TSTP Solution File: NUM410+1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n015.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 : Mon Jul 18 10:57:02 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
input ).
fof(t6_boole_0,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(orientation,[status(thm)],[t6_boole]) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
input ).
fof(t4_subset_0,plain,
! [A,B,C] :
( element(A,C)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(orientation,[status(thm)],[t4_subset]) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
input ).
fof(t3_subset_0,plain,
! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ),
inference(orientation,[status(thm)],[t3_subset]) ).
fof(t3_subset_1,plain,
! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) ),
inference(orientation,[status(thm)],[t3_subset]) ).
fof(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(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(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
input ).
fof(fc8_relat_1_0,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
inference(orientation,[status(thm)],[fc8_relat_1]) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
input ).
fof(fc7_relat_1_0,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
inference(orientation,[status(thm)],[fc7_relat_1]) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_rng(A)) ),
input ).
fof(fc6_relat_1_0,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ ( ~ empty(A)
& relation(A) ) ),
inference(orientation,[status(thm)],[fc6_relat_1]) ).
fof(fc6_funct_1,axiom,
! [A] :
( ( relation(A)
& relation_non_empty(A)
& function(A) )
=> with_non_empty_elements(relation_rng(A)) ),
input ).
fof(fc6_funct_1_0,plain,
! [A] :
( with_non_empty_elements(relation_rng(A))
| ~ ( relation(A)
& relation_non_empty(A)
& function(A) ) ),
inference(orientation,[status(thm)],[fc6_funct_1]) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ),
input ).
fof(fc5_relat_1_0,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ ( ~ empty(A)
& relation(A) ) ),
inference(orientation,[status(thm)],[fc5_relat_1]) ).
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(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(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(dt_m1_ordinal1,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
input ).
fof(dt_m1_ordinal1_0,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
inference(orientation,[status(thm)],[dt_m1_ordinal1]) ).
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(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(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
input ).
fof(antisymmetry_r2_hidden_0,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(orientation,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(def_lhs_atom1,axiom,
! [B,A] :
( lhs_atom1(B,A)
<=> ~ in(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [A,B] :
( lhs_atom1(B,A)
| ~ in(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [A] :
( lhs_atom2(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A] :
( lhs_atom2(A)
| function(A) ),
inference(fold_definition,[status(thm)],[cc1_funct_1_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [A] :
( lhs_atom3(A)
<=> ~ ordinal(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A] :
( lhs_atom3(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[cc1_ordinal1_0,def_lhs_atom3]) ).
fof(to_be_clausified_3,plain,
! [A] :
( lhs_atom2(A)
| relation(A) ),
inference(fold_definition,[status(thm)],[cc1_relat_1_0,def_lhs_atom2]) ).
fof(def_lhs_atom4,axiom,
! [A] :
( lhs_atom4(A)
<=> ordinal(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [A] :
( lhs_atom4(A)
| ~ ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[cc2_ordinal1_0,def_lhs_atom4]) ).
fof(to_be_clausified_5,plain,
! [A] :
( lhs_atom2(A)
| ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
inference(fold_definition,[status(thm)],[cc3_ordinal1_0,def_lhs_atom2]) ).
fof(def_lhs_atom5,axiom,
! [B,A] :
( lhs_atom5(B,A)
<=> ~ transfinite_sequence_of(B,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A,B] :
( lhs_atom5(B,A)
| ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
inference(fold_definition,[status(thm)],[dt_m1_ordinal1_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
( lhs_atom6
<=> relation_empty_yielding(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_2,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> relation(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_1,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_0,def_lhs_atom8]) ).
fof(to_be_clausified_10,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> ordinal(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_7,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> epsilon_connected(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_6,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> epsilon_transitive(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_5,def_lhs_atom11]) ).
fof(to_be_clausified_14,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_4,def_lhs_atom8]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> one_to_one(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_3,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> function(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_2,def_lhs_atom13]) ).
fof(to_be_clausified_17,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_1,def_lhs_atom6]) ).
fof(to_be_clausified_18,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc2_ordinal1_0,def_lhs_atom7]) ).
fof(to_be_clausified_19,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc4_relat_1_1,def_lhs_atom7]) ).
fof(to_be_clausified_20,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc4_relat_1_0,def_lhs_atom8]) ).
fof(def_lhs_atom14,axiom,
! [A] :
( lhs_atom14(A)
<=> ~ empty(relation_dom(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [A] :
( lhs_atom14(A)
| ~ ( ~ empty(A)
& relation(A) ) ),
inference(fold_definition,[status(thm)],[fc5_relat_1_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [A] :
( lhs_atom15(A)
<=> with_non_empty_elements(relation_rng(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [A] :
( lhs_atom15(A)
| ~ ( relation(A)
& relation_non_empty(A)
& function(A) ) ),
inference(fold_definition,[status(thm)],[fc6_funct_1_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [A] :
( lhs_atom16(A)
<=> ~ empty(relation_rng(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [A] :
( lhs_atom16(A)
| ~ ( ~ empty(A)
& relation(A) ) ),
inference(fold_definition,[status(thm)],[fc6_relat_1_0,def_lhs_atom16]) ).
fof(to_be_clausified_24,plain,
! [A] :
( lhs_atom2(A)
| ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
inference(fold_definition,[status(thm)],[fc7_relat_1_0,def_lhs_atom2]) ).
fof(to_be_clausified_25,plain,
! [A] :
( lhs_atom2(A)
| ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
inference(fold_definition,[status(thm)],[fc8_relat_1_0,def_lhs_atom2]) ).
fof(def_lhs_atom17,axiom,
! [A] :
( lhs_atom17(A)
<=> subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [A] :
( lhs_atom17(A)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0,def_lhs_atom17]) ).
fof(to_be_clausified_27,plain,
! [A,B] :
( lhs_atom1(B,A)
| element(A,B) ),
inference(fold_definition,[status(thm)],[t1_subset_0,def_lhs_atom1]) ).
fof(def_lhs_atom18,axiom,
! [B,A] :
( lhs_atom18(B,A)
<=> ~ element(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [A,B] :
( lhs_atom18(B,A)
| empty(B)
| in(A,B) ),
inference(fold_definition,[status(thm)],[t2_subset_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [B,A] :
( lhs_atom19(B,A)
<=> ~ element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [A,B] :
( lhs_atom19(B,A)
| subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_1,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [B,A] :
( lhs_atom20(B,A)
<=> element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [A,B] :
( lhs_atom20(B,A)
| ~ subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [C,A] :
( lhs_atom21(C,A)
<=> element(A,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [A,B,C] :
( lhs_atom21(C,A)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(fold_definition,[status(thm)],[t4_subset_0,def_lhs_atom21]) ).
fof(to_be_clausified_32,plain,
! [A] :
( lhs_atom2(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom2]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X1,X2] :
( lhs_atom21(X3,X2)
| ~ ( in(X2,X1)
& element(X1,powerset(X3)) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_1,axiom,
! [X1,X2] :
( lhs_atom20(X1,X2)
| ~ subset(X2,X1) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_2,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_3,axiom,
! [X1,X2] :
( lhs_atom18(X1,X2)
| empty(X1)
| in(X2,X1) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_4,axiom,
! [X1,X2] :
( lhs_atom19(X1,X2)
| subset(X2,X1) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_5,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| element(X2,X1) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_6,axiom,
! [X2] :
( lhs_atom15(X2)
| ~ ( relation(X2)
& relation_non_empty(X2)
& function(X2) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_7,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ( relation(X1)
& function(X1)
& transfinite_sequence(X1) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_8,axiom,
! [X2] :
( lhs_atom4(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_9,axiom,
! [X2] :
( lhs_atom16(X2)
| ~ ( ~ empty(X2)
& relation(X2) ) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_10,axiom,
! [X2] :
( lhs_atom14(X2)
| ~ ( ~ empty(X2)
& relation(X2) ) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_11,axiom,
! [X2] :
( lhs_atom2(X2)
| ( empty(relation_rng(X2))
& relation(relation_rng(X2)) ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_12,axiom,
! [X2] :
( lhs_atom2(X2)
| ( empty(relation_dom(X2))
& relation(relation_dom(X2)) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_13,axiom,
! [X2] :
( lhs_atom2(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_14,axiom,
! [X2] :
( lhs_atom2(X2)
| relation(X2) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_15,axiom,
! [X2] :
( lhs_atom3(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_16,axiom,
! [X2] :
( lhs_atom2(X2)
| function(X2) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_17,axiom,
! [X2] :
( lhs_atom2(X2)
| X2 = empty_set ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_18,axiom,
! [X2] :
( lhs_atom17(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_19,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_20,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_21,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_22,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_23,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_24,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_25,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_26,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_27,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_28,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_29,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_30,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_31,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_32,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_33,axiom,
! [X3,X1,X2] :
( lhs_atom21(X3,X2)
| ~ ( in(X2,X1)
& element(X1,powerset(X3)) ) ),
c_0_0 ).
fof(c_0_34,plain,
! [X1,X2] :
( lhs_atom20(X1,X2)
| ~ subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_35,plain,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_36,axiom,
! [X1,X2] :
( lhs_atom18(X1,X2)
| empty(X1)
| in(X2,X1) ),
c_0_3 ).
