],[t2_subset_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [B,A] :
( lhs_atom22(B,A)
<=> subset(set_difference(A,B),A) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [A,B] :
( lhs_atom22(B,A)
| $false ),
inference(fold_definition,[status(thm)],[t36_xboole_1_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [A] :
( lhs_atom23(A)
<=> set_difference(A,empty_set) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [A] :
( lhs_atom23(A)
| $false ),
inference(fold_definition,[status(thm)],[t3_boole_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [B,A] :
( lhs_atom24(B,A)
<=> ~ element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [A,B] :
( lhs_atom24(B,A)
| subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_1,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [B,A] :
( lhs_atom25(B,A)
<=> element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [A,B] :
( lhs_atom25(B,A)
| ~ subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [A] :
( lhs_atom26(A)
<=> set_difference(empty_set,A) = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [A] :
( lhs_atom26(A)
| $false ),
inference(fold_definition,[status(thm)],[t4_boole_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [C,A] :
( lhs_atom27(C,A)
<=> element(A,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [A,B,C] :
( lhs_atom27(C,A)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(fold_definition,[status(thm)],[t4_subset_0,def_lhs_atom27]) ).
fof(to_be_clausified_40,plain,
! [A] :
( lhs_atom3(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom3]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X1,X2] :
( lhs_atom27(X3,X2)
| ~ ( in(X2,X1)
& element(X1,powerset(X3)) ) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_1,axiom,
! [X2] :
( lhs_atom4(X2)
| ! [X1] :
( element(X1,powerset(X2))
=> finite(X1) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_2,axiom,
! [X1,X2] :
( lhs_atom25(X1,X2)
| ~ subset(X2,X1) ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_3,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_4,axiom,
! [X1,X2] :
( lhs_atom4(X2)
| finite(set_difference(X2,X1)) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_5,axiom,
! [X1,X2] :
( lhs_atom20(X2)
| ~ ( subset(X2,X1)
& finite(X1) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_6,axiom,
! [X1,X2] :
( lhs_atom21(X1,X2)
| empty(X1)
| in(X2,X1) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_7,axiom,
! [X2] :
( lhs_atom2(X2)
| ! [X1] :
( element(X1,X2)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_8,axiom,
! [X2] :
( lhs_atom18(X2)
| ? [X1] :
( element(X1,powerset(X2))
& ~ empty(X1)
& finite(X1) ) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_9,axiom,
! [X2] :
( lhs_atom18(X2)
| ? [X1] :
( element(X1,powerset(X2))
& ~ empty(X1) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_10,axiom,
! [X1,X2] :
( lhs_atom24(X1,X2)
| subset(X2,X1) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_11,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| element(X2,X1) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_12,axiom,
! [X1,X2] :
( lhs_atom16(X1,X2)
| ~ ( relation(X2)
& relation(X1) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_13,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_14,axiom,
! [X2] :
( lhs_atom6(X2)
| ( ordinal(X2)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2) ) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_15,axiom,
! [X1,X2] :
( lhs_atom22(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_16,axiom,
! [X2] :
( lhs_atom3(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_17,axiom,
! [X2] :
( lhs_atom3(X2)
| relation(X2) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_18,axiom,
! [X2] :
( lhs_atom2(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_19,axiom,
! [X2] :
( lhs_atom3(X2)
| function(X2) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_20,axiom,
! [X2] :
( lhs_atom3(X2)
| finite(X2) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_21,axiom,
! [X2] :
( lhs_atom3(X2)
| X2 = empty_set ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_22,axiom,
! [X2] :
( lhs_atom26(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_23,axiom,
! [X2] :
( lhs_atom23(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_24,axiom,
! [X2] :
( lhs_atom19(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_25,axiom,
! [X2] :
( lhs_atom10(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_26,axiom,
( lhs_atom17
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_27,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_28,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_29,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_30,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_31,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_32,axiom,
( lhs_atom14
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_33,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_34,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_35,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_36,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_37,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_38,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_39,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_40,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_41,axiom,
! [X3,X1,X2] :
( lhs_atom27(X3,X2)
| ~ ( in(X2,X1)
& element(X1,powerset(X3)) ) ),
c_0_0 ).
fof(c_0_42,axiom,
! [X2] :
( lhs_atom4(X2)
| ! [X1] :
( element(X1,powerset(X2))
=> finite(X1) ) ),
c_0_1 ).
fof(c_0_43,plain,
! [X1,X2] :
( lhs_atom25(X1,X2)
| ~ subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_44,plain,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_45,axiom,
! [X1,X2] :
( lhs_atom4(X2)
| finite(set_difference(X2,X1)) ),
c_0_4 ).
fof(c_0_46,axiom,
! [X1,X2] :
( lhs_atom20(X2)
| ~ ( subset(X2,X1)
& finite(X1) ) ),
c_0_5 ).
fof(c_0_47,axiom,
! [X1,X2] :
( lhs_atom21(X1,X2)
| empty(X1)
| in(X2,X1) ),
c_0_6 ).
fof(c_0_48,axiom,
! [X2] :
( lhs_atom2(X2)
| ! [X1] :
( element(X1,X2)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ) ),
c_0_7 ).
fof(c_0_49,plain,
! [X2] :
( lhs_atom18(X2)
| ? [X1] :
( element(X1,powerset(X2))
& ~ empty(X1)
& finite(X1) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_50,plain,
! [X2] :
( lhs_atom18(X2)
| ? [X1] :
( element(X1,powerset(X2))
& ~ empty(X1) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_51,axiom,
! [X1,X2] :
( lhs_atom24(X1,X2)
| subset(X2,X1) ),
c_0_10 ).
fof(c_0_52,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| element(X2,X1) ),
c_0_11 ).
fof(c_0_53,axiom,
! [X1,X2] :
( lhs_atom16(X1,X2)
| ~ ( relation(X2)
& relation(X1) ) ),
c_0_12 ).
fof(c_0_54,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_13 ).
fof(c_0_55,axiom,
! [X2] :
( lhs_atom6(X2)
| ( ordinal(X2)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2) ) ) ),
c_0_14 ).
fof(c_0_56,plain,
! [X1,X2] : lhs_atom22(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_57,axiom,
! [X2] :
( lhs_atom3(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ),
c_0_16 ).
fof(c_0_58,axiom,
! [X2] :
( lhs_atom3(X2)
| relation(X2) ),
c_0_17 ).
fof(c_0_59,axiom,
! [X2] :
( lhs_atom2(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_18 ).
fof(c_0_60,axiom,
! [X2] :
( lhs_atom3(X2)
| function(X2) ),
c_0_19 ).
fof(c_0_61,axiom,
! [X2] :
( lhs_atom3(X2)
| finite(X2) ),
c_0_20 ).
fof(c_0_62,axiom,
! [X2] :
( lhs_atom3(X2)
| X2 = empty_set ),
c_0_21 ).
fof(c_0_63,plain,
! [X2] : lhs_atom26(X2),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_64,plain,
! [X2] : lhs_atom23(X2),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_65,plain,
! [X2] : lhs_atom19(X2),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_66,plain,
! [X2] : lhs_atom10(X2),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_67,plain,
lhs_atom17,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_68,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_69,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_70,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_71,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_72,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_73,plain,
lhs_atom14,
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_74,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_75,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_76,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_77,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_78,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_79,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_80,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_81,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_82,plain,
! [X4,X5,X6] :
( lhs_atom27(X4,X6)
| ~ in(X6,X5)
| ~ element(X5,powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
fof(c_0_83,plain,
! [X3,X4] :
( lhs_atom4(X3)
| ~ element(X4,powerset(X3))
| finite(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_84,plain,
! [X3,X4] :
( lhs_atom25(X3,X4)
| ~ subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_43]) ).
fof(c_0_85,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_44]) ).
fof(c_0_86,plain,
! [X3,X4] :
( lhs_atom4(X4)
| finite(set_difference(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_45]) ).
fof(c_0_87,plain,
! [X3,X4] :
( lhs_atom20(X4)
| ~ subset(X4,X3)
| ~ finite(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])]) ).
fof(c_0_88,plain,
! [X3,X4] :
( lhs_atom21(X3,X4)
| empty(X3)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_89,plain,
! [X3,X4] :
( ( epsilon_transitive(X4)
| ~ element(X4,X3)
| lhs_atom2(X3) )
& ( epsilon_connected(X4)
| ~ element(X4,X3)
| lhs_atom2(X3) )
& ( ordinal(X4)
| ~ element(X4,X3)
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
fof(c_0_90,plain,
! [X3] :
( ( element(esk2_1(X3),powerset(X3))
| lhs_atom18(X3) )
& ( ~ empty(esk2_1(X3))
| lhs_atom18(X3) )
& ( finite(esk2_1(X3))
| lhs_atom18(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_49])])]) ).
fof(c_0_91,plain,
! [X3] :
( ( element(esk1_1(X3),powerset(X3))
| lhs_atom18(X3) )
& ( ~ empty(esk1_1(X3))
| lhs_atom18(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_50])])]) ).
fof(c_0_92,plain,
! [X3,X4] :
( lhs_atom24(X3,X4)
| subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_93,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| element(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_52]) ).
fof(c_0_94,plain,
! [X3,X4] :
( lhs_atom16(X3,X4)
| ~ relation(X4)
| ~ relation(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])]) ).
fof(c_0_95,plain,
! [X3] :
( lhs_atom5(X3)
| ~ epsilon_transitive(X3)
| ~ epsilon_connected(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
fof(c_0_96,plain,
! [X3] :
( ( epsilon_transitive(X3)
| ~ ordinal(X3)
| lhs_atom6(X3) )
& ( epsilon_connected(X3)
| ~ ordinal(X3)
| lhs_atom6(X3) )
& ( ordinal(X3)
| ~ ordinal(X3)
| lhs_atom6(X3) )
& ( natural(X3)
| ~ ordinal(X3)
| lhs_atom6(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
fof(c_0_97,plain,
! [X3,X4] : lhs_atom22(X3,X4),
inference(variable_rename,[status(thm)],[c_0_56]) ).
fof(c_0_98,plain,
! [X3] :
( ( epsilon_transitive(X3)
| lhs_atom3(X3) )
& ( epsilon_connected(X3)
| lhs_atom3(X3) )
& ( ordinal(X3)
| lhs_atom3(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_57])]) ).
fof(c_0_99,plain,
! [X3] :
( lhs_atom3(X3)
| relation(X3) ),
inference(variable_rename,[status(thm)],[c_0_58]) ).
fof(c_0_100,plain,
! [X3] :
( ( epsilon_transitive(X3)
| lhs_atom2(X3) )
& ( epsilon_connected(X3)
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_59])]) ).
fof(c_0_101,plain,
! [X3] :
( lhs_atom3(X3)
| function(X3) ),
inference(variable_rename,[status(thm)],[c_0_60]) ).
fof(c_0_102,plain,
! [X3] :
( lhs_atom3(X3)
| finite(X3) ),
inference(variable_rename,[status(thm)],[c_0_61]) ).
fof(c_0_103,plain,
! [X3] :
( lhs_atom3(X3)
| X3 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_62]) ).
fof(c_0_104,plain,
! [X3] : lhs_atom26(X3),
inference(variable_rename,[status(thm)],[c_0_63]) ).
fof(c_0_105,plain,
! [X3] : lhs_atom23(X3),
inference(variable_rename,[status(thm)],[c_0_64]) ).
fof(c_0_106,plain,
! [X3] : lhs_atom19(X3),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_107,plain,
! [X3] : lhs_atom10(X3),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_108,plain,
lhs_atom17,
c_0_67 ).
fof(c_0_109,plain,
lhs_atom9,
c_0_68 ).
fof(c_0_110,plain,
lhs_atom8,
c_0_69 ).
fof(c_0_111,plain,
lhs_atom8,
c_0_70 ).
fof(c_0_112,plain,
lhs_atom7,
c_0_71 ).
fof(c_0_113,plain,
lhs_atom15,
c_0_72 ).
fof(c_0_114,plain,
lhs_atom14,
c_0_73 ).
fof(c_0_115,plain,
lhs_atom9,
c_0_74 ).
fof(c_0_116,plain,
lhs_atom13,
c_0_75 ).
fof(c_0_117,plain,
lhs_atom12,
c_0_76 ).
fof(c_0_118,plain,
lhs_atom11,
c_0_77 ).
fof(c_0_119,plain,
lhs_atom9,
c_0_78 ).
fof(c_0_120,plain,
lhs_atom9,
c_0_79 ).
fof(c_0_121,plain,
lhs_atom8,
c_0_80 ).
fof(c_0_122,plain,
lhs_atom7,
c_0_81 ).
cnf(c_0_123,plain,
( lhs_atom27(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_124,plain,
( finite(X1)
| lhs_atom4(X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_125,plain,
( lhs_atom25(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_126,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_127,plain,
( finite(set_difference(X1,X2))
| lhs_atom4(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_128,plain,
( lhs_atom20(X2)
| ~ finite(X1)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_129,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom21(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_130,plain,
( lhs_atom2(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_131,plain,
( lhs_atom2(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_132,plain,
( lhs_atom2(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_133,plain,
( lhs_atom18(X1)
| element(esk2_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_134,plain,
( lhs_atom18(X1)
| element(esk1_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_135,plain,
( subset(X1,X2)
| lhs_atom24(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_136,plain,
( element(X1,X2)
| lhs_atom1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_137,plain,
( lhs_atom16(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_138,plain,
( lhs_atom18(X1)
| ~ empty(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_139,plain,
( lhs_atom18(X1)
| ~ empty(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_140,plain,
( lhs_atom5(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_141,plain,
( lhs_atom6(X1)
| epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_142,plain,
( lhs_atom6(X1)
| epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_143,plain,
( lhs_atom6(X1)
| ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_144,plain,
( lhs_atom6(X1)
| natural(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_145,plain,
( lhs_atom18(X1)
| finite(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_146,plain,
lhs_atom22(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_147,plain,
( lhs_atom3(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_148,plain,
( lhs_atom3(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_149,plain,
( lhs_atom3(X1)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_150,plain,
( relation(X1)
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_151,plain,
( lhs_atom2(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_152,plain,
( lhs_atom2(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_153,plain,
( function(X1)
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_154,plain,
( finite(X1)
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_155,plain,
( X1 = empty_set
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_156,plain,
lhs_atom26(X1),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_157,plain,
lhs_atom23(X1),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_158,plain,
lhs_atom19(X1),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_159,plain,
lhs_atom10(X1),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_160,plain,
lhs_atom17,
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_161,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_162,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_163,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_164,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_165,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_166,plain,
lhs_atom14,
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_167,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_168,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_169,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_170,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_171,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_172,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_173,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_174,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_175,plain,
( lhs_atom27(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
c_0_123,
[final] ).
cnf(c_0_176,plain,
( finite(X1)
| lhs_atom4(X2)
| ~ element(X1,powerset(X2)) ),
c_0_124,
[final] ).
cnf(c_0_177,plain,
( lhs_atom25(X2,X1)
| ~ subset(X1,X2) ),
c_0_125,
[final] ).
cnf(c_0_178,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
c_0_126,
[final] ).
cnf(c_0_179,plain,
( finite(set_difference(X1,X2))
| lhs_atom4(X1) ),
c_0_127,
[final] ).
cnf(c_0_180,plain,
( lhs_atom20(X2)
| ~ finite(X1)
| ~ subset(X2,X1) ),
c_0_128,
[final] ).
cnf(c_0_181,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom21(X2,X1) ),
c_0_129,
[final] ).
cnf(c_0_182,plain,
( lhs_atom2(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
c_0_130,
[final] ).
cnf(c_0_183,plain,
( lhs_atom2(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
c_0_131,
[final] ).
cnf(c_0_184,plain,
( lhs_atom2(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
c_0_132,
[final] ).
cnf(c_0_185,plain,
( lhs_atom18(X1)
| element(esk2_1(X1),powerset(X1)) ),
c_0_133,
[final] ).
cnf(c_0_186,plain,
( lhs_atom18(X1)
| element(esk1_1(X1),powerset(X1)) ),
c_0_134,
[final] ).
cnf(c_0_187,plain,
( subset(X1,X2)
| lhs_atom24(X2,X1) ),
c_0_135,
[final] ).
cnf(c_0_188,plain,
( element(X1,X2)
| lhs_atom1(X2,X1) ),
c_0_136,
[final] ).
cnf(c_0_189,plain,
( lhs_atom16(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_137,
[final] ).
cnf(c_0_190,plain,
( lhs_atom18(X1)
| ~ empty(esk2_1(X1)) ),
c_0_138,
[final] ).
cnf(c_0_191,plain,
( lhs_atom18(X1)
| ~ empty(esk1_1(X1)) ),
c_0_139,
[final] ).
cnf(c_0_192,plain,
( lhs_atom5(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_140,
[final] ).
cnf(c_0_193,plain,
( lhs_atom6(X1)
| epsilon_transitive(X1)
| ~ ordinal(X1) ),
c_0_141,
[final] ).
cnf(c_0_194,plain,
( lhs_atom6(X1)
| epsilon_connected(X1)
| ~ ordinal(X1) ),
c_0_142,
[final] ).
cnf(c_0_195,plain,
( lhs_atom6(X1)
| ordinal(X1)
| ~ ordinal(X1) ),
c_0_143,
[final] ).
cnf(c_0_196,plain,
( lhs_atom6(X1)
| natural(X1)
| ~ ordinal(X1) ),
c_0_144,
[final] ).
cnf(c_0_197,plain,
( lhs_atom18(X1)
| finite(esk2_1(X1)) ),
c_0_145,
[final] ).
cnf(c_0_198,plain,
lhs_atom22(X1,X2),
c_0_146,
[final] ).
cnf(c_0_199,plain,
( lhs_atom3(X1)
| epsilon_transitive(X1) ),
c_0_147,
[final] ).
cnf(c_0_200,plain,
( lhs_atom3(X1)
| epsilon_connected(X1) ),
c_0_148,
[final] ).
cnf(c_0_201,plain,
( lhs_atom3(X1)
| ordinal(X1) ),
c_0_149,
[final] ).
cnf(c_0_202,plain,
( relation(X1)
| lhs_atom3(X1) ),
c_0_150,
[final] ).
cnf(c_0_203,plain,
( lhs_atom2(X1)
| epsilon_transitive(X1) ),
c_0_151,
[final] ).
cnf(c_0_204,plain,
( lhs_atom2(X1)
| epsilon_connected(X1) ),
c_0_152,
[final] ).
cnf(c_0_205,plain,
( function(X1)
| lhs_atom3(X1) ),
c_0_153,
[final] ).
cnf(c_0_206,plain,
( finite(X1)
| lhs_atom3(X1) ),
c_0_154,
[final] ).
cnf(c_0_207,plain,
( X1 = empty_set
| lhs_atom3(X1) ),
c_0_155,
[final] ).
cnf(c_0_208,plain,
lhs_atom26(X1),
c_0_156,
[final] ).
cnf(c_0_209,plain,
lhs_atom23(X1),
c_0_157,
[final] ).
cnf(c_0_210,plain,
lhs_atom19(X1),
c_0_158,
[final] ).
cnf(c_0_211,plain,
lhs_atom10(X1),
c_0_159,
[final] ).
cnf(c_0_212,plain,
lhs_atom17,
c_0_160,
[final] ).
cnf(c_0_213,plain,
lhs_atom9,
c_0_161,
[final] ).
cnf(c_0_214,plain,
lhs_atom8,
c_0_162,
[final] ).
cnf(c_0_215,plain,
lhs_atom8,
c_0_163,
[final] ).
cnf(c_0_216,plain,
lhs_atom7,
c_0_164,
[final] ).
cnf(c_0_217,plain,
lhs_atom15,
c_0_165,
[final] ).
cnf(c_0_218,plain,
lhs_atom14,
c_0_166,
[final] ).
cnf(c_0_219,plain,
lhs_atom9,
c_0_167,
[final] ).
cnf(c_0_220,plain,
lhs_atom13,
c_0_168,
[final] ).
cnf(c_0_221,plain,
lhs_atom12,
c_0_169,
[final] ).
cnf(c_0_222,plain,
lhs_atom11,
c_0_170,
[final] ).
cnf(c_0_223,plain,
lhs_atom9,
c_0_171,
[final] ).
cnf(c_0_224,plain,
lhs_atom9,
c_0_172,
[final] ).
cnf(c_0_225,plain,
lhs_atom8,
c_0_173,
[final] ).
cnf(c_0_226,plain,
lhs_atom7,
c_0_174,
[final] ).