fof(c_0_37,axiom,
! [X1,X2] :
( lhs_atom19(X1,X2)
| subset(X2,X1) ),
c_0_4 ).
fof(c_0_38,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| element(X2,X1) ),
c_0_5 ).
fof(c_0_39,axiom,
! [X2] :
( lhs_atom15(X2)
| ~ ( relation(X2)
& relation_non_empty(X2)
& function(X2) ) ),
c_0_6 ).
fof(c_0_40,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ( relation(X1)
& function(X1)
& transfinite_sequence(X1) ) ),
c_0_7 ).
fof(c_0_41,axiom,
! [X2] :
( lhs_atom4(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_8 ).
fof(c_0_42,plain,
! [X2] :
( lhs_atom16(X2)
| ~ ( ~ empty(X2)
& relation(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_43,plain,
! [X2] :
( lhs_atom14(X2)
| ~ ( ~ empty(X2)
& relation(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_44,axiom,
! [X2] :
( lhs_atom2(X2)
| ( empty(relation_rng(X2))
& relation(relation_rng(X2)) ) ),
c_0_11 ).
fof(c_0_45,axiom,
! [X2] :
( lhs_atom2(X2)
| ( empty(relation_dom(X2))
& relation(relation_dom(X2)) ) ),
c_0_12 ).
fof(c_0_46,axiom,
! [X2] :
( lhs_atom2(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ),
c_0_13 ).
fof(c_0_47,axiom,
! [X2] :
( lhs_atom2(X2)
| relation(X2) ),
c_0_14 ).
fof(c_0_48,axiom,
! [X2] :
( lhs_atom3(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_15 ).
fof(c_0_49,axiom,
! [X2] :
( lhs_atom2(X2)
| function(X2) ),
c_0_16 ).
fof(c_0_50,axiom,
! [X2] :
( lhs_atom2(X2)
| X2 = empty_set ),
c_0_17 ).
fof(c_0_51,plain,
! [X2] : lhs_atom17(X2),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_52,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_53,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_54,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_55,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_56,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_57,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_58,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_59,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_60,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_61,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_62,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_63,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_64,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_65,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_66,plain,
! [X4,X5,X6] :
( lhs_atom21(X4,X6)
| ~ in(X6,X5)
| ~ element(X5,powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
fof(c_0_67,plain,
! [X3,X4] :
( lhs_atom20(X3,X4)
| ~ subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_34]) ).
fof(c_0_68,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_35]) ).
fof(c_0_69,plain,
! [X3,X4] :
( lhs_atom18(X3,X4)
| empty(X3)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_36]) ).
fof(c_0_70,plain,
! [X3,X4] :
( lhs_atom19(X3,X4)
| subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_37]) ).
fof(c_0_71,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| element(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
fof(c_0_72,plain,
! [X3] :
( lhs_atom15(X3)
| ~ relation(X3)
| ~ relation_non_empty(X3)
| ~ function(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
fof(c_0_73,plain,
! [X3,X4] :
( ( relation(X3)
| lhs_atom5(X3,X4) )
& ( function(X3)
| lhs_atom5(X3,X4) )
& ( transfinite_sequence(X3)
| lhs_atom5(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_40])])])]) ).
fof(c_0_74,plain,
! [X3] :
( lhs_atom4(X3)
| ~ epsilon_transitive(X3)
| ~ epsilon_connected(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
fof(c_0_75,plain,
! [X3] :
( lhs_atom16(X3)
| empty(X3)
| ~ relation(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])]) ).
fof(c_0_76,plain,
! [X3] :
( lhs_atom14(X3)
| empty(X3)
| ~ relation(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).
fof(c_0_77,plain,
! [X3] :
( ( empty(relation_rng(X3))
| lhs_atom2(X3) )
& ( relation(relation_rng(X3))
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_44])]) ).
fof(c_0_78,plain,
! [X3] :
( ( empty(relation_dom(X3))
| lhs_atom2(X3) )
& ( relation(relation_dom(X3))
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_45])]) ).
fof(c_0_79,plain,
! [X3] :
( ( epsilon_transitive(X3)
| lhs_atom2(X3) )
& ( epsilon_connected(X3)
| lhs_atom2(X3) )
& ( ordinal(X3)
| lhs_atom2(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_46])]) ).
fof(c_0_80,plain,
! [X3] :
( lhs_atom2(X3)
| relation(X3) ),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_81,plain,
! [X3] :
( ( epsilon_transitive(X3)
| lhs_atom3(X3) )
& ( epsilon_connected(X3)
| lhs_atom3(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
fof(c_0_82,plain,
! [X3] :
( lhs_atom2(X3)
| function(X3) ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
fof(c_0_83,plain,
! [X3] :
( lhs_atom2(X3)
| X3 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_50]) ).
fof(c_0_84,plain,
! [X3] : lhs_atom17(X3),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_85,plain,
lhs_atom8,
c_0_52 ).
fof(c_0_86,plain,
lhs_atom7,
c_0_53 ).
fof(c_0_87,plain,
lhs_atom7,
c_0_54 ).
fof(c_0_88,plain,
lhs_atom6,
c_0_55 ).
fof(c_0_89,plain,
lhs_atom13,
c_0_56 ).
fof(c_0_90,plain,
lhs_atom12,
c_0_57 ).
fof(c_0_91,plain,
lhs_atom8,
c_0_58 ).
fof(c_0_92,plain,
lhs_atom11,
c_0_59 ).
fof(c_0_93,plain,
lhs_atom10,
c_0_60 ).
fof(c_0_94,plain,
lhs_atom9,
c_0_61 ).
fof(c_0_95,plain,
lhs_atom8,
c_0_62 ).
fof(c_0_96,plain,
lhs_atom8,
c_0_63 ).
fof(c_0_97,plain,
lhs_atom7,
c_0_64 ).
fof(c_0_98,plain,
lhs_atom6,
c_0_65 ).
cnf(c_0_99,plain,
( lhs_atom21(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_100,plain,
( lhs_atom20(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_101,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_102,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom18(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_103,plain,
( subset(X1,X2)
| lhs_atom19(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_104,plain,
( element(X1,X2)
| lhs_atom1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_105,plain,
( lhs_atom15(X1)
| ~ function(X1)
| ~ relation_non_empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_106,plain,
( lhs_atom5(X1,X2)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_107,plain,
( lhs_atom5(X1,X2)
| function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_108,plain,
( lhs_atom5(X1,X2)
| transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_109,plain,
( lhs_atom4(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_110,plain,
( empty(X1)
| lhs_atom16(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_111,plain,
( empty(X1)
| lhs_atom14(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_112,plain,
( lhs_atom2(X1)
| empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_113,plain,
( lhs_atom2(X1)
| relation(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_114,plain,
( lhs_atom2(X1)
| empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_115,plain,
( lhs_atom2(X1)
| relation(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_116,plain,
( lhs_atom2(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_117,plain,
( lhs_atom2(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_118,plain,
( lhs_atom2(X1)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_119,plain,
( relation(X1)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_120,plain,
( lhs_atom3(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_121,plain,
( lhs_atom3(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_122,plain,
( function(X1)
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_123,plain,
( X1 = empty_set
| lhs_atom2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_124,plain,
lhs_atom17(X1),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_125,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_126,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_127,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_128,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_129,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_130,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_131,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_132,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_133,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_134,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_135,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_136,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_137,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_138,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_139,plain,
( lhs_atom21(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
c_0_99,
[final] ).
cnf(c_0_140,plain,
( lhs_atom20(X2,X1)
| ~ subset(X1,X2) ),
c_0_100,
[final] ).
cnf(c_0_141,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
c_0_101,
[final] ).
cnf(c_0_142,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom18(X2,X1) ),
c_0_102,
[final] ).
cnf(c_0_143,plain,
( subset(X1,X2)
| lhs_atom19(X2,X1) ),
c_0_103,
[final] ).
cnf(c_0_144,plain,
( element(X1,X2)
| lhs_atom1(X2,X1) ),
c_0_104,
[final] ).
cnf(c_0_145,plain,
( lhs_atom15(X1)
| ~ function(X1)
| ~ relation_non_empty(X1)
| ~ relation(X1) ),
c_0_105,
[final] ).
cnf(c_0_146,plain,
( lhs_atom5(X1,X2)
| relation(X1) ),
c_0_106,
[final] ).
cnf(c_0_147,plain,
( lhs_atom5(X1,X2)
| function(X1) ),
c_0_107,
[final] ).
cnf(c_0_148,plain,
( lhs_atom5(X1,X2)
| transfinite_sequence(X1) ),
c_0_108,
[final] ).
cnf(c_0_149,plain,
( lhs_atom4(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_109,
[final] ).
cnf(c_0_150,plain,
( empty(X1)
| lhs_atom16(X1)
| ~ relation(X1) ),
c_0_110,
[final] ).
cnf(c_0_151,plain,
( empty(X1)
| lhs_atom14(X1)
| ~ relation(X1) ),
c_0_111,
[final] ).
cnf(c_0_152,plain,
( lhs_atom2(X1)
| empty(relation_rng(X1)) ),
c_0_112,
[final] ).