% End CNF derivation
cnf(c_0_175_0,axiom,
( element(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_175,def_lhs_atom27]) ).
cnf(c_0_176_0,axiom,
( ~ finite(X2)
| finite(X1)
| ~ element(X1,powerset(X2)) ),
inference(unfold_definition,[status(thm)],[c_0_176,def_lhs_atom4]) ).
cnf(c_0_177_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_177,def_lhs_atom25]) ).
cnf(c_0_178_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_178,def_lhs_atom1]) ).
cnf(c_0_179_0,axiom,
( ~ finite(X1)
| finite(set_difference(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_179,def_lhs_atom4]) ).
cnf(c_0_180_0,axiom,
( finite(X2)
| ~ finite(X1)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_180,def_lhs_atom20]) ).
cnf(c_0_181_0,axiom,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(unfold_definition,[status(thm)],[c_0_181,def_lhs_atom21]) ).
cnf(c_0_182_0,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_182,def_lhs_atom2]) ).
cnf(c_0_183_0,axiom,
( ~ ordinal(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_183,def_lhs_atom2]) ).
cnf(c_0_184_0,axiom,
( ~ ordinal(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_184,def_lhs_atom2]) ).
cnf(c_0_185_0,axiom,
( empty(X1)
| element(sk1_esk2_1(X1),powerset(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_185,def_lhs_atom18]) ).
cnf(c_0_186_0,axiom,
( empty(X1)
| element(sk1_esk1_1(X1),powerset(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_186,def_lhs_atom18]) ).
cnf(c_0_187_0,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_187,def_lhs_atom24]) ).
cnf(c_0_188_0,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_188,def_lhs_atom1]) ).
cnf(c_0_189_0,axiom,
( relation(set_difference(X2,X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(unfold_definition,[status(thm)],[c_0_189,def_lhs_atom16]) ).
cnf(c_0_190_0,axiom,
( empty(X1)
| ~ empty(sk1_esk2_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_190,def_lhs_atom18]) ).
cnf(c_0_191_0,axiom,
( empty(X1)
| ~ empty(sk1_esk1_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_191,def_lhs_atom18]) ).
cnf(c_0_192_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_192,def_lhs_atom5]) ).
cnf(c_0_193_0,axiom,
( ~ element(X1,positive_rationals)
| epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(unfold_definition,[status(thm)],[c_0_193,def_lhs_atom6]) ).
cnf(c_0_194_0,axiom,
( ~ element(X1,positive_rationals)
| epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(unfold_definition,[status(thm)],[c_0_194,def_lhs_atom6]) ).
cnf(c_0_195_0,axiom,
( ~ element(X1,positive_rationals)
| ordinal(X1)
| ~ ordinal(X1) ),
inference(unfold_definition,[status(thm)],[c_0_195,def_lhs_atom6]) ).
cnf(c_0_196_0,axiom,
( ~ element(X1,positive_rationals)
| natural(X1)
| ~ ordinal(X1) ),
inference(unfold_definition,[status(thm)],[c_0_196,def_lhs_atom6]) ).
cnf(c_0_197_0,axiom,
( empty(X1)
| finite(sk1_esk2_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_197,def_lhs_atom18]) ).
cnf(c_0_199_0,axiom,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_199,def_lhs_atom3]) ).
cnf(c_0_200_0,axiom,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(unfold_definition,[status(thm)],[c_0_200,def_lhs_atom3]) ).
cnf(c_0_201_0,axiom,
( ~ empty(X1)
| ordinal(X1) ),
inference(unfold_definition,[status(thm)],[c_0_201,def_lhs_atom3]) ).
cnf(c_0_202_0,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_202,def_lhs_atom3]) ).
cnf(c_0_203_0,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_203,def_lhs_atom2]) ).
cnf(c_0_204_0,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(unfold_definition,[status(thm)],[c_0_204,def_lhs_atom2]) ).
cnf(c_0_205_0,axiom,
( ~ empty(X1)
| function(X1) ),
inference(unfold_definition,[status(thm)],[c_0_205,def_lhs_atom3]) ).
cnf(c_0_206_0,axiom,
( ~ empty(X1)
| finite(X1) ),
inference(unfold_definition,[status(thm)],[c_0_206,def_lhs_atom3]) ).
cnf(c_0_207_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_207,def_lhs_atom3]) ).
cnf(c_0_198_0,axiom,
subset(set_difference(X2,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_198,def_lhs_atom22]) ).
cnf(c_0_208_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(unfold_definition,[status(thm)],[c_0_208,def_lhs_atom26]) ).
cnf(c_0_209_0,axiom,
set_difference(X1,empty_set) = X1,
inference(unfold_definition,[status(thm)],[c_0_209,def_lhs_atom23]) ).
cnf(c_0_210_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_210,def_lhs_atom19]) ).
cnf(c_0_211_0,axiom,
~ empty(powerset(X1)),
inference(unfold_definition,[status(thm)],[c_0_211,def_lhs_atom10]) ).
cnf(c_0_212_0,axiom,
~ empty(positive_rationals),
inference(unfold_definition,[status(thm)],[c_0_212,def_lhs_atom17]) ).
cnf(c_0_213_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_213,def_lhs_atom9]) ).
cnf(c_0_214_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_214,def_lhs_atom8]) ).
cnf(c_0_215_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_215,def_lhs_atom8]) ).
cnf(c_0_216_0,axiom,
relation_empty_yielding(empty_set),
inference(unfold_definition,[status(thm)],[c_0_216,def_lhs_atom7]) ).
cnf(c_0_217_0,axiom,
function(empty_set),
inference(unfold_definition,[status(thm)],[c_0_217,def_lhs_atom15]) ).
cnf(c_0_218_0,axiom,
one_to_one(empty_set),
inference(unfold_definition,[status(thm)],[c_0_218,def_lhs_atom14]) ).
cnf(c_0_219_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_219,def_lhs_atom9]) ).
cnf(c_0_220_0,axiom,
epsilon_transitive(empty_set),
inference(unfold_definition,[status(thm)],[c_0_220,def_lhs_atom13]) ).
cnf(c_0_221_0,axiom,
epsilon_connected(empty_set),
inference(unfold_definition,[status(thm)],[c_0_221,def_lhs_atom12]) ).
cnf(c_0_222_0,axiom,
ordinal(empty_set),
inference(unfold_definition,[status(thm)],[c_0_222,def_lhs_atom11]) ).
cnf(c_0_223_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_223,def_lhs_atom9]) ).
cnf(c_0_224_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_224,def_lhs_atom9]) ).
cnf(c_0_225_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_225,def_lhs_atom8]) ).
cnf(c_0_226_0,axiom,
relation_empty_yielding(empty_set),
inference(unfold_definition,[status(thm)],[c_0_226,def_lhs_atom7]) ).
% 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] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('<stdin>',rc2_finset_1) ).
fof(c_0_3_004,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_4_005,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_5_006,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_6_007,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('<stdin>',cc2_arytm_3) ).
fof(c_0_7_008,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_8_009,axiom,
? [X1] :
( element(X1,positive_rationals)
& ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc2_arytm_3) ).
fof(c_0_9_010,axiom,
? [X1] :
( element(X1,positive_rationals)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('<stdin>',rc3_arytm_3) ).
fof(c_0_10_011,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('<stdin>',rc1_arytm_3) ).
fof(c_0_11_012,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('<stdin>',rc1_finset_1) ).
fof(c_0_12_013,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_13_014,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_14_015,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc3_ordinal1) ).
fof(c_0_15_016,axiom,
? [X1] :
( relation(X1)
& function(X1)
& function_yielding(X1) ),
file('<stdin>',rc1_funcop_1) ).
fof(c_0_16_017,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_17_018,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc1_ordinal1) ).
fof(c_0_18_019,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& being_limit_ordinal(X1) ),
file('<stdin>',rc1_ordinal2) ).
fof(c_0_19_020,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_20_021,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_21_022,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_22_023,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc2_ordinal1) ).
fof(c_0_23_024,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1)
& ordinal_yielding(X1) ),
file('<stdin>',rc2_ordinal2) ).
fof(c_0_24_025,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_25_026,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_26_027,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('<stdin>',rc4_funct_1) ).
fof(c_0_27_028,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
file('<stdin>',rc4_ordinal1) ).
fof(c_0_28_029,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('<stdin>',rc5_funct_1) ).
fof(c_0_29_030,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_0 ).
fof(c_0_30_031,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_1 ).
fof(c_0_31_032,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
c_0_2 ).
fof(c_0_32_033,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_3 ).
fof(c_0_33_034,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_4 ).
fof(c_0_34_035,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_5 ).
fof(c_0_35_036,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
c_0_6 ).
fof(c_0_36_037,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_7 ).
fof(c_0_37_038,plain,
? [X1] :
( element(X1,positive_rationals)
& ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_38_039,axiom,
? [X1] :
( element(X1,positive_rationals)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
c_0_9 ).
fof(c_0_39_040,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_40_041,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_41_042,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_42_043,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_43_044,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_44_045,axiom,
? [X1] :
( relation(X1)
& function(X1)
& function_yielding(X1) ),
c_0_15 ).
fof(c_0_45_046,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_16 ).
fof(c_0_46_047,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_17 ).
fof(c_0_47_048,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& being_limit_ordinal(X1) ),
c_0_18 ).
fof(c_0_48_049,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_19 ).
fof(c_0_49_050,axiom,
? [X1] : empty(X1),
c_0_20 ).
fof(c_0_50_051,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_21 ).
fof(c_0_51_052,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_22 ).
fof(c_0_52_053,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1)
& ordinal_yielding(X1) ),
c_0_23 ).
fof(c_0_53_054,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_24 ).
fof(c_0_54_055,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_25 ).
fof(c_0_55_056,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
c_0_26 ).
fof(c_0_56_057,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
c_0_27 ).
fof(c_0_57_058,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
c_0_28 ).
fof(c_0_58_059,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_29])])])]) ).
fof(c_0_59_060,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_60_061,plain,
! [X3] :
( element(esk14_1(X3),powerset(X3))
& empty(esk14_1(X3))
& relation(esk14_1(X3))
& function(esk14_1(X3))
& one_to_one(esk14_1(X3))
& epsilon_transitive(esk14_1(X3))
& epsilon_connected(esk14_1(X3))
& ordinal(esk14_1(X3))
& natural(esk14_1(X3))
& finite(esk14_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_61_062,plain,
! [X3] :
( element(esk9_1(X3),powerset(X3))
& empty(esk9_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).
fof(c_0_62_063,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_33])])]) ).
fof(c_0_63_064,plain,
! [X3] : element(esk24_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
fof(c_0_64_065,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ empty(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ empty(X2)
| ~ ordinal(X2) )
& ( ordinal(X2)
| ~ empty(X2)
| ~ ordinal(X2) )
& ( natural(X2)
| ~ empty(X2)
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_65_066,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_36])])])]) ).
fof(c_0_66_067,plain,
( element(esk15_0,positive_rationals)
& ~ empty(esk15_0)
& epsilon_transitive(esk15_0)
& epsilon_connected(esk15_0)
& ordinal(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
fof(c_0_67_068,plain,
( element(esk7_0,positive_rationals)
& empty(esk7_0)
& epsilon_transitive(esk7_0)
& epsilon_connected(esk7_0)
& ordinal(esk7_0)
& natural(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
fof(c_0_68_069,plain,
( ~ empty(esk23_0)
& epsilon_transitive(esk23_0)
& epsilon_connected(esk23_0)
& ordinal(esk23_0)
& natural(esk23_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_39])]) ).
fof(c_0_69_070,plain,
( ~ empty(esk22_0)
& finite(esk22_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
fof(c_0_70_071,plain,
( ~ empty(esk10_0)
& relation(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_41])]) ).
fof(c_0_71_072,plain,
~ empty(esk8_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_42])]) ).
fof(c_0_72_073,plain,
( ~ empty(esk5_0)
& epsilon_transitive(esk5_0)
& epsilon_connected(esk5_0)
& ordinal(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_43])]) ).
fof(c_0_73_074,plain,
( relation(esk21_0)
& function(esk21_0)
& function_yielding(esk21_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_44])]) ).
fof(c_0_74_075,plain,
( relation(esk20_0)
& function(esk20_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_45])]) ).
fof(c_0_75_076,plain,
( epsilon_transitive(esk19_0)
& epsilon_connected(esk19_0)
& ordinal(esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_46])]) ).
fof(c_0_76_077,plain,
( epsilon_transitive(esk18_0)
& epsilon_connected(esk18_0)
& ordinal(esk18_0)
& being_limit_ordinal(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_47])]) ).
fof(c_0_77_078,plain,
( empty(esk17_0)
& relation(esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
fof(c_0_78_079,plain,
empty(esk16_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_49])]) ).
fof(c_0_79_080,plain,
( relation(esk13_0)
& empty(esk13_0)
& function(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_50])]) ).
fof(c_0_80_081,plain,
( relation(esk12_0)
& function(esk12_0)
& one_to_one(esk12_0)
& empty(esk12_0)
& epsilon_transitive(esk12_0)
& epsilon_connected(esk12_0)
& ordinal(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_51])]) ).
fof(c_0_81_082,plain,
( relation(esk11_0)
& function(esk11_0)
& transfinite_sequence(esk11_0)
& ordinal_yielding(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_52])]) ).
fof(c_0_82_083,plain,
( relation(esk6_0)
& function(esk6_0)
& one_to_one(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_53])]) ).
fof(c_0_83_084,plain,
( relation(esk4_0)
& relation_empty_yielding(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_54])]) ).
fof(c_0_84_085,plain,
( relation(esk3_0)
& relation_empty_yielding(esk3_0)
& function(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_55])]) ).
fof(c_0_85_086,plain,
( relation(esk2_0)
& function(esk2_0)
& transfinite_sequence(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_56])]) ).
fof(c_0_86_087,plain,
( relation(esk1_0)
& relation_non_empty(esk1_0)
& function(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_57])]) ).
cnf(c_0_87_088,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_88_089,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_89_090,plain,
element(esk14_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_90_091,plain,
element(esk9_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_91_092,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_92_093,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_93_094,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_94_095,plain,
element(esk24_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_95_096,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_96_097,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_97_098,plain,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_98_099,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_99_100,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_100_101,plain,
element(esk15_0,positive_rationals),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_101_102,plain,
element(esk7_0,positive_rationals),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_102_103,plain,
empty(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_103_104,plain,
relation(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_104_105,plain,
function(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_105_106,plain,
one_to_one(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_106_107,plain,
epsilon_transitive(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_107_108,plain,
epsilon_connected(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_108_109,plain,
ordinal(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_109_110,plain,
natural(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_110_111,plain,
finite(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_111_112,plain,
empty(esk9_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_112_113,plain,
~ empty(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_113_114,plain,
~ empty(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_114_115,plain,
~ empty(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_115_116,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_116_117,plain,
~ empty(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_117_118,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_118_119,plain,
epsilon_transitive(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_119_120,plain,
epsilon_connected(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_120_121,plain,
ordinal(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_121_122,plain,
natural(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_122_123,plain,
finite(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_123_124,plain,
relation(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_124_125,plain,
function(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_125_126,plain,
function_yielding(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_126_127,plain,
relation(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_127_128,plain,
function(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_128_129,plain,
epsilon_transitive(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_129_130,plain,
epsilon_connected(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_130_131,plain,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_131_132,plain,
epsilon_transitive(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_132_133,plain,
epsilon_connected(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_133_134,plain,
ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_134_135,plain,
being_limit_ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_135_136,plain,
empty(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_136_137,plain,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_137_138,plain,
empty(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_138_139,plain,
epsilon_transitive(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_139_140,plain,
epsilon_connected(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_140_141,plain,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_141_142,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_142_143,plain,
empty(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_143_144,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_144_145,plain,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_145_146,plain,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_146_147,plain,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_147_148,plain,
empty(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_148_149,plain,
epsilon_transitive(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_149_150,plain,
epsilon_connected(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_150_151,plain,
ordinal(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_151_152,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_152_153,plain,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_153_154,plain,
transfinite_sequence(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_154_155,plain,
ordinal_yielding(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_155_156,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_156_157,plain,
empty(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_157_158,plain,
epsilon_transitive(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_158_159,plain,
epsilon_connected(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_159_160,plain,
ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_160_161,plain,
natural(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_161_162,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_162_163,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_163_164,plain,
one_to_one(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_164_165,plain,
epsilon_transitive(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_165_166,plain,
epsilon_connected(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_166_167,plain,
ordinal(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_167_168,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_168_169,plain,
relation_empty_yielding(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_169_170,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_170_171,plain,
relation_empty_yielding(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_171_172,plain,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_172_173,plain,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_173_174,plain,
function(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_174_175,plain,
transfinite_sequence(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_175_176,plain,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_176_177,plain,
relation_non_empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_177_178,plain,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_178_179,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_87,
[final] ).
cnf(c_0_179_180,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_88,
[final] ).
cnf(c_0_180_181,plain,
element(esk14_1(X1),powerset(X1)),
c_0_89,
[final] ).
cnf(c_0_181_182,plain,
element(esk9_1(X1),powerset(X1)),
c_0_90,
[final] ).
cnf(c_0_182_183,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_91,
[final] ).
cnf(c_0_183_184,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_92,
[final] ).
cnf(c_0_184_185,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_93,
[final] ).
cnf(c_0_185_186,plain,
element(esk24_1(X1),X1),
c_0_94,
[final] ).
cnf(c_0_186_187,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_95,
[final] ).
cnf(c_0_187_188,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_96,
[final] ).
cnf(c_0_188_189,plain,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_97,
[final] ).
cnf(c_0_189_190,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
c_0_98,
[final] ).
cnf(c_0_190_191,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_99,
[final] ).
cnf(c_0_191_192,plain,
element(esk15_0,positive_rationals),
c_0_100,
[final] ).
cnf(c_0_192_193,plain,
element(esk7_0,positive_rationals),
c_0_101,
[final] ).
cnf(c_0_193_194,plain,
empty(esk14_1(X1)),
c_0_102,
[final] ).
cnf(c_0_194_195,plain,
relation(esk14_1(X1)),
c_0_103,
[final] ).
cnf(c_0_195_196,plain,
function(esk14_1(X1)),
c_0_104,
[final] ).
cnf(c_0_196_197,plain,
one_to_one(esk14_1(X1)),
c_0_105,
[final] ).
cnf(c_0_197_198,plain,
epsilon_transitive(esk14_1(X1)),
c_0_106,
[final] ).
cnf(c_0_198_199,plain,
epsilon_connected(esk14_1(X1)),
c_0_107,
[final] ).
cnf(c_0_199_200,plain,
ordinal(esk14_1(X1)),
c_0_108,
[final] ).
cnf(c_0_200_201,plain,
natural(esk14_1(X1)),
c_0_109,
[final] ).
cnf(c_0_201_202,plain,
finite(esk14_1(X1)),
c_0_110,
[final] ).
cnf(c_0_202_203,plain,
empty(esk9_1(X1)),
c_0_111,
[final] ).
cnf(c_0_203_204,plain,
~ empty(esk23_0),
c_0_112,
[final] ).
cnf(c_0_204_205,plain,
~ empty(esk22_0),
c_0_113,
[final] ).
cnf(c_0_205_206,plain,
~ empty(esk15_0),
c_0_114,
[final] ).
cnf(c_0_206_207,plain,
~ empty(esk10_0),
c_0_115,
[final] ).
cnf(c_0_207_208,plain,
~ empty(esk8_0),
c_0_116,
[final] ).
cnf(c_0_208_209,plain,
~ empty(esk5_0),
c_0_117,
[final] ).
cnf(c_0_209_210,plain,
epsilon_transitive(esk23_0),
c_0_118,
[final] ).
cnf(c_0_210_211,plain,
epsilon_connected(esk23_0),
c_0_119,
[final] ).
cnf(c_0_211_212,plain,
ordinal(esk23_0),
c_0_120,
[final] ).
cnf(c_0_212_213,plain,
natural(esk23_0),
c_0_121,
[final] ).
cnf(c_0_213_214,plain,
finite(esk22_0),
c_0_122,
[final] ).
cnf(c_0_214_215,plain,
relation(esk21_0),
c_0_123,
[final] ).
cnf(c_0_215_216,plain,
function(esk21_0),
c_0_124,
[final] ).
cnf(c_0_216_217,plain,
function_yielding(esk21_0),
c_0_125,
[final] ).
cnf(c_0_217_218,plain,
relation(esk20_0),
c_0_126,
[final] ).
cnf(c_0_218_219,plain,
function(esk20_0),
c_0_127,
[final] ).
cnf(c_0_219_220,plain,
epsilon_transitive(esk19_0),
c_0_128,
[final] ).
cnf(c_0_220_221,plain,
epsilon_connected(esk19_0),
c_0_129,
[final] ).
cnf(c_0_221_222,plain,
ordinal(esk19_0),
c_0_130,
[final] ).
cnf(c_0_222_223,plain,
epsilon_transitive(esk18_0),
c_0_131,
[final] ).
cnf(c_0_223_224,plain,
epsilon_connected(esk18_0),
c_0_132,
[final] ).