cnf(c_0_153,plain,
( lhs_atom2(X1)
| relation(relation_rng(X1)) ),
c_0_113,
[final] ).
cnf(c_0_154,plain,
( lhs_atom2(X1)
| empty(relation_dom(X1)) ),
c_0_114,
[final] ).
cnf(c_0_155,plain,
( lhs_atom2(X1)
| relation(relation_dom(X1)) ),
c_0_115,
[final] ).
cnf(c_0_156,plain,
( lhs_atom2(X1)
| epsilon_transitive(X1) ),
c_0_116,
[final] ).
cnf(c_0_157,plain,
( lhs_atom2(X1)
| epsilon_connected(X1) ),
c_0_117,
[final] ).
cnf(c_0_158,plain,
( lhs_atom2(X1)
| ordinal(X1) ),
c_0_118,
[final] ).
cnf(c_0_159,plain,
( relation(X1)
| lhs_atom2(X1) ),
c_0_119,
[final] ).
cnf(c_0_160,plain,
( lhs_atom3(X1)
| epsilon_transitive(X1) ),
c_0_120,
[final] ).
cnf(c_0_161,plain,
( lhs_atom3(X1)
| epsilon_connected(X1) ),
c_0_121,
[final] ).
cnf(c_0_162,plain,
( function(X1)
| lhs_atom2(X1) ),
c_0_122,
[final] ).
cnf(c_0_163,plain,
( X1 = empty_set
| lhs_atom2(X1) ),
c_0_123,
[final] ).
cnf(c_0_164,plain,
lhs_atom17(X1),
c_0_124,
[final] ).
cnf(c_0_165,plain,
lhs_atom8,
c_0_125,
[final] ).
cnf(c_0_166,plain,
lhs_atom7,
c_0_126,
[final] ).
cnf(c_0_167,plain,
lhs_atom7,
c_0_127,
[final] ).
cnf(c_0_168,plain,
lhs_atom6,
c_0_128,
[final] ).
cnf(c_0_169,plain,
lhs_atom13,
c_0_129,
[final] ).
cnf(c_0_170,plain,
lhs_atom12,
c_0_130,
[final] ).
cnf(c_0_171,plain,
lhs_atom8,
c_0_131,
[final] ).
cnf(c_0_172,plain,
lhs_atom11,
c_0_132,
[final] ).
cnf(c_0_173,plain,
lhs_atom10,
c_0_133,
[final] ).
cnf(c_0_174,plain,
lhs_atom9,
c_0_134,
[final] ).
cnf(c_0_175,plain,
lhs_atom8,
c_0_135,
[final] ).
cnf(c_0_176,plain,
lhs_atom8,
c_0_136,
[final] ).
cnf(c_0_177,plain,
lhs_atom7,
c_0_137,
[final] ).
cnf(c_0_178,plain,
lhs_atom6,
c_0_138,
[final] ).
% End CNF derivation
cnf(c_0_139_0,axiom,
( element(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_139,def_lhs_atom21]) ).
cnf(c_0_140_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_140,def_lhs_atom20]) ).
cnf(c_0_141_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_141,def_lhs_atom1]) ).
cnf(c_0_142_0,axiom,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(unfold_definition,[status(thm)],[c_0_142,def_lhs_atom18]) ).
cnf(c_0_143_0,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_143,def_lhs_atom19]) ).
cnf(c_0_144_0,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_144,def_lhs_atom1]) ).
cnf(c_0_145_0,axiom,
( with_non_empty_elements(relation_rng(X1))
| ~ function(X1)
| ~ relation_non_empty(X1)
| ~ relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_145,def_lhs_atom15]) ).
cnf(c_0_146_0,axiom,
( ~ transfinite_sequence_of(X1,X2)
| relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_146,def_lhs_atom5]) ).
cnf(c_0_147_0,axiom,
( ~ transfinite_sequence_of(X1,X2)
| function(X1) ),
inference(unfold_definition,[status(thm)],[c_0_147,def_lhs_atom5]) ).
cnf(c_0_148_0,axiom,
( ~ transfinite_sequence_of(X1,X2)
| transfinite_sequence(X1) ),
inference(unfold_definition,[status(thm)],[c_0_148,def_lhs_atom5]) ).
cnf(c_0_149_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_149,def_lhs_atom4]) ).
cnf(c_0_150_0,axiom,
( ~ empty(relation_rng(X1))
| empty(X1)
| ~ relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_150,def_lhs_atom16]) ).
cnf(c_0_151_0,axiom,
( ~ empty(relation_dom(X1))
| empty(X1)
| ~ relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_151,def_lhs_atom14]) ).
cnf(c_0_152_0,axiom,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_152,def_lhs_atom2]) ).
cnf(c_0_153_0,axiom,
( ~ empty(X1)
| relation(relation_rng(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_153,def_lhs_atom2]) ).
cnf(c_0_154_0,axiom,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_154,def_lhs_atom2]) ).
cnf(c_0_155_0,axiom,
( ~ empty(X1)
| relation(relation_dom(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_155,def_lhs_atom2]) ).
cnf(c_0_156_0,axiom,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_156,def_lhs_atom2]) ).
cnf(c_0_157_0,axiom,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(unfold_definition,[status(thm)],[c_0_157,def_lhs_atom2]) ).
cnf(c_0_158_0,axiom,
( ~ empty(X1)
| ordinal(X1) ),
inference(unfold_definition,[status(thm)],[c_0_158,def_lhs_atom2]) ).
cnf(c_0_159_0,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_159,def_lhs_atom2]) ).
cnf(c_0_160_0,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_160,def_lhs_atom3]) ).
cnf(c_0_161_0,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(unfold_definition,[status(thm)],[c_0_161,def_lhs_atom3]) ).
cnf(c_0_162_0,axiom,
( ~ empty(X1)
| function(X1) ),
inference(unfold_definition,[status(thm)],[c_0_162,def_lhs_atom2]) ).
cnf(c_0_163_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_163,def_lhs_atom2]) ).
cnf(c_0_164_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_164,def_lhs_atom17]) ).
cnf(c_0_165_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_165,def_lhs_atom8]) ).
cnf(c_0_166_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_166,def_lhs_atom7]) ).
cnf(c_0_167_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_167,def_lhs_atom7]) ).
cnf(c_0_168_0,axiom,
relation_empty_yielding(empty_set),
inference(unfold_definition,[status(thm)],[c_0_168,def_lhs_atom6]) ).
cnf(c_0_169_0,axiom,
function(empty_set),
inference(unfold_definition,[status(thm)],[c_0_169,def_lhs_atom13]) ).
cnf(c_0_170_0,axiom,
one_to_one(empty_set),
inference(unfold_definition,[status(thm)],[c_0_170,def_lhs_atom12]) ).
cnf(c_0_171_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_171,def_lhs_atom8]) ).
cnf(c_0_172_0,axiom,
epsilon_transitive(empty_set),
inference(unfold_definition,[status(thm)],[c_0_172,def_lhs_atom11]) ).
cnf(c_0_173_0,axiom,
epsilon_connected(empty_set),
inference(unfold_definition,[status(thm)],[c_0_173,def_lhs_atom10]) ).
cnf(c_0_174_0,axiom,
ordinal(empty_set),
inference(unfold_definition,[status(thm)],[c_0_174,def_lhs_atom9]) ).
cnf(c_0_175_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_175,def_lhs_atom8]) ).
cnf(c_0_176_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_176,def_lhs_atom8]) ).
cnf(c_0_177_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_177,def_lhs_atom7]) ).
cnf(c_0_178_0,axiom,
relation_empty_yielding(empty_set),
inference(unfold_definition,[status(thm)],[c_0_178,def_lhs_atom6]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('<stdin>',d8_ordinal1) ).
fof(c_0_1_002,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_2_003,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
file('<stdin>',d7_ordinal1) ).
fof(c_0_3_004,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
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] : transfinite_sequence_of(X2,X1),
file('<stdin>',existence_m1_ordinal1) ).
fof(c_0_6_007,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
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] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_9_010,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_10_011,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc3_ordinal1) ).
fof(c_0_11_012,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_12_013,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc1_ordinal1) ).
fof(c_0_13_014,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_14_015,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_15_016,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_16_017,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_17_018,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_18_019,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_19_020,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('<stdin>',rc4_funct_1) ).
fof(c_0_20_021,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
file('<stdin>',rc4_ordinal1) ).
fof(c_0_21_022,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('<stdin>',rc5_funct_1) ).
fof(c_0_22_023,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
c_0_0 ).
fof(c_0_23_024,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_1 ).
fof(c_0_24_025,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
c_0_2 ).
fof(c_0_25_026,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_3 ).
fof(c_0_26_027,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_4 ).
fof(c_0_27_028,axiom,
! [X1] :
? [X2] : transfinite_sequence_of(X2,X1),
c_0_5 ).
fof(c_0_28_029,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_6 ).
fof(c_0_29_030,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_7 ).
fof(c_0_30_031,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_31_032,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_32_033,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_33_034,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_11 ).
fof(c_0_34_035,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_12 ).
fof(c_0_35_036,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_13 ).
fof(c_0_36_037,axiom,
? [X1] : empty(X1),
c_0_14 ).