cnf(c_0_224_225,plain,
ordinal(esk18_0),
c_0_133,
[final] ).
cnf(c_0_225_226,plain,
being_limit_ordinal(esk18_0),
c_0_134,
[final] ).
cnf(c_0_226_227,plain,
empty(esk17_0),
c_0_135,
[final] ).
cnf(c_0_227,plain,
relation(esk17_0),
c_0_136,
[final] ).
cnf(c_0_228,plain,
empty(esk16_0),
c_0_137,
[final] ).
cnf(c_0_229,plain,
epsilon_transitive(esk15_0),
c_0_138,
[final] ).
cnf(c_0_230,plain,
epsilon_connected(esk15_0),
c_0_139,
[final] ).
cnf(c_0_231,plain,
ordinal(esk15_0),
c_0_140,
[final] ).
cnf(c_0_232,plain,
relation(esk13_0),
c_0_141,
[final] ).
cnf(c_0_233,plain,
empty(esk13_0),
c_0_142,
[final] ).
cnf(c_0_234,plain,
function(esk13_0),
c_0_143,
[final] ).
cnf(c_0_235,plain,
relation(esk12_0),
c_0_144,
[final] ).
cnf(c_0_236,plain,
function(esk12_0),
c_0_145,
[final] ).
cnf(c_0_237,plain,
one_to_one(esk12_0),
c_0_146,
[final] ).
cnf(c_0_238,plain,
empty(esk12_0),
c_0_147,
[final] ).
cnf(c_0_239,plain,
epsilon_transitive(esk12_0),
c_0_148,
[final] ).
cnf(c_0_240,plain,
epsilon_connected(esk12_0),
c_0_149,
[final] ).
cnf(c_0_241,plain,
ordinal(esk12_0),
c_0_150,
[final] ).
cnf(c_0_242,plain,
relation(esk11_0),
c_0_151,
[final] ).
cnf(c_0_243,plain,
function(esk11_0),
c_0_152,
[final] ).
cnf(c_0_244,plain,
transfinite_sequence(esk11_0),
c_0_153,
[final] ).
cnf(c_0_245,plain,
ordinal_yielding(esk11_0),
c_0_154,
[final] ).
cnf(c_0_246,plain,
relation(esk10_0),
c_0_155,
[final] ).
cnf(c_0_247,plain,
empty(esk7_0),
c_0_156,
[final] ).
cnf(c_0_248,plain,
epsilon_transitive(esk7_0),
c_0_157,
[final] ).
cnf(c_0_249,plain,
epsilon_connected(esk7_0),
c_0_158,
[final] ).
cnf(c_0_250,plain,
ordinal(esk7_0),
c_0_159,
[final] ).
cnf(c_0_251,plain,
natural(esk7_0),
c_0_160,
[final] ).
cnf(c_0_252,plain,
relation(esk6_0),
c_0_161,
[final] ).
cnf(c_0_253,plain,
function(esk6_0),
c_0_162,
[final] ).
cnf(c_0_254,plain,
one_to_one(esk6_0),
c_0_163,
[final] ).
cnf(c_0_255,plain,
epsilon_transitive(esk5_0),
c_0_164,
[final] ).
cnf(c_0_256,plain,
epsilon_connected(esk5_0),
c_0_165,
[final] ).
cnf(c_0_257,plain,
ordinal(esk5_0),
c_0_166,
[final] ).
cnf(c_0_258,plain,
relation(esk4_0),
c_0_167,
[final] ).
cnf(c_0_259,plain,
relation_empty_yielding(esk4_0),
c_0_168,
[final] ).
cnf(c_0_260,plain,
relation(esk3_0),
c_0_169,
[final] ).
cnf(c_0_261,plain,
relation_empty_yielding(esk3_0),
c_0_170,
[final] ).
cnf(c_0_262,plain,
function(esk3_0),
c_0_171,
[final] ).
cnf(c_0_263,plain,
relation(esk2_0),
c_0_172,
[final] ).
cnf(c_0_264,plain,
function(esk2_0),
c_0_173,
[final] ).
cnf(c_0_265,plain,
transfinite_sequence(esk2_0),
c_0_174,
[final] ).
cnf(c_0_266,plain,
relation(esk1_0),
c_0_175,
[final] ).
cnf(c_0_267,plain,
relation_non_empty(esk1_0),
c_0_176,
[final] ).
cnf(c_0_268,plain,
function(esk1_0),
c_0_177,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_178_1,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_178]) ).
cnf(c_0_178_2,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_178]) ).
cnf(c_0_178_3,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_178]) ).
cnf(c_0_179_1,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_179]) ).
cnf(c_0_179_2,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_179]) ).
cnf(c_0_182_1,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_182_2,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_182_3,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_182_4,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_182]) ).
cnf(c_0_183_1,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_183]) ).
cnf(c_0_183_2,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_183]) ).
cnf(c_0_183_3,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_183]) ).
cnf(c_0_183_4,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_183]) ).
cnf(c_0_184_1,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_184]) ).
cnf(c_0_184_2,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_184]) ).
cnf(c_0_184_3,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_184]) ).
cnf(c_0_184_4,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_184]) ).
cnf(c_0_186_1,axiom,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_186]) ).
cnf(c_0_186_2,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_186]) ).
cnf(c_0_186_3,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_186]) ).
cnf(c_0_187_1,axiom,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_187_2,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_187_3,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(literals_permutation,[status(thm)],[c_0_187]) ).
cnf(c_0_188_1,axiom,
( ordinal(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_188_2,axiom,
( ~ ordinal(X1)
| ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_188_3,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| ordinal(X1) ),
inference(literals_permutation,[status(thm)],[c_0_188]) ).
cnf(c_0_189_1,axiom,
( natural(X1)
| ~ ordinal(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_189_2,axiom,
( ~ ordinal(X1)
| natural(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_189_3,axiom,
( ~ empty(X1)
| ~ ordinal(X1)
| natural(X1) ),
inference(literals_permutation,[status(thm)],[c_0_189]) ).
cnf(c_0_190_1,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_190_2,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_190_3,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_190]) ).
cnf(c_0_203_1,axiom,
~ empty(sk2_esk23_0),
inference(literals_permutation,[status(thm)],[c_0_203]) ).
cnf(c_0_204_1,axiom,
~ empty(sk2_esk22_0),
inference(literals_permutation,[status(thm)],[c_0_204]) ).
cnf(c_0_205_1,axiom,
~ empty(sk2_esk15_0),
inference(literals_permutation,[status(thm)],[c_0_205]) ).
cnf(c_0_206_1,axiom,
~ empty(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_206]) ).
cnf(c_0_207_1,axiom,
~ empty(sk2_esk8_0),
inference(literals_permutation,[status(thm)],[c_0_207]) ).
cnf(c_0_208_1,axiom,
~ empty(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_208]) ).
cnf(c_0_180_1,axiom,
element(sk2_esk14_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_180]) ).
cnf(c_0_181_1,axiom,
element(sk2_esk9_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_181]) ).
cnf(c_0_185_1,axiom,
element(sk2_esk24_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_185]) ).
cnf(c_0_191_1,axiom,
element(sk2_esk15_0,positive_rationals),
inference(literals_permutation,[status(thm)],[c_0_191]) ).
cnf(c_0_192_1,axiom,
element(sk2_esk7_0,positive_rationals),
inference(literals_permutation,[status(thm)],[c_0_192]) ).
cnf(c_0_193_1,axiom,
empty(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_193]) ).
cnf(c_0_194_1,axiom,
relation(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_194]) ).
cnf(c_0_195_1,axiom,
function(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_195]) ).
cnf(c_0_196_1,axiom,
one_to_one(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_196]) ).
cnf(c_0_197_1,axiom,
epsilon_transitive(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_197]) ).
cnf(c_0_198_1,axiom,
epsilon_connected(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_198]) ).
cnf(c_0_199_1,axiom,
ordinal(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_199]) ).
cnf(c_0_200_1,axiom,
natural(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_200]) ).
cnf(c_0_201_1,axiom,
finite(sk2_esk14_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_201]) ).
cnf(c_0_202_1,axiom,
empty(sk2_esk9_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_202]) ).
cnf(c_0_209_1,axiom,
epsilon_transitive(sk2_esk23_0),
inference(literals_permutation,[status(thm)],[c_0_209]) ).
cnf(c_0_210_1,axiom,
epsilon_connected(sk2_esk23_0),
inference(literals_permutation,[status(thm)],[c_0_210]) ).
cnf(c_0_211_1,axiom,
ordinal(sk2_esk23_0),
inference(literals_permutation,[status(thm)],[c_0_211]) ).
cnf(c_0_212_1,axiom,
natural(sk2_esk23_0),
inference(literals_permutation,[status(thm)],[c_0_212]) ).
cnf(c_0_213_1,axiom,
finite(sk2_esk22_0),
inference(literals_permutation,[status(thm)],[c_0_213]) ).
cnf(c_0_214_1,axiom,
relation(sk2_esk21_0),
inference(literals_permutation,[status(thm)],[c_0_214]) ).
cnf(c_0_215_1,axiom,
function(sk2_esk21_0),
inference(literals_permutation,[status(thm)],[c_0_215]) ).
cnf(c_0_216_1,axiom,
function_yielding(sk2_esk21_0),
inference(literals_permutation,[status(thm)],[c_0_216]) ).
cnf(c_0_217_1,axiom,
relation(sk2_esk20_0),
inference(literals_permutation,[status(thm)],[c_0_217]) ).
cnf(c_0_218_1,axiom,
function(sk2_esk20_0),
inference(literals_permutation,[status(thm)],[c_0_218]) ).
cnf(c_0_219_1,axiom,
epsilon_transitive(sk2_esk19_0),
inference(literals_permutation,[status(thm)],[c_0_219]) ).
cnf(c_0_220_1,axiom,
epsilon_connected(sk2_esk19_0),
inference(literals_permutation,[status(thm)],[c_0_220]) ).
cnf(c_0_221_1,axiom,
ordinal(sk2_esk19_0),
inference(literals_permutation,[status(thm)],[c_0_221]) ).
cnf(c_0_222_1,axiom,
epsilon_transitive(sk2_esk18_0),
inference(literals_permutation,[status(thm)],[c_0_222]) ).
cnf(c_0_223_1,axiom,
epsilon_connected(sk2_esk18_0),
inference(literals_permutation,[status(thm)],[c_0_223]) ).
cnf(c_0_224_1,axiom,
ordinal(sk2_esk18_0),
inference(literals_permutation,[status(thm)],[c_0_224]) ).