fof(c_0_37_038,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_15 ).
fof(c_0_38_039,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_16 ).
fof(c_0_39_040,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_17 ).
fof(c_0_40_041,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_18 ).
fof(c_0_41_042,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
c_0_19 ).
fof(c_0_42_043,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
c_0_20 ).
fof(c_0_43_044,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
c_0_21 ).
fof(c_0_44_045,plain,
! [X3,X4] :
( ( ~ transfinite_sequence_of(X4,X3)
| subset(relation_rng(X4),X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) )
& ( ~ subset(relation_rng(X4),X3)
| transfinite_sequence_of(X4,X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_45_046,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_23])])])]) ).
fof(c_0_46_047,plain,
! [X2] :
( ( ~ transfinite_sequence(X2)
| ordinal(relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( ~ ordinal(relation_dom(X2))
| transfinite_sequence(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_47_048,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
fof(c_0_48_049,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_26])])]) ).
fof(c_0_49_050,plain,
! [X3] : transfinite_sequence_of(esk16_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_50_051,plain,
! [X3] : element(esk15_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_51_052,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_29])])])]) ).
fof(c_0_52_053,plain,
( ~ empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_53_054,plain,
~ empty(esk7_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_54_055,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_32])]) ).
fof(c_0_55_056,plain,
( relation(esk14_0)
& function(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
fof(c_0_56_057,plain,
( epsilon_transitive(esk13_0)
& epsilon_connected(esk13_0)
& ordinal(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
fof(c_0_57_058,plain,
( empty(esk12_0)
& relation(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
fof(c_0_58_059,plain,
empty(esk11_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_36])]) ).
fof(c_0_59_060,plain,
( relation(esk10_0)
& empty(esk10_0)
& function(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
fof(c_0_60_061,plain,
( relation(esk9_0)
& function(esk9_0)
& one_to_one(esk9_0)
& empty(esk9_0)
& epsilon_transitive(esk9_0)
& epsilon_connected(esk9_0)
& ordinal(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
fof(c_0_61_062,plain,
( relation(esk6_0)
& function(esk6_0)
& one_to_one(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_39])]) ).
fof(c_0_62_063,plain,
( relation(esk4_0)
& relation_empty_yielding(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
fof(c_0_63_064,plain,
( relation(esk3_0)
& relation_empty_yielding(esk3_0)
& function(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_41])]) ).
fof(c_0_64_065,plain,
( relation(esk2_0)
& function(esk2_0)
& transfinite_sequence(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_42])]) ).
fof(c_0_65_066,plain,
( relation(esk1_0)
& relation_non_empty(esk1_0)
& function(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_43])]) ).
cnf(c_0_66_067,plain,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_67_068,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_68_069,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_69_070,plain,
( transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_70_071,plain,
( ordinal(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_71_072,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_72_073,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_73_074,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_74_075,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_75_076,plain,
transfinite_sequence_of(esk16_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_76_077,plain,
element(esk15_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_77_078,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_78_079,plain,
~ empty(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_79_080,plain,
~ empty(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_80_081,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_81_082,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_82_083,plain,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_83_084,plain,
epsilon_transitive(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_84_085,plain,
epsilon_connected(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_85_086,plain,
ordinal(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_86_087,plain,
empty(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_87_088,plain,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_88_089,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_89_090,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_90_091,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_91_092,plain,
function(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_92_093,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_93_094,plain,
function(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_94_095,plain,
one_to_one(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_95_096,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_96_097,plain,
epsilon_transitive(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_97_098,plain,
epsilon_connected(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_98_099,plain,
ordinal(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_99_100,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_100_101,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_101_102,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_102_103,plain,
one_to_one(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_103_104,plain,
epsilon_transitive(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_104_105,plain,
epsilon_connected(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_105_106,plain,
ordinal(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_106_107,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_107_108,plain,
relation_empty_yielding(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_108_109,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_109_110,plain,
relation_empty_yielding(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_110_111,plain,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_111_112,plain,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_112_113,plain,
function(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_113_114,plain,
transfinite_sequence(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_114_115,plain,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_115_116,plain,
relation_non_empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_116_117,plain,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_117_118,plain,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
c_0_66,
[final] ).
cnf(c_0_118_119,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
c_0_67,
[final] ).
cnf(c_0_119_120,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_68,
[final] ).
cnf(c_0_120_121,plain,
( transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1)) ),
c_0_69,
[final] ).
cnf(c_0_121_122,plain,
( ordinal(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence(X1) ),
c_0_70,
[final] ).
cnf(c_0_122_123,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_71,
[final] ).
cnf(c_0_123_124,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_72,
[final] ).
cnf(c_0_124_125,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_73,
[final] ).
cnf(c_0_125_126,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_74,
[final] ).
cnf(c_0_126_127,plain,
transfinite_sequence_of(esk16_1(X1),X1),
c_0_75,
[final] ).
cnf(c_0_127_128,plain,
element(esk15_1(X1),X1),
c_0_76,
[final] ).
cnf(c_0_128_129,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_77,
[final] ).
cnf(c_0_129_130,plain,
~ empty(esk8_0),
c_0_78,
[final] ).
cnf(c_0_130_131,plain,
~ empty(esk7_0),
c_0_79,
[final] ).
cnf(c_0_131_132,plain,
~ empty(esk5_0),
c_0_80,
[final] ).
cnf(c_0_132_133,plain,
relation(esk14_0),
c_0_81,
[final] ).
cnf(c_0_133_134,plain,
function(esk14_0),
c_0_82,
[final] ).
cnf(c_0_134_135,plain,
epsilon_transitive(esk13_0),
c_0_83,
[final] ).
cnf(c_0_135_136,plain,
epsilon_connected(esk13_0),
c_0_84,
[final] ).
cnf(c_0_136_137,plain,
ordinal(esk13_0),
c_0_85,
[final] ).
cnf(c_0_137_138,plain,
empty(esk12_0),
c_0_86,
[final] ).
cnf(c_0_138_139,plain,
relation(esk12_0),
c_0_87,
[final] ).
cnf(c_0_139_140,plain,
empty(esk11_0),
c_0_88,
[final] ).
cnf(c_0_140_141,plain,
relation(esk10_0),
c_0_89,
[final] ).
cnf(c_0_141_142,plain,
empty(esk10_0),
c_0_90,
[final] ).
cnf(c_0_142_143,plain,
function(esk10_0),
c_0_91,
[final] ).
cnf(c_0_143_144,plain,
relation(esk9_0),
c_0_92,
[final] ).
cnf(c_0_144_145,plain,
function(esk9_0),
c_0_93,
[final] ).
cnf(c_0_145_146,plain,
one_to_one(esk9_0),
c_0_94,
[final] ).
cnf(c_0_146_147,plain,
empty(esk9_0),
c_0_95,
[final] ).
cnf(c_0_147_148,plain,
epsilon_transitive(esk9_0),
c_0_96,
[final] ).
cnf(c_0_148_149,plain,
epsilon_connected(esk9_0),
c_0_97,
[final] ).
cnf(c_0_149_150,plain,
ordinal(esk9_0),
c_0_98,
[final] ).
cnf(c_0_150_151,plain,
relation(esk8_0),
c_0_99,
[final] ).
cnf(c_0_151_152,plain,
relation(esk6_0),
c_0_100,
[final] ).
cnf(c_0_152_153,plain,
function(esk6_0),
c_0_101,
[final] ).
cnf(c_0_153_154,plain,
one_to_one(esk6_0),
c_0_102,
[final] ).
cnf(c_0_154_155,plain,
epsilon_transitive(esk5_0),
c_0_103,
[final] ).
cnf(c_0_155_156,plain,
epsilon_connected(esk5_0),
c_0_104,
[final] ).
cnf(c_0_156_157,plain,
ordinal(esk5_0),
c_0_105,
[final] ).
cnf(c_0_157_158,plain,
relation(esk4_0),
c_0_106,
[final] ).
cnf(c_0_158_159,plain,
relation_empty_yielding(esk4_0),
c_0_107,
[final] ).
cnf(c_0_159_160,plain,
relation(esk3_0),
c_0_108,
[final] ).
cnf(c_0_160_161,plain,
relation_empty_yielding(esk3_0),
c_0_109,
[final] ).
cnf(c_0_161_162,plain,
function(esk3_0),
c_0_110,
[final] ).
cnf(c_0_162_163,plain,
relation(esk2_0),
c_0_111,
[final] ).
cnf(c_0_163_164,plain,
function(esk2_0),
c_0_112,
[final] ).
cnf(c_0_164_165,plain,
transfinite_sequence(esk2_0),
c_0_113,
[final] ).
cnf(c_0_165_166,plain,
relation(esk1_0),
c_0_114,
[final] ).
cnf(c_0_166_167,plain,
relation_non_empty(esk1_0),
c_0_115,
[final] ).
cnf(c_0_167_168,plain,
function(esk1_0),
c_0_116,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_117_0,axiom,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_117]) ).
cnf(c_0_117_1,axiom,
( ~ transfinite_sequence(X1)
| transfinite_sequence_of(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_117]) ).
cnf(c_0_117_2,axiom,
( ~ function(X1)
| ~ transfinite_sequence(X1)
| transfinite_sequence_of(X1,X2)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_117]) ).