cnf(c_0_225_1,axiom,
being_limit_ordinal(sk2_esk18_0),
inference(literals_permutation,[status(thm)],[c_0_225]) ).
cnf(c_0_226_1,axiom,
empty(sk2_esk17_0),
inference(literals_permutation,[status(thm)],[c_0_226]) ).
cnf(c_0_227_0,axiom,
relation(sk2_esk17_0),
inference(literals_permutation,[status(thm)],[c_0_227]) ).
cnf(c_0_228_0,axiom,
empty(sk2_esk16_0),
inference(literals_permutation,[status(thm)],[c_0_228]) ).
cnf(c_0_229_0,axiom,
epsilon_transitive(sk2_esk15_0),
inference(literals_permutation,[status(thm)],[c_0_229]) ).
cnf(c_0_230_0,axiom,
epsilon_connected(sk2_esk15_0),
inference(literals_permutation,[status(thm)],[c_0_230]) ).
cnf(c_0_231_0,axiom,
ordinal(sk2_esk15_0),
inference(literals_permutation,[status(thm)],[c_0_231]) ).
cnf(c_0_232_0,axiom,
relation(sk2_esk13_0),
inference(literals_permutation,[status(thm)],[c_0_232]) ).
cnf(c_0_233_0,axiom,
empty(sk2_esk13_0),
inference(literals_permutation,[status(thm)],[c_0_233]) ).
cnf(c_0_234_0,axiom,
function(sk2_esk13_0),
inference(literals_permutation,[status(thm)],[c_0_234]) ).
cnf(c_0_235_0,axiom,
relation(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_235]) ).
cnf(c_0_236_0,axiom,
function(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_236]) ).
cnf(c_0_237_0,axiom,
one_to_one(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_237]) ).
cnf(c_0_238_0,axiom,
empty(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_238]) ).
cnf(c_0_239_0,axiom,
epsilon_transitive(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_239]) ).
cnf(c_0_240_0,axiom,
epsilon_connected(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_240]) ).
cnf(c_0_241_0,axiom,
ordinal(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_241]) ).
cnf(c_0_242_0,axiom,
relation(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_242]) ).
cnf(c_0_243_0,axiom,
function(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_243]) ).
cnf(c_0_244_0,axiom,
transfinite_sequence(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_244]) ).
cnf(c_0_245_0,axiom,
ordinal_yielding(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_245]) ).
cnf(c_0_246_0,axiom,
relation(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_246]) ).
cnf(c_0_247_0,axiom,
empty(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_247]) ).
cnf(c_0_248_0,axiom,
epsilon_transitive(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_248]) ).
cnf(c_0_249_0,axiom,
epsilon_connected(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_249]) ).
cnf(c_0_250_0,axiom,
ordinal(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_250]) ).
cnf(c_0_251_0,axiom,
natural(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_251]) ).
cnf(c_0_252_0,axiom,
relation(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_252]) ).
cnf(c_0_253_0,axiom,
function(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_253]) ).
cnf(c_0_254_0,axiom,
one_to_one(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_254]) ).
cnf(c_0_255_0,axiom,
epsilon_transitive(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_255]) ).
cnf(c_0_256_0,axiom,
epsilon_connected(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_256]) ).
cnf(c_0_257_0,axiom,
ordinal(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_257]) ).
cnf(c_0_258_0,axiom,
relation(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_258]) ).
cnf(c_0_259_0,axiom,
relation_empty_yielding(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_259]) ).
cnf(c_0_260_0,axiom,
relation(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_260]) ).
cnf(c_0_261_0,axiom,
relation_empty_yielding(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_261]) ).
cnf(c_0_262_0,axiom,
function(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_262]) ).
cnf(c_0_263_0,axiom,
relation(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_263]) ).
cnf(c_0_264_0,axiom,
function(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_264]) ).
cnf(c_0_265_0,axiom,
transfinite_sequence(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_265]) ).
cnf(c_0_266_0,axiom,
relation(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_266]) ).
cnf(c_0_267_0,axiom,
relation_non_empty(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_267]) ).
cnf(c_0_268_0,axiom,
function(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_268]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_228,conjecture,
! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
file('<stdin>',t16_finset_1) ).
fof(c_0_1_229,negated_conjecture,
~ ! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_230,negated_conjecture,
( finite(esk1_0)
& ~ finite(set_difference(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).
cnf(c_0_3_231,negated_conjecture,
~ finite(set_difference(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_232,negated_conjecture,
finite(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_233,negated_conjecture,
~ finite(set_difference(esk1_0,esk2_0)),
c_0_3,
[final] ).
cnf(c_0_6_234,negated_conjecture,
finite(esk1_0),
c_0_4,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_166,negated_conjecture,
finite(sk3_esk1_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_96415b.p',c_0_6) ).
cnf(c_214,negated_conjecture,
finite(sk3_esk1_0),
inference(copy,[status(esa)],[c_166]) ).
cnf(c_221,negated_conjecture,
finite(sk3_esk1_0),
inference(copy,[status(esa)],[c_214]) ).
cnf(c_222,negated_conjecture,
finite(sk3_esk1_0),
inference(copy,[status(esa)],[c_221]) ).
cnf(c_224,negated_conjecture,
finite(sk3_esk1_0),
inference(copy,[status(esa)],[c_222]) ).
cnf(c_721,negated_conjecture,
finite(sk3_esk1_0),
inference(copy,[status(esa)],[c_224]) ).
cnf(c_160,plain,
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_96415b.p',c_0_179_0) ).
cnf(c_711,plain,
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(copy,[status(esa)],[c_160]) ).
cnf(c_727,plain,
finite(set_difference(sk3_esk1_0,X0)),
inference(resolution,[status(thm)],[c_721,c_711]) ).
cnf(c_728,plain,
finite(set_difference(sk3_esk1_0,X0)),
inference(rewriting,[status(thm)],[c_727]) ).
cnf(c_165,negated_conjecture,
~ finite(set_difference(sk3_esk1_0,sk3_esk2_0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_96415b.p',c_0_5) ).
cnf(c_212,negated_conjecture,
~ finite(set_difference(sk3_esk1_0,sk3_esk2_0)),
inference(copy,[status(esa)],[c_165]) ).
cnf(c_220,negated_conjecture,
~ finite(set_difference(sk3_esk1_0,sk3_esk2_0)),
inference(copy,[status(esa)],[c_212]) ).
cnf(c_223,negated_conjecture,
~ finite(set_difference(sk3_esk1_0,sk3_esk2_0)),
inference(copy,[status(esa)],[c_220]) ).
cnf(c_225,negated_conjecture,
~ finite(set_difference(sk3_esk1_0,sk3_esk2_0)),
inference(copy,[status(esa)],[c_223]) ).
cnf(c_723,plain,
~ finite(set_difference(sk3_esk1_0,sk3_esk2_0)),
inference(copy,[status(esa)],[c_225]) ).
cnf(c_737,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_728,c_723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU085+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 03:14:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.40 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.40 % FOF problem with conjecture
% 0.19/0.40 % 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_96dc0a.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_96415b.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_00469e | grep -v "SZS"
% 0.19/0.43
% 0.19/0.43 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ iProver source info
% 0.19/0.43
% 0.19/0.43 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.43 % git: non_committed_changes: true
% 0.19/0.43 % git: last_make_outside_of_git: true
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ Input Options
% 0.19/0.43
% 0.19/0.43 % --out_options all
% 0.19/0.43 % --tptp_safe_out true
% 0.19/0.43 % --problem_path ""
% 0.19/0.43 % --include_path ""
% 0.19/0.43 % --clausifier .//eprover
% 0.19/0.43 % --clausifier_options --tstp-format
% 0.19/0.43 % --stdin false
% 0.19/0.43 % --dbg_backtrace false
% 0.19/0.43 % --dbg_dump_prop_clauses false
% 0.19/0.43 % --dbg_dump_prop_clauses_file -
% 0.19/0.43 % --dbg_out_stat false
% 0.19/0.43
% 0.19/0.43 % ------ General Options
% 0.19/0.43
% 0.19/0.43 % --fof false
% 0.19/0.43 % --time_out_real 150.
% 0.19/0.43 % --time_out_prep_mult 0.2
% 0.19/0.43 % --time_out_virtual -1.