cnf(c_0_117_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1)
| transfinite_sequence_of(X1,X2)
| ~ subset(relation_rng(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_117]) ).
cnf(c_0_117_4,axiom,
( ~ subset(relation_rng(X1),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1)
| transfinite_sequence_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_117]) ).
cnf(c_0_118_0,axiom,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_118]) ).
cnf(c_0_118_1,axiom,
( ~ transfinite_sequence(X1)
| subset(relation_rng(X1),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_118]) ).
cnf(c_0_118_2,axiom,
( ~ function(X1)
| ~ transfinite_sequence(X1)
| subset(relation_rng(X1),X2)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_118]) ).
cnf(c_0_118_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1)
| subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_118]) ).
cnf(c_0_118_4,axiom,
( ~ transfinite_sequence_of(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1)
| subset(relation_rng(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_118]) ).
cnf(c_0_119_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_119]) ).
cnf(c_0_119_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_119]) ).
cnf(c_0_119_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_119]) ).
cnf(c_0_120_0,axiom,
( transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_120]) ).
cnf(c_0_120_1,axiom,
( ~ function(X1)
| transfinite_sequence(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_120]) ).
cnf(c_0_120_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| transfinite_sequence(X1)
| ~ ordinal(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_120]) ).
cnf(c_0_120_3,axiom,
( ~ ordinal(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| transfinite_sequence(X1) ),
inference(literals_permutation,[status(thm)],[c_0_120]) ).
cnf(c_0_121_0,axiom,
( ordinal(relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence(X1) ),
inference(literals_permutation,[status(thm)],[c_0_121]) ).
cnf(c_0_121_1,axiom,
( ~ function(X1)
| ordinal(relation_dom(X1))
| ~ relation(X1)
| ~ transfinite_sequence(X1) ),
inference(literals_permutation,[status(thm)],[c_0_121]) ).
cnf(c_0_121_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| ordinal(relation_dom(X1))
| ~ transfinite_sequence(X1) ),
inference(literals_permutation,[status(thm)],[c_0_121]) ).
cnf(c_0_121_3,axiom,
( ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ function(X1)
| ordinal(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_121]) ).
cnf(c_0_122_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_122]) ).
cnf(c_0_122_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_122]) ).
cnf(c_0_123_0,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_123]) ).
cnf(c_0_123_1,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_123]) ).
cnf(c_0_123_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_123]) ).
cnf(c_0_123_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_123]) ).
cnf(c_0_124_0,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_124]) ).
cnf(c_0_124_1,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_124]) ).
cnf(c_0_124_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_124]) ).
cnf(c_0_124_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_124]) ).
cnf(c_0_125_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_125]) ).
cnf(c_0_125_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_125]) ).
cnf(c_0_125_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_125]) ).
cnf(c_0_125_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_125]) ).
cnf(c_0_128_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_128]) ).
cnf(c_0_128_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_128]) ).
cnf(c_0_128_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_128]) ).
cnf(c_0_129_0,axiom,
~ empty(sk2_esk8_0),
inference(literals_permutation,[status(thm)],[c_0_129]) ).
cnf(c_0_130_0,axiom,
~ empty(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_130]) ).
cnf(c_0_131_0,axiom,
~ empty(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_131]) ).
cnf(c_0_126_0,axiom,
transfinite_sequence_of(sk2_esk16_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_126]) ).
cnf(c_0_127_0,axiom,
element(sk2_esk15_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_127]) ).
cnf(c_0_132_0,axiom,
relation(sk2_esk14_0),
inference(literals_permutation,[status(thm)],[c_0_132]) ).
cnf(c_0_133_0,axiom,
function(sk2_esk14_0),
inference(literals_permutation,[status(thm)],[c_0_133]) ).
cnf(c_0_134_0,axiom,
epsilon_transitive(sk2_esk13_0),
inference(literals_permutation,[status(thm)],[c_0_134]) ).
cnf(c_0_135_0,axiom,
epsilon_connected(sk2_esk13_0),
inference(literals_permutation,[status(thm)],[c_0_135]) ).
cnf(c_0_136_0,axiom,
ordinal(sk2_esk13_0),
inference(literals_permutation,[status(thm)],[c_0_136]) ).
cnf(c_0_137_0,axiom,
empty(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_137]) ).
cnf(c_0_138_0,axiom,
relation(sk2_esk12_0),
inference(literals_permutation,[status(thm)],[c_0_138]) ).
cnf(c_0_139_1,axiom,
empty(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_139]) ).
cnf(c_0_140_1,axiom,
relation(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_140]) ).
cnf(c_0_141_1,axiom,
empty(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_141]) ).
cnf(c_0_142_1,axiom,
function(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_142]) ).
cnf(c_0_143_1,axiom,
relation(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_143]) ).
cnf(c_0_144_1,axiom,
function(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_144]) ).
cnf(c_0_145_1,axiom,
one_to_one(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_145]) ).
cnf(c_0_146_1,axiom,
empty(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_146]) ).
cnf(c_0_147_1,axiom,
epsilon_transitive(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_147]) ).
cnf(c_0_148_1,axiom,
epsilon_connected(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_148]) ).
cnf(c_0_149_1,axiom,
ordinal(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_149]) ).
cnf(c_0_150_1,axiom,
relation(sk2_esk8_0),
inference(literals_permutation,[status(thm)],[c_0_150]) ).
cnf(c_0_151_1,axiom,
relation(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_151]) ).
cnf(c_0_152_1,axiom,
function(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_152]) ).
cnf(c_0_153_1,axiom,
one_to_one(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_153]) ).
cnf(c_0_154_1,axiom,
epsilon_transitive(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_154]) ).
cnf(c_0_155_1,axiom,
epsilon_connected(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_155]) ).
cnf(c_0_156_1,axiom,
ordinal(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_156]) ).
cnf(c_0_157_1,axiom,
relation(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_157]) ).
cnf(c_0_158_1,axiom,
relation_empty_yielding(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_158]) ).
cnf(c_0_159_1,axiom,
relation(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_159]) ).
cnf(c_0_160_1,axiom,
relation_empty_yielding(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_160]) ).
cnf(c_0_161_1,axiom,
function(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_161]) ).
cnf(c_0_162_1,axiom,
relation(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_162]) ).
cnf(c_0_163_1,axiom,
function(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_163]) ).
cnf(c_0_164_1,axiom,
transfinite_sequence(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_164]) ).
cnf(c_0_165_1,axiom,
relation(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_165]) ).
cnf(c_0_166_1,axiom,
relation_non_empty(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_166]) ).
cnf(c_0_167_1,axiom,
function(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_167]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_169,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
file('<stdin>',t46_ordinal1) ).
fof(c_0_1_170,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_171,negated_conjecture,
( relation(esk1_0)
& function(esk1_0)
& ordinal(relation_dom(esk1_0))
& ~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_172,negated_conjecture,
~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_173,negated_conjecture,
ordinal(relation_dom(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_174,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_175,negated_conjecture,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7_176,negated_conjecture,
~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0)),
c_0_3,
[final] ).
cnf(c_0_8_177,negated_conjecture,
ordinal(relation_dom(esk1_0)),
c_0_4,
[final] ).
cnf(c_0_9_178,negated_conjecture,
relation(esk1_0),
c_0_5,
[final] ).
cnf(c_0_10_179,negated_conjecture,
function(esk1_0),
c_0_6,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_119,negated_conjecture,
~ transfinite_sequence_of(sk3_esk1_0,relation_rng(sk3_esk1_0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_7) ).
cnf(c_154,negated_conjecture,
~ transfinite_sequence_of(sk3_esk1_0,relation_rng(sk3_esk1_0)),
inference(copy,[status(esa)],[c_119]) ).
cnf(c_170,negated_conjecture,
~ transfinite_sequence_of(sk3_esk1_0,relation_rng(sk3_esk1_0)),
inference(copy,[status(esa)],[c_154]) ).
cnf(c_177,negated_conjecture,
~ transfinite_sequence_of(sk3_esk1_0,relation_rng(sk3_esk1_0)),
inference(copy,[status(esa)],[c_170]) ).
cnf(c_178,negated_conjecture,
~ transfinite_sequence_of(sk3_esk1_0,relation_rng(sk3_esk1_0)),
inference(copy,[status(esa)],[c_177]) ).
cnf(c_543,negated_conjecture,
~ transfinite_sequence_of(sk3_esk1_0,relation_rng(sk3_esk1_0)),
inference(copy,[status(esa)],[c_178]) ).
cnf(c_0,plain,
( ~ subset(relation_rng(X0),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(X0,X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_117_0) ).
cnf(c_305,plain,
( ~ subset(relation_rng(X0),X1)
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(X0,X1) ),
inference(copy,[status(esa)],[c_0]) ).
cnf(c_306,plain,
( transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(rewriting,[status(thm)],[c_305]) ).
cnf(c_563,plain,
( ~ transfinite_sequence(sk3_esk1_0)
| ~ function(sk3_esk1_0)
| ~ relation(sk3_esk1_0)
| ~ subset(relation_rng(sk3_esk1_0),relation_rng(sk3_esk1_0)) ),
inference(resolution,[status(thm)],[c_543,c_306]) ).
cnf(c_564,plain,
( ~ transfinite_sequence(sk3_esk1_0)
| ~ function(sk3_esk1_0)
| ~ relation(sk3_esk1_0)
| ~ subset(relation_rng(sk3_esk1_0),relation_rng(sk3_esk1_0)) ),
inference(rewriting,[status(thm)],[c_563]) ).
cnf(c_93,plain,
subset(X0,X0),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_164_0) ).
cnf(c_491,plain,
subset(X0,X0),
inference(copy,[status(esa)],[c_93]) ).
cnf(c_121,negated_conjecture,
relation(sk3_esk1_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_9) ).
cnf(c_158,negated_conjecture,
relation(sk3_esk1_0),
inference(copy,[status(esa)],[c_121]) ).
cnf(c_172,negated_conjecture,
relation(sk3_esk1_0),
inference(copy,[status(esa)],[c_158]) ).
cnf(c_175,negated_conjecture,
relation(sk3_esk1_0),
inference(copy,[status(esa)],[c_172]) ).
cnf(c_180,negated_conjecture,
relation(sk3_esk1_0),
inference(copy,[status(esa)],[c_175]) ).
cnf(c_547,negated_conjecture,
relation(sk3_esk1_0),
inference(copy,[status(esa)],[c_180]) ).
cnf(c_122,negated_conjecture,
function(sk3_esk1_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_10) ).
cnf(c_160,negated_conjecture,
function(sk3_esk1_0),
inference(copy,[status(esa)],[c_122]) ).
cnf(c_173,negated_conjecture,
function(sk3_esk1_0),
inference(copy,[status(esa)],[c_160]) ).
cnf(c_174,negated_conjecture,
function(sk3_esk1_0),
inference(copy,[status(esa)],[c_173]) ).
cnf(c_181,negated_conjecture,
function(sk3_esk1_0),
inference(copy,[status(esa)],[c_174]) ).
cnf(c_549,negated_conjecture,
function(sk3_esk1_0),
inference(copy,[status(esa)],[c_181]) ).
cnf(c_573,plain,
~ transfinite_sequence(sk3_esk1_0),
inference(forward_subsumption_resolution,[status(thm)],[c_564,c_491,c_547,c_549]) ).
cnf(c_574,plain,
~ transfinite_sequence(sk3_esk1_0),
inference(rewriting,[status(thm)],[c_573]) ).
cnf(c_13,plain,
( ~ ordinal(relation_dom(X0))
| ~ relation(X0)
| ~ function(X0)
| transfinite_sequence(X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_120_0) ).
cnf(c_331,plain,
( ~ ordinal(relation_dom(X0))
| ~ relation(X0)
| ~ function(X0)
| transfinite_sequence(X0) ),
inference(copy,[status(esa)],[c_13]) ).
cnf(c_332,plain,
( transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(rewriting,[status(thm)],[c_331]) ).
cnf(c_576,plain,
( ~ function(sk3_esk1_0)
| ~ relation(sk3_esk1_0)
| ~ ordinal(relation_dom(sk3_esk1_0)) ),
inference(resolution,[status(thm)],[c_574,c_332]) ).
cnf(c_577,plain,
( ~ function(sk3_esk1_0)
| ~ relation(sk3_esk1_0)
| ~ ordinal(relation_dom(sk3_esk1_0)) ),
inference(rewriting,[status(thm)],[c_576]) ).
cnf(c_120,negated_conjecture,
ordinal(relation_dom(sk3_esk1_0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p',c_0_8) ).
cnf(c_156,negated_conjecture,
ordinal(relation_dom(sk3_esk1_0)),
inference(copy,[status(esa)],[c_120]) ).
cnf(c_171,negated_conjecture,
ordinal(relation_dom(sk3_esk1_0)),
inference(copy,[status(esa)],[c_156]) ).
cnf(c_176,negated_conjecture,
ordinal(relation_dom(sk3_esk1_0)),
inference(copy,[status(esa)],[c_171]) ).
cnf(c_179,negated_conjecture,
ordinal(relation_dom(sk3_esk1_0)),
inference(copy,[status(esa)],[c_176]) ).
cnf(c_545,negated_conjecture,
ordinal(relation_dom(sk3_esk1_0)),
inference(copy,[status(esa)],[c_179]) ).
cnf(c_581,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_577,c_545,c_547,c_549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 15:18:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.41 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.41 % FOF problem with conjecture
% 0.20/0.41 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_189512.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_1d3de5.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_849824 | grep -v "SZS"
% 0.20/0.44
% 0.20/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ iProver source info
% 0.20/0.44
% 0.20/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.44 % git: non_committed_changes: true
% 0.20/0.44 % git: last_make_outside_of_git: true
% 0.20/0.44
% 0.20/0.44 %
% 0.20/0.44 % ------ Input Options
% 0.20/0.44
% 0.20/0.44 % --out_options all
% 0.20/0.44 % --tptp_safe_out true
% 0.20/0.44 % --problem_path ""
% 0.20/0.44 % --include_path ""
% 0.20/0.44 % --clausifier .//eprover
% 0.20/0.44 % --clausifier_options --tstp-format
% 0.20/0.44 % --stdin false
% 0.20/0.44 % --dbg_backtrace false
% 0.20/0.44 % --dbg_dump_prop_clauses false
% 0.20/0.44 % --dbg_dump_prop_clauses_file -
% 0.20/0.44 % --dbg_out_stat false
% 0.20/0.44
% 0.20/0.44 % ------ General Options
% 0.20/0.44
% 0.20/0.44 % --fof false
% 0.20/0.44 % --time_out_real 150.
% 0.20/0.44 % --time_out_prep_mult 0.2
% 0.20/0.44 % --time_out_virtual -1.
% 0.20/0.44 % --schedule none
% 0.20/0.44 % --ground_splitting input
% 0.20/0.44 % --splitting_nvd 16
% 0.20/0.44 % --non_eq_to_eq false
% 0.20/0.44 % --prep_gs_sim true
% 0.20/0.44 % --prep_unflatten false
% 0.20/0.44 % --prep_res_sim true
% 0.20/0.44 % --prep_upred true
% 0.20/0.44 % --res_sim_input true
% 0.20/0.44 % --clause_weak_htbl true
% 0.20/0.44 % --gc_record_bc_elim false
% 0.20/0.44 % --symbol_type_check false
% 0.20/0.44 % --clausify_out false
% 0.20/0.44 % --large_theory_mode false
% 0.20/0.44 % --prep_sem_filter none
% 0.20/0.44 % --prep_sem_filter_out false
% 0.20/0.44 % --preprocessed_out false
% 0.20/0.44 % --sub_typing false
% 0.20/0.44 % --brand_transform false
% 0.20/0.44 % --pure_diseq_elim true
% 0.20/0.44 % --min_unsat_core false
% 0.20/0.44 % --pred_elim true
% 0.20/0.44 % --add_important_lit false
% 0.20/0.44 % --soft_assumptions false
% 0.20/0.44 % --reset_solvers false
% 0.20/0.44 % --bc_imp_inh []
% 0.20/0.44 % --conj_cone_tolerance 1.5
% 0.20/0.44 % --prolific_symb_bound 500
% 0.20/0.44 % --lt_threshold 2000
% 0.20/0.44
% 0.20/0.44 % ------ SAT Options
% 0.20/0.44
% 0.20/0.44 % --sat_mode false
% 0.20/0.44 % --sat_fm_restart_options ""
% 0.20/0.44 % --sat_gr_def false
% 0.20/0.44 % --sat_epr_types true
% 0.20/0.44 % --sat_non_cyclic_types false
% 0.20/0.44 % --sat_finite_models false
% 0.20/0.44 % --sat_fm_lemmas false
% 0.20/0.44 % --sat_fm_prep false
% 0.20/0.44 % --sat_fm_uc_incr true
% 0.20/0.44 % --sat_out_model small
% 0.20/0.44 % --sat_out_clauses false
% 0.20/0.44
% 0.20/0.44 % ------ QBF Options
% 0.20/0.44
% 0.20/0.44 % --qbf_mode false
% 0.20/0.44 % --qbf_elim_univ true
% 0.20/0.44 % --qbf_sk_in true
% 0.20/0.44 % --qbf_pred_elim true
% 0.20/0.44 % --qbf_split 32
% 0.20/0.44
% 0.20/0.44 % ------ BMC1 Options
% 0.20/0.44
% 0.20/0.44 % --bmc1_incremental false
% 0.20/0.44 % --bmc1_axioms reachable_all
% 0.20/0.44 % --bmc1_min_bound 0
% 0.20/0.44 % --bmc1_max_bound -1
% 0.20/0.44 % --bmc1_max_bound_default -1
% 0.20/0.44 % --bmc1_symbol_reachability true
% 0.20/0.44 % --bmc1_property_lemmas false
% 0.20/0.44 % --bmc1_k_induction false
% 0.20/0.44 % --bmc1_non_equiv_states false
% 0.20/0.44 % --bmc1_deadlock false
% 0.20/0.44 % --bmc1_ucm false