% 0.19/0.43 % --schedule none
% 0.19/0.43 % --ground_splitting input
% 0.19/0.43 % --splitting_nvd 16
% 0.19/0.43 % --non_eq_to_eq false
% 0.19/0.43 % --prep_gs_sim true
% 0.19/0.43 % --prep_unflatten false
% 0.19/0.43 % --prep_res_sim true
% 0.19/0.43 % --prep_upred true
% 0.19/0.43 % --res_sim_input true
% 0.19/0.43 % --clause_weak_htbl true
% 0.19/0.43 % --gc_record_bc_elim false
% 0.19/0.43 % --symbol_type_check false
% 0.19/0.43 % --clausify_out false
% 0.19/0.43 % --large_theory_mode false
% 0.19/0.43 % --prep_sem_filter none
% 0.19/0.43 % --prep_sem_filter_out false
% 0.19/0.43 % --preprocessed_out false
% 0.19/0.43 % --sub_typing false
% 0.19/0.43 % --brand_transform false
% 0.19/0.43 % --pure_diseq_elim true
% 0.19/0.43 % --min_unsat_core false
% 0.19/0.43 % --pred_elim true
% 0.19/0.43 % --add_important_lit false
% 0.19/0.43 % --soft_assumptions false
% 0.19/0.43 % --reset_solvers false
% 0.19/0.43 % --bc_imp_inh []
% 0.19/0.43 % --conj_cone_tolerance 1.5
% 0.19/0.43 % --prolific_symb_bound 500
% 0.19/0.43 % --lt_threshold 2000
% 0.19/0.43
% 0.19/0.43 % ------ SAT Options
% 0.19/0.43
% 0.19/0.43 % --sat_mode false
% 0.19/0.43 % --sat_fm_restart_options ""
% 0.19/0.43 % --sat_gr_def false
% 0.19/0.43 % --sat_epr_types true
% 0.19/0.43 % --sat_non_cyclic_types false
% 0.19/0.43 % --sat_finite_models false
% 0.19/0.43 % --sat_fm_lemmas false
% 0.19/0.43 % --sat_fm_prep false
% 0.19/0.43 % --sat_fm_uc_incr true
% 0.19/0.43 % --sat_out_model small
% 0.19/0.43 % --sat_out_clauses false
% 0.19/0.43
% 0.19/0.43 % ------ QBF Options
% 0.19/0.43
% 0.19/0.43 % --qbf_mode false
% 0.19/0.43 % --qbf_elim_univ true
% 0.19/0.43 % --qbf_sk_in true
% 0.19/0.43 % --qbf_pred_elim true
% 0.19/0.43 % --qbf_split 32
% 0.19/0.43
% 0.19/0.43 % ------ BMC1 Options
% 0.19/0.43
% 0.19/0.43 % --bmc1_incremental false
% 0.19/0.43 % --bmc1_axioms reachable_all
% 0.19/0.43 % --bmc1_min_bound 0
% 0.19/0.43 % --bmc1_max_bound -1
% 0.19/0.43 % --bmc1_max_bound_default -1
% 0.19/0.43 % --bmc1_symbol_reachability true
% 0.19/0.43 % --bmc1_property_lemmas false
% 0.19/0.43 % --bmc1_k_induction false
% 0.19/0.43 % --bmc1_non_equiv_states false
% 0.19/0.43 % --bmc1_deadlock false
% 0.19/0.43 % --bmc1_ucm false
% 0.19/0.43 % --bmc1_add_unsat_core none
% 0.19/0.43 % --bmc1_unsat_core_children false
% 0.19/0.43 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.43 % --bmc1_out_stat full
% 0.19/0.43 % --bmc1_ground_init false
% 0.19/0.43 % --bmc1_pre_inst_next_state false
% 0.19/0.43 % --bmc1_pre_inst_state false
% 0.19/0.43 % --bmc1_pre_inst_reach_state false
% 0.19/0.43 % --bmc1_out_unsat_core false
% 0.19/0.43 % --bmc1_aig_witness_out false
% 0.19/0.43 % --bmc1_verbose false
% 0.19/0.43 % --bmc1_dump_clauses_tptp false
% 0.32/0.55 % --bmc1_dump_unsat_core_tptp false
% 0.32/0.55 % --bmc1_dump_file -
% 0.32/0.55 % --bmc1_ucm_expand_uc_limit 128
% 0.32/0.55 % --bmc1_ucm_n_expand_iterations 6
% 0.32/0.55 % --bmc1_ucm_extend_mode 1
% 0.32/0.55 % --bmc1_ucm_init_mode 2
% 0.32/0.55 % --bmc1_ucm_cone_mode none
% 0.32/0.55 % --bmc1_ucm_reduced_relation_type 0
% 0.32/0.55 % --bmc1_ucm_relax_model 4
% 0.32/0.55 % --bmc1_ucm_full_tr_after_sat true
% 0.32/0.55 % --bmc1_ucm_expand_neg_assumptions false
% 0.32/0.55 % --bmc1_ucm_layered_model none
% 0.32/0.55 % --bmc1_ucm_max_lemma_size 10
% 0.32/0.55
% 0.32/0.55 % ------ AIG Options
% 0.32/0.55
% 0.32/0.55 % --aig_mode false
% 0.32/0.55
% 0.32/0.55 % ------ Instantiation Options
% 0.32/0.55
% 0.32/0.55 % --instantiation_flag true
% 0.32/0.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.32/0.55 % --inst_solver_per_active 750
% 0.32/0.55 % --inst_solver_calls_frac 0.5
% 0.32/0.55 % --inst_passive_queue_type priority_queues
% 0.32/0.55 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.32/0.55 % --inst_passive_queues_freq [25;2]
% 0.32/0.55 % --inst_dismatching true
% 0.32/0.55 % --inst_eager_unprocessed_to_passive true
% 0.32/0.55 % --inst_prop_sim_given true
% 0.32/0.55 % --inst_prop_sim_new false
% 0.32/0.55 % --inst_orphan_elimination true
% 0.32/0.55 % --inst_learning_loop_flag true
% 0.32/0.55 % --inst_learning_start 3000
% 0.32/0.55 % --inst_learning_factor 2
% 0.32/0.55 % --inst_start_prop_sim_after_learn 3
% 0.32/0.55 % --inst_sel_renew solver
% 0.32/0.55 % --inst_lit_activity_flag true
% 0.32/0.55 % --inst_out_proof true
% 0.32/0.55
% 0.32/0.55 % ------ Resolution Options
% 0.32/0.55
% 0.32/0.55 % --resolution_flag true
% 0.32/0.55 % --res_lit_sel kbo_max
% 0.32/0.55 % --res_to_prop_solver none
% 0.32/0.55 % --res_prop_simpl_new false
% 0.32/0.55 % --res_prop_simpl_given false
% 0.32/0.55 % --res_passive_queue_type priority_queues
% 0.32/0.55 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.32/0.55 % --res_passive_queues_freq [15;5]
% 0.32/0.55 % --res_forward_subs full
% 0.32/0.55 % --res_backward_subs full
% 0.32/0.55 % --res_forward_subs_resolution true
% 0.32/0.55 % --res_backward_subs_resolution true
% 0.32/0.55 % --res_orphan_elimination false
% 0.32/0.55 % --res_time_limit 1000.
% 0.32/0.55 % --res_out_proof true
% 0.32/0.55 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_96dc0a.s
% 0.32/0.55 % --modulo true
% 0.32/0.55
% 0.32/0.55 % ------ Combination Options
% 0.32/0.55
% 0.32/0.55 % --comb_res_mult 1000
% 0.32/0.55 % --comb_inst_mult 300
% 0.32/0.55 % ------
% 0.32/0.55
% 0.32/0.55 % ------ Parsing...% successful
% 0.32/0.55
% 0.32/0.55 % ------ 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 %
% 0.32/0.55
% 0.32/0.55 % ------ Proving...
% 0.32/0.55 % ------ Problem Properties
% 0.32/0.55
% 0.32/0.55 %
% 0.32/0.55 % EPR false
% 0.32/0.55 % Horn false
% 0.32/0.55 % Has equality true
% 0.32/0.55
% 0.32/0.55 % % ------ Input Options Time Limit: Unbounded
% 0.32/0.55
% 0.32/0.55
% 0.32/0.55 Compiling...
% 0.32/0.55 Loading plugin: done.
% 0.32/0.55 % % ------ Current options:
% 0.32/0.55
% 0.32/0.55 % ------ Input Options
% 0.32/0.55
% 0.32/0.55 % --out_options all
% 0.32/0.55 % --tptp_safe_out true
% 0.32/0.55 % --problem_path ""
% 0.32/0.55 % --include_path ""
% 0.32/0.55 % --clausifier .//eprover
% 0.32/0.55 % --clausifier_options --tstp-format
% 0.32/0.55 % --stdin false
% 0.32/0.55 % --dbg_backtrace false
% 0.32/0.55 % --dbg_dump_prop_clauses false
% 0.32/0.55 % --dbg_dump_prop_clauses_file -
% 0.32/0.55 % --dbg_out_stat false
% 0.32/0.55
% 0.32/0.55 % ------ General Options
% 0.32/0.55
% 0.32/0.55 % --fof false
% 0.32/0.55 % --time_out_real 150.
% 0.32/0.55 % --time_out_prep_mult 0.2
% 0.32/0.55 % --time_out_virtual -1.
% 0.32/0.55 % --schedule none
% 0.32/0.55 % --ground_splitting input
% 0.32/0.55 % --splitting_nvd 16
% 0.32/0.55 % --non_eq_to_eq false
% 0.32/0.55 % --prep_gs_sim true
% 0.32/0.55 % --prep_unflatten false
% 0.32/0.55 % --prep_res_sim true
% 0.32/0.55 % --prep_upred true
% 0.32/0.55 % --res_sim_input true
% 0.32/0.55 % --clause_weak_htbl true
% 0.32/0.55 % --gc_record_bc_elim false
% 0.32/0.55 % --symbol_type_check false
% 0.32/0.55 % --clausify_out false
% 0.32/0.55 % --large_theory_mode false
% 0.32/0.55 % --prep_sem_filter none
% 0.32/0.55 % --prep_sem_filter_out false
% 0.32/0.55 % --preprocessed_out false
% 0.32/0.55 % --sub_typing false
% 0.32/0.55 % --brand_transform false
% 0.32/0.55 % --pure_diseq_elim true
% 0.32/0.55 % --min_unsat_core false
% 0.32/0.55 % --pred_elim true
% 0.32/0.55 % --add_important_lit false
% 0.32/0.55 % --soft_assumptions false
% 0.32/0.55 % --reset_solvers false
% 0.32/0.55 % --bc_imp_inh []
% 0.32/0.55 % --conj_cone_tolerance 1.5
% 0.32/0.55 % --prolific_symb_bound 500
% 0.32/0.55 % --lt_threshold 2000
% 0.32/0.55
% 0.32/0.55 % ------ SAT Options
% 0.32/0.55
% 0.32/0.55 % --sat_mode false
% 0.32/0.55 % --sat_fm_restart_options ""
% 0.32/0.55 % --sat_gr_def false
% 0.32/0.55 % --sat_epr_types true
% 0.32/0.55 % --sat_non_cyclic_types false
% 0.32/0.55 % --sat_finite_models false
% 0.32/0.55 % --sat_fm_lemmas false
% 0.32/0.55 % --sat_fm_prep false