% 0.20/0.44 % --bmc1_add_unsat_core none
% 0.20/0.44 % --bmc1_unsat_core_children false
% 0.20/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.44 % --bmc1_out_stat full
% 0.20/0.44 % --bmc1_ground_init false
% 0.20/0.44 % --bmc1_pre_inst_next_state false
% 0.20/0.44 % --bmc1_pre_inst_state false
% 0.20/0.44 % --bmc1_pre_inst_reach_state false
% 0.20/0.44 % --bmc1_out_unsat_core false
% 0.20/0.44 % --bmc1_aig_witness_out false
% 0.20/0.44 % --bmc1_verbose false
% 0.20/0.44 % --bmc1_dump_clauses_tptp false
% 0.20/0.45 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.45 % --bmc1_dump_file -
% 0.20/0.45 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.45 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.45 % --bmc1_ucm_extend_mode 1
% 0.20/0.45 % --bmc1_ucm_init_mode 2
% 0.20/0.45 % --bmc1_ucm_cone_mode none
% 0.20/0.45 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.45 % --bmc1_ucm_relax_model 4
% 0.20/0.45 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.45 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.45 % --bmc1_ucm_layered_model none
% 0.20/0.45 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.45
% 0.20/0.45 % ------ AIG Options
% 0.20/0.45
% 0.20/0.45 % --aig_mode false
% 0.20/0.45
% 0.20/0.45 % ------ Instantiation Options
% 0.20/0.45
% 0.20/0.45 % --instantiation_flag true
% 0.20/0.45 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.45 % --inst_solver_per_active 750
% 0.20/0.45 % --inst_solver_calls_frac 0.5
% 0.20/0.45 % --inst_passive_queue_type priority_queues
% 0.20/0.45 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.45 % --inst_passive_queues_freq [25;2]
% 0.20/0.45 % --inst_dismatching true
% 0.20/0.45 % --inst_eager_unprocessed_to_passive true
% 0.20/0.45 % --inst_prop_sim_given true
% 0.20/0.45 % --inst_prop_sim_new false
% 0.20/0.45 % --inst_orphan_elimination true
% 0.20/0.45 % --inst_learning_loop_flag true
% 0.20/0.45 % --inst_learning_start 3000
% 0.20/0.45 % --inst_learning_factor 2
% 0.20/0.45 % --inst_start_prop_sim_after_learn 3
% 0.20/0.45 % --inst_sel_renew solver
% 0.20/0.45 % --inst_lit_activity_flag true
% 0.20/0.45 % --inst_out_proof true
% 0.20/0.45
% 0.20/0.45 % ------ Resolution Options
% 0.20/0.45
% 0.20/0.45 % --resolution_flag true
% 0.20/0.45 % --res_lit_sel kbo_max
% 0.20/0.45 % --res_to_prop_solver none
% 0.20/0.45 % --res_prop_simpl_new false
% 0.20/0.45 % --res_prop_simpl_given false
% 0.20/0.45 % --res_passive_queue_type priority_queues
% 0.20/0.45 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.45 % --res_passive_queues_freq [15;5]
% 0.20/0.45 % --res_forward_subs full
% 0.20/0.45 % --res_backward_subs full
% 0.20/0.45 % --res_forward_subs_resolution true
% 0.20/0.45 % --res_backward_subs_resolution true
% 0.20/0.45 % --res_orphan_elimination false
% 0.20/0.45 % --res_time_limit 1000.
% 0.20/0.45 % --res_out_proof true
% 0.20/0.45 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_189512.s
% 0.20/0.45 % --modulo true
% 0.20/0.45
% 0.20/0.45 % ------ Combination Options
% 0.20/0.45
% 0.20/0.45 % --comb_res_mult 1000
% 0.20/0.45 % --comb_inst_mult 300
% 0.20/0.45 % ------
% 0.20/0.45
% 0.20/0.45 % ------ Parsing...% successful
% 0.20/0.45
% 0.20/0.45 % ------ 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 %
% 0.20/0.45
% 0.20/0.45 % ------ Proving...
% 0.20/0.45 % ------ Problem Properties
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % EPR false
% 0.20/0.45 % Horn false
% 0.20/0.45 % Has equality true
% 0.20/0.45
% 0.20/0.45 % % ------ Input Options Time Limit: Unbounded
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 % % ------ Current options:
% 0.20/0.45
% 0.20/0.45 % ------ Input Options
% 0.20/0.45
% 0.20/0.45 % --out_options all
% 0.20/0.45 % --tptp_safe_out true
% 0.20/0.45 % --problem_path ""
% 0.20/0.45 % --include_path ""
% 0.20/0.45 % --clausifier .//eprover
% 0.20/0.45 % --clausifier_options --tstp-format
% 0.20/0.45 % --stdin false
% 0.20/0.45 % --dbg_backtrace false
% 0.20/0.45 % --dbg_dump_prop_clauses false
% 0.20/0.45 % --dbg_dump_prop_clauses_file -
% 0.20/0.45 % --dbg_out_stat false
% 0.20/0.45
% 0.20/0.45 % ------ General Options
% 0.20/0.45
% 0.20/0.45 % --fof false
% 0.20/0.45 % --time_out_real 150.
% 0.20/0.45 % --time_out_prep_mult 0.2
% 0.20/0.45 % --time_out_virtual -1.
% 0.20/0.45 % --schedule none
% 0.20/0.45 % --ground_splitting input
% 0.20/0.45 % --splitting_nvd 16
% 0.20/0.45 % --non_eq_to_eq false
% 0.20/0.45 % --prep_gs_sim true
% 0.20/0.45 % --prep_unflatten false
% 0.20/0.45 % --prep_res_sim true
% 0.20/0.45 % --prep_upred true
% 0.20/0.45 % --res_sim_input true
% 0.20/0.45 % --clause_weak_htbl true
% 0.20/0.45 % --gc_record_bc_elim false
% 0.20/0.45 % --symbol_type_check false
% 0.20/0.45 % --clausify_out false
% 0.20/0.45 % --large_theory_mode false
% 0.20/0.45 % --prep_sem_filter none
% 0.20/0.45 % --prep_sem_filter_out false
% 0.20/0.45 % --preprocessed_out false
% 0.20/0.45 % --sub_typing false
% 0.20/0.45 % --brand_transform false
% 0.20/0.45 % --pure_diseq_elim true
% 0.20/0.45 % --min_unsat_core false
% 0.20/0.45 % --pred_elim true
% 0.20/0.45 % --add_important_lit false
% 0.20/0.45 % --soft_assumptions false
% 0.20/0.45 % --reset_solvers false
% 0.20/0.45 % --bc_imp_inh []
% 0.20/0.45 % --conj_cone_tolerance 1.5
% 0.20/0.45 % --prolific_symb_bound 500
% 0.20/0.45 % --lt_threshold 2000
% 0.20/0.45
% 0.20/0.45 % ------ SAT Options
% 0.20/0.45
% 0.20/0.45 % --sat_mode false
% 0.20/0.45 % --sat_fm_restart_options ""
% 0.20/0.45 % --sat_gr_def false
% 0.20/0.45 % --sat_epr_types true
% 0.20/0.45 % --sat_non_cyclic_types false
% 0.20/0.45 % --sat_finite_models false
% 0.20/0.45 % --sat_fm_lemmas false
% 0.20/0.45 % --sat_fm_prep false
% 0.20/0.45 % --sat_fm_uc_incr true
% 0.20/0.45 % --sat_out_model small
% 0.20/0.45 % --sat_out_clauses false
% 0.20/0.45
% 0.20/0.45 % ------ QBF Options
% 0.20/0.45
% 0.20/0.45 % --qbf_mode false
% 0.20/0.45 % --qbf_elim_univ true
% 0.20/0.45 % --qbf_sk_in true
% 0.20/0.45 % --qbf_pred_elim true
% 0.20/0.45 % --qbf_split 32
% 0.20/0.45
% 0.20/0.45 % ------ BMC1 Options
% 0.20/0.45
% 0.20/0.45 % --bmc1_incremental false
% 0.20/0.45 % --bmc1_axioms reachable_all
% 0.20/0.45 % --bmc1_min_bound 0
% 0.20/0.45 % --bmc1_max_bound -1
% 0.20/0.45 % --bmc1_max_bound_default -1
% 0.20/0.45 % --bmc1_symbol_reachability true
% 0.20/0.45 % --bmc1_property_lemmas false
% 0.20/0.45 % --bmc1_k_induction false
% 0.20/0.45 % --bmc1_non_equiv_states false
% 0.20/0.45 % --bmc1_deadlock false
% 0.20/0.45 % --bmc1_ucm false
% 0.20/0.45 % --bmc1_add_unsat_core none
% 0.20/0.45 % --bmc1_unsat_core_children false
% 0.20/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.45 % --bmc1_out_stat full
% 0.20/0.45 % --bmc1_ground_init false
% 0.20/0.45 % --bmc1_pre_inst_next_state false
% 0.20/0.45 % --bmc1_pre_inst_state false
% 0.20/0.45 % --bmc1_pre_inst_reach_state false
% 0.20/0.45 % --bmc1_out_unsat_core false
% 0.20/0.45 % --bmc1_aig_witness_out false
% 0.20/0.45 % --bmc1_verbose false
% 0.20/0.45 % --bmc1_dump_clauses_tptp false
% 0.20/0.45 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.45 % --bmc1_dump_file -
% 0.20/0.45 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.45 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.45 % --bmc1_ucm_extend_mode 1
% 0.20/0.45 % --bmc1_ucm_init_mode 2
% 0.20/0.45 % --bmc1_ucm_cone_mode none
% 0.20/0.45 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.45 % --bmc1_ucm_relax_model 4
% 0.20/0.45 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.45 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.45 % --bmc1_ucm_layered_model none
% 0.20/0.45 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.45
% 0.20/0.45 % ------ AIG Options
% 0.20/0.45
% 0.20/0.45 % --aig_mode false
% 0.20/0.45
% 0.20/0.45 % ------ Instantiation Options
% 0.20/0.45
% 0.20/0.45 % --instantiation_flag true
% 0.20/0.45 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.45 % --inst_solver_per_active 750
% 0.20/0.45 % --inst_solver_calls_frac 0.5
% 0.20/0.45 % --inst_passive_queue_type priority_queues
% 0.20/0.45 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.45 % --inst_passive_queues_freq [25;2]
% 0.20/0.45 % --inst_dismatching true
% 0.20/0.45 % --inst_eager_unprocessed_to_passive true
% 0.20/0.45 % --inst_prop_sim_given true
% 0.20/0.45 % --inst_prop_sim_new false
% 0.20/0.45 % --inst_orphan_elimination true
% 0.20/0.45 % --inst_learning_loop_flag true
% 0.20/0.45 % --inst_learning_start 3000
% 0.20/0.45 % --inst_learning_factor 2
% 0.20/0.45 % --inst_start_prop_sim_after_learn 3
% 0.20/0.45 % --inst_sel_renew solver
% 0.20/0.45 % --inst_lit_activity_flag true
% 0.20/0.45 % --inst_out_proof true
% 0.20/0.45
% 0.20/0.45 % ------ Resolution Options
% 0.20/0.45
% 0.20/0.45 % --resolution_flag true
% 0.20/0.45 % --res_lit_sel kbo_max
% 0.20/0.45 % --res_to_prop_solver none
% 0.20/0.45 % --res_prop_simpl_new false
% 0.20/0.45 % --res_prop_simpl_given false
% 0.20/0.45 % --res_passive_queue_type priority_queues
% 0.20/0.45 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.45 % --res_passive_queues_freq [15;5]
% 0.20/0.45 % --res_forward_subs full
% 0.20/0.45 % --res_backward_subs full
% 0.20/0.45 % --res_forward_subs_resolution true
% 0.20/0.45 % --res_backward_subs_resolution true
% 0.20/0.45 % --res_orphan_elimination false
% 0.20/0.45 % --res_time_limit 1000.
% 0.20/0.45 % --res_out_proof true
% 0.20/0.45 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_189512.s
% 0.20/0.45 % --modulo true
% 0.20/0.45
% 0.20/0.45 % ------ Combination Options
% 0.20/0.45
% 0.20/0.45 % --comb_res_mult 1000
% 0.20/0.45 % --comb_inst_mult 300
% 0.20/0.45 % ------
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 % ------ Proving...
% 0.20/0.45 %
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 % Resolution empty clause
% 0.20/0.45
% 0.20/0.45 % ------ Statistics
% 0.20/0.45
% 0.20/0.45 % ------ General
% 0.20/0.45
% 0.20/0.45 % num_of_input_clauses: 123
% 0.20/0.45 % num_of_input_neg_conjectures: 4
% 0.20/0.45 % num_of_splits: 0
% 0.20/0.45 % num_of_split_atoms: 0
% 0.20/0.45 % num_of_sem_filtered_clauses: 0
% 0.20/0.45 % num_of_subtypes: 0
% 0.20/0.45 % monotx_restored_types: 0
% 0.20/0.45 % sat_num_of_epr_types: 0
% 0.20/0.45 % sat_num_of_non_cyclic_types: 0
% 0.20/0.45 % sat_guarded_non_collapsed_types: 0
% 0.20/0.45 % is_epr: 0
% 0.20/0.45 % is_horn: 0
% 0.20/0.45 % has_eq: 1
% 0.20/0.45 % num_pure_diseq_elim: 0
% 0.20/0.45 % simp_replaced_by: 0
% 0.20/0.45 % res_preprocessed: 8
% 0.20/0.45 % prep_upred: 0
% 0.20/0.45 % prep_unflattend: 0
% 0.20/0.45 % pred_elim_cands: 0
% 0.20/0.45 % pred_elim: 0
% 0.20/0.45 % pred_elim_cl: 0
% 0.20/0.45 % pred_elim_cycles: 0
% 0.20/0.45 % forced_gc_time: 0
% 0.20/0.45 % gc_basic_clause_elim: 0
% 0.20/0.45 % parsing_time: 0.003
% 0.20/0.45 % sem_filter_time: 0.
% 0.20/0.45 % pred_elim_time: 0.
% 0.20/0.45 % out_proof_time: 0.001
% 0.20/0.45 % monotx_time: 0.
% 0.20/0.45 % subtype_inf_time: 0.
% 0.20/0.45 % unif_index_cands_time: 0.
% 0.20/0.45 % unif_index_add_time: 0.
% 0.20/0.45 % total_time: 0.029
% 0.20/0.45 % num_of_symbols: 61
% 0.20/0.45 % num_of_terms: 203
% 0.20/0.45
% 0.20/0.45 % ------ Propositional Solver
% 0.20/0.45
% 0.20/0.45 % prop_solver_calls: 1
% 0.20/0.45 % prop_fast_solver_calls: 12
% 0.20/0.45 % prop_num_of_clauses: 120
% 0.20/0.45 % prop_preprocess_simplified: 290
% 0.20/0.45 % prop_fo_subsumed: 0
% 0.20/0.45 % prop_solver_time: 0.
% 0.20/0.45 % prop_fast_solver_time: 0.
% 0.20/0.45 % prop_unsat_core_time: 0.
% 0.20/0.45
% 0.20/0.45 % ------ QBF
% 0.20/0.45
% 0.20/0.45 % qbf_q_res: 0
% 0.20/0.45 % qbf_num_tautologies: 0
% 0.20/0.45 % qbf_prep_cycles: 0
% 0.20/0.45
% 0.20/0.45 % ------ BMC1
% 0.20/0.45
% 0.20/0.45 % bmc1_current_bound: -1
% 0.20/0.45 % bmc1_last_solved_bound: -1
% 0.20/0.45 % bmc1_unsat_core_size: -1
% 0.20/0.45 % bmc1_unsat_core_parents_size: -1
% 0.20/0.45 % bmc1_merge_next_fun: 0
% 0.20/0.45 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.45
% 0.20/0.45 % ------ Instantiation
% 0.20/0.45
% 0.20/0.45 % inst_num_of_clauses: 117
% 0.20/0.45 % inst_num_in_passive: 0
% 0.20/0.45 % inst_num_in_active: 0
% 0.20/0.45 % inst_num_in_unprocessed: 123
% 0.20/0.45 % inst_num_of_loops: 0
% 0.20/0.45 % inst_num_of_learning_restarts: 0
% 0.20/0.45 % inst_num_moves_active_passive: 0
% 0.20/0.45 % inst_lit_activity: 0
% 0.20/0.45 % inst_lit_activity_moves: 0
% 0.20/0.45 % inst_num_tautologies: 0
% 0.20/0.45 % inst_num_prop_implied: 0
% 0.20/0.45 % inst_num_existing_simplified: 0
% 0.20/0.45 % inst_num_eq_res_simplified: 0
% 0.20/0.45 % inst_num_child_elim: 0
% 0.20/0.45 % inst_num_of_dismatching_blockings: 0
% 0.20/0.45 % inst_num_of_non_proper_insts: 0
% 0.20/0.45 % inst_num_of_duplicates: 0
% 0.20/0.45 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.45 % inst_dismatching_checking_time: 0.
% 0.20/0.45
% 0.20/0.45 % ------ Resolution
% 0.20/0.45
% 0.20/0.45 % res_num_of_clauses: 140
% 0.20/0.45 % res_num_in_passive: 0
% 0.20/0.45 % res_num_in_active: 91
% 0.20/0.45 % res_num_of_loops: 8
% 0.20/0.45 % res_forward_subset_subsumed: 27
% 0.20/0.45 % res_backward_subset_subsumed: 0
% 0.20/0.45 % res_forward_subsumed: 0
% 0.20/0.45 % res_backward_subsumed: 0
% 0.20/0.45 % res_forward_subsumption_resolution: 6
% 0.20/0.45 % res_backward_subsumption_resolution: 0
% 0.20/0.45 % res_clause_to_clause_subsumption: 6
% 0.20/0.45 % res_orphan_elimination: 0
% 0.20/0.45 % res_tautology_del: 8
% 0.20/0.45 % res_num_eq_res_simplified: 0
% 0.20/0.45 % res_num_sel_changes: 0
% 0.20/0.45 % res_moves_from_active_to_pass: 0
% 0.20/0.45
% 0.20/0.45 % Status Unsatisfiable
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------