% 0.32/0.55 % --sat_fm_uc_incr true
% 0.32/0.55 % --sat_out_model small
% 0.32/0.55 % --sat_out_clauses false
% 0.32/0.55
% 0.32/0.55 % ------ QBF Options
% 0.32/0.55
% 0.32/0.55 % --qbf_mode false
% 0.32/0.55 % --qbf_elim_univ true
% 0.32/0.55 % --qbf_sk_in true
% 0.32/0.55 % --qbf_pred_elim true
% 0.32/0.55 % --qbf_split 32
% 0.32/0.55
% 0.32/0.55 % ------ BMC1 Options
% 0.32/0.55
% 0.32/0.55 % --bmc1_incremental false
% 0.32/0.55 % --bmc1_axioms reachable_all
% 0.32/0.55 % --bmc1_min_bound 0
% 0.32/0.55 % --bmc1_max_bound -1
% 0.32/0.55 % --bmc1_max_bound_default -1
% 0.32/0.55 % --bmc1_symbol_reachability true
% 0.32/0.55 % --bmc1_property_lemmas false
% 0.32/0.55 % --bmc1_k_induction false
% 0.32/0.55 % --bmc1_non_equiv_states false
% 0.32/0.55 % --bmc1_deadlock false
% 0.32/0.55 % --bmc1_ucm false
% 0.32/0.55 % --bmc1_add_unsat_core none
% 0.32/0.55 % --bmc1_unsat_core_children false
% 0.32/0.55 % --bmc1_unsat_core_extrapolate_axioms false
% 0.32/0.55 % --bmc1_out_stat full
% 0.32/0.55 % --bmc1_ground_init false
% 0.32/0.55 % --bmc1_pre_inst_next_state false
% 0.32/0.55 % --bmc1_pre_inst_state false
% 0.32/0.55 % --bmc1_pre_inst_reach_state false
% 0.32/0.55 % --bmc1_out_unsat_core false
% 0.32/0.55 % --bmc1_aig_witness_out false
% 0.32/0.55 % --bmc1_verbose false
% 0.32/0.55 % --bmc1_dump_clauses_tptp false
% 0.32/0.55 % --bmc1_dump_unsat_core_tptp false
% 0.32/0.55 % --bmc1_dump_file -
% 0.32/0.55 % --bmc1_ucm_expand_uc_limit 128
% 0.32/0.55 % --bmc1_ucm_n_expand_iterations 6
% 0.32/0.55 % --bmc1_ucm_extend_mode 1
% 0.32/0.55 % --bmc1_ucm_init_mode 2
% 0.32/0.55 % --bmc1_ucm_cone_mode none
% 0.32/0.55 % --bmc1_ucm_reduced_relation_type 0
% 0.32/0.55 % --bmc1_ucm_relax_model 4
% 0.32/0.55 % --bmc1_ucm_full_tr_after_sat true
% 0.32/0.55 % --bmc1_ucm_expand_neg_assumptions false
% 0.32/0.55 % --bmc1_ucm_layered_model none
% 0.32/0.55 % --bmc1_ucm_max_lemma_size 10
% 0.32/0.55
% 0.32/0.55 % ------ AIG Options
% 0.32/0.55
% 0.32/0.55 % --aig_mode false
% 0.32/0.55
% 0.32/0.55 % ------ Instantiation Options
% 0.32/0.55
% 0.32/0.55 % --instantiation_flag true
% 0.32/0.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.32/0.55 % --inst_solver_per_active 750
% 0.32/0.55 % --inst_solver_calls_frac 0.5
% 0.32/0.55 % --inst_passive_queue_type priority_queues
% 0.32/0.55 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.32/0.55 % --inst_passive_queues_freq [25;2]
% 0.32/0.55 % --inst_dismatching true
% 0.32/0.55 % --inst_eager_unprocessed_to_passive true
% 0.32/0.55 % --inst_prop_sim_given true
% 0.32/0.55 % --inst_prop_sim_new false
% 0.32/0.55 % --inst_orphan_elimination true
% 0.32/0.55 % --inst_learning_loop_flag true
% 0.32/0.55 % --inst_learning_start 3000
% 0.32/0.55 % --inst_learning_factor 2
% 0.32/0.55 % --inst_start_prop_sim_after_learn 3
% 0.32/0.55 % --inst_sel_renew solver
% 0.32/0.55 % --inst_lit_activity_flag true
% 0.32/0.55 % --inst_out_proof true
% 0.32/0.55
% 0.32/0.55 % ------ Resolution Options
% 0.32/0.55
% 0.32/0.55 % --resolution_flag true
% 0.32/0.55 % --res_lit_sel kbo_max
% 0.32/0.55 % --res_to_prop_solver none
% 0.32/0.55 % --res_prop_simpl_new false
% 0.32/0.55 % --res_prop_simpl_given false
% 0.32/0.55 % --res_passive_queue_type priority_queues
% 0.32/0.55 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.32/0.55 % --res_passive_queues_freq [15;5]
% 0.32/0.55 % --res_forward_subs full
% 0.32/0.55 % --res_backward_subs full
% 0.32/0.55 % --res_forward_subs_resolution true
% 0.32/0.55 % --res_backward_subs_resolution true
% 0.32/0.55 % --res_orphan_elimination false
% 0.32/0.55 % --res_time_limit 1000.
% 0.32/0.55 % --res_out_proof true
% 0.32/0.55 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_96dc0a.s
% 0.32/0.55 % --modulo true
% 0.32/0.55
% 0.32/0.55 % ------ Combination Options
% 0.32/0.55
% 0.32/0.55 % --comb_res_mult 1000
% 0.32/0.55 % --comb_inst_mult 300
% 0.32/0.55 % ------
% 0.32/0.55
% 0.32/0.55
% 0.32/0.55
% 0.32/0.55 % ------ Proving...
% 0.32/0.55 %
% 0.32/0.55
% 0.32/0.55
% 0.32/0.55 % Resolution empty clause
% 0.32/0.55
% 0.32/0.55 % ------ Statistics
% 0.32/0.55
% 0.32/0.55 % ------ General
% 0.32/0.55
% 0.32/0.55 % num_of_input_clauses: 167
% 0.32/0.55 % num_of_input_neg_conjectures: 2
% 0.32/0.55 % num_of_splits: 0
% 0.32/0.55 % num_of_split_atoms: 0
% 0.32/0.55 % num_of_sem_filtered_clauses: 0
% 0.32/0.55 % num_of_subtypes: 0
% 0.32/0.55 % monotx_restored_types: 0
% 0.32/0.55 % sat_num_of_epr_types: 0
% 0.32/0.55 % sat_num_of_non_cyclic_types: 0
% 0.32/0.55 % sat_guarded_non_collapsed_types: 0
% 0.32/0.55 % is_epr: 0
% 0.32/0.55 % is_horn: 0
% 0.32/0.55 % has_eq: 1
% 0.32/0.55 % num_pure_diseq_elim: 0
% 0.32/0.55 % simp_replaced_by: 0
% 0.32/0.55 % res_preprocessed: 4
% 0.32/0.55 % prep_upred: 0
% 0.32/0.55 % prep_unflattend: 0
% 0.32/0.55 % pred_elim_cands: 0
% 0.32/0.55 % pred_elim: 0
% 0.32/0.55 % pred_elim_cl: 0
% 0.32/0.55 % pred_elim_cycles: 0
% 0.32/0.55 % forced_gc_time: 0
% 0.32/0.55 % gc_basic_clause_elim: 0
% 0.32/0.55 % parsing_time: 0.003
% 0.32/0.55 % sem_filter_time: 0.
% 0.32/0.55 % pred_elim_time: 0.
% 0.32/0.55 % out_proof_time: 0.
% 0.32/0.55 % monotx_time: 0.
% 0.32/0.55 % subtype_inf_time: 0.
% 0.32/0.55 % unif_index_cands_time: 0.
% 0.32/0.55 % unif_index_add_time: 0.
% 0.32/0.55 % total_time: 0.143
% 0.32/0.55 % num_of_symbols: 75
% 0.32/0.55 % num_of_terms: 280
% 0.32/0.55
% 0.32/0.55 % ------ Propositional Solver
% 0.32/0.55
% 0.32/0.55 % prop_solver_calls: 1
% 0.32/0.55 % prop_fast_solver_calls: 6
% 0.32/0.55 % prop_num_of_clauses: 180
% 0.32/0.55 % prop_preprocess_simplified: 334
% 0.32/0.55 % prop_fo_subsumed: 0
% 0.32/0.55 % prop_solver_time: 0.
% 0.32/0.55 % prop_fast_solver_time: 0.
% 0.32/0.55 % prop_unsat_core_time: 0.
% 0.32/0.55
% 0.32/0.55 % ------ QBF
% 0.32/0.55
% 0.32/0.55 % qbf_q_res: 0
% 0.32/0.55 % qbf_num_tautologies: 0
% 0.32/0.55 % qbf_prep_cycles: 0
% 0.32/0.55
% 0.32/0.55 % ------ BMC1
% 0.32/0.55
% 0.32/0.55 % bmc1_current_bound: -1
% 0.32/0.55 % bmc1_last_solved_bound: -1
% 0.32/0.55 % bmc1_unsat_core_size: -1
% 0.32/0.55 % bmc1_unsat_core_parents_size: -1
% 0.32/0.55 % bmc1_merge_next_fun: 0
% 0.32/0.55 % bmc1_unsat_core_clauses_time: 0.
% 0.32/0.55
% 0.32/0.55 % ------ Instantiation
% 0.32/0.55
% 0.32/0.55 % inst_num_of_clauses: 161
% 0.32/0.55 % inst_num_in_passive: 0
% 0.32/0.55 % inst_num_in_active: 0
% 0.32/0.55 % inst_num_in_unprocessed: 167
% 0.32/0.55 % inst_num_of_loops: 0
% 0.32/0.55 % inst_num_of_learning_restarts: 0
% 0.32/0.55 % inst_num_moves_active_passive: 0
% 0.32/0.55 % inst_lit_activity: 0
% 0.32/0.55 % inst_lit_activity_moves: 0
% 0.32/0.55 % inst_num_tautologies: 0
% 0.32/0.55 % inst_num_prop_implied: 0
% 0.32/0.55 % inst_num_existing_simplified: 0
% 0.32/0.55 % inst_num_eq_res_simplified: 0
% 0.32/0.55 % inst_num_child_elim: 0
% 0.32/0.55 % inst_num_of_dismatching_blockings: 0
% 0.32/0.55 % inst_num_of_non_proper_insts: 0
% 0.32/0.55 % inst_num_of_duplicates: 0
% 0.32/0.55 % inst_inst_num_from_inst_to_res: 0
% 0.32/0.55 % inst_dismatching_checking_time: 0.
% 0.32/0.55
% 0.32/0.55 % ------ Resolution
% 0.32/0.55
% 0.32/0.55 % res_num_of_clauses: 184
% 0.32/0.55 % res_num_in_passive: 1
% 0.32/0.55 % res_num_in_active: 131
% 0.32/0.55 % res_num_of_loops: 3
% 0.32/0.55 % res_forward_subset_subsumed: 22
% 0.32/0.55 % res_backward_subset_subsumed: 1
% 0.32/0.55 % res_forward_subsumed: 0
% 0.32/0.55 % res_backward_subsumed: 0
% 0.32/0.55 % res_forward_subsumption_resolution: 0
% 0.32/0.55 % res_backward_subsumption_resolution: 1
% 0.32/0.55 % res_clause_to_clause_subsumption: 1
% 0.32/0.55 % res_orphan_elimination: 0
% 0.32/0.55 % res_tautology_del: 12
% 0.32/0.55 % res_num_eq_res_simplified: 0
% 0.32/0.55 % res_num_sel_changes: 0
% 0.32/0.55 % res_moves_from_active_to_pass: 0
% 0.32/0.55
% 0.32/0.56 % Status Unsatisfiable
% 0.32/0.56 % SZS status Theorem
% 0.32/0.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------