TSTP Solution File: NUM395+1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM395+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n004.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 10:56:56 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% 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(l18_ordinal1,axiom,
( epsilon_transitive(empty_set)
& epsilon_connected(empty_set) ),
input ).
fof(l18_ordinal1_0,plain,
( epsilon_transitive(empty_set)
| $false ),
inference(orientation,[status(thm)],[l18_ordinal1]) ).
fof(l18_ordinal1_1,plain,
( epsilon_connected(empty_set)
| $false ),
inference(orientation,[status(thm)],[l18_ordinal1]) ).
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
input ).
fof(d4_ordinal1_0,plain,
! [A] :
( ordinal(A)
| ~ ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(orientation,[status(thm)],[d4_ordinal1]) ).
fof(d4_ordinal1_1,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(orientation,[status(thm)],[d4_ordinal1]) ).
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(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(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(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_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_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_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(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(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(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(def_lhs_atom1,axiom,
! [B,A] :
( lhs_atom1(B,A)
<=> ~ element(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [A,B] :
( lhs_atom1(B,A)
| empty(B)
| in(A,B) ),
inference(fold_definition,[status(thm)],[t2_subset_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [B,A] :
( lhs_atom2(B,A)
<=> ~ in(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A,B] :
( lhs_atom2(B,A)
| ~ in(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0,def_lhs_atom2]) ).
fof(to_be_clausified_2,plain,
! [A,B] :
( lhs_atom2(B,A)
| element(A,B) ),
inference(fold_definition,[status(thm)],[t1_subset_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [A] :
( lhs_atom3(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
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_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)
<=> ~ ordinal(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [A] :
( lhs_atom4(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[cc1_ordinal1_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [A] :
( lhs_atom5(A)
<=> ordinal(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A] :
( lhs_atom5(A)
| ~ ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[cc2_ordinal1_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
( lhs_atom6
<=> relation(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[fc4_relat_1_1,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc4_relat_1_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> relation_empty_yielding(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_2,def_lhs_atom8]) ).
fof(to_be_clausified_10,plain,
( lhs_atom6
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_1,def_lhs_atom6]) ).
fof(to_be_clausified_11,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc12_relat_1_0,def_lhs_atom7]) ).
fof(to_be_clausified_12,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom7]) ).
fof(to_be_clausified_13,plain,
! [A] :
( lhs_atom3(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom3]) ).
fof(to_be_clausified_14,plain,
! [A] :
( lhs_atom4(A)
| ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[d4_ordinal1_1,def_lhs_atom4]) ).
fof(to_be_clausified_15,plain,
! [A] :
( lhs_atom5(A)
| ~ ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(fold_definition,[status(thm)],[d4_ordinal1_0,def_lhs_atom5]) ).
fof(def_lhs_atom9,axiom,
( lhs_atom9
<=> epsilon_connected(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
( lhs_atom9
| $false ),
inference(fold_definition,[status(thm)],[l18_ordinal1_1,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> epsilon_transitive(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[l18_ordinal1_0,def_lhs_atom10]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_1,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| empty(X1)
| in(X2,X1) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_2,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| element(X2,X1) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_3,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_4,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_5,axiom,
! [X2] :
( lhs_atom4(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_6,axiom,
! [X2] :
( lhs_atom4(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_7,axiom,
! [X2] :
( lhs_atom3(X2)
| relation(X2) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_8,axiom,
! [X2] :
( lhs_atom3(X2)
| function(X2) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_9,axiom,
! [X2] :
( lhs_atom3(X2)
| X2 = empty_set ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_10,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_11,axiom,
( lhs_atom9
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_12,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_13,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_14,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_15,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_16,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_17,axiom,
( lhs_atom6
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_18,plain,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_19,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| empty(X1)
| in(X2,X1) ),
c_0_1 ).
fof(c_0_20,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| element(X2,X1) ),
c_0_2 ).
fof(c_0_21,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_3 ).
fof(c_0_22,axiom,
! [X2] :
( lhs_atom5(X2)
| ~ ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_4 ).
fof(c_0_23,axiom,
! [X2] :
( lhs_atom4(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_5 ).
fof(c_0_24,axiom,
! [X2] :
( lhs_atom4(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
c_0_6 ).
fof(c_0_25,axiom,
! [X2] :
( lhs_atom3(X2)
| relation(X2) ),
c_0_7 ).
fof(c_0_26,axiom,
! [X2] :
( lhs_atom3(X2)
| function(X2) ),
c_0_8 ).
fof(c_0_27,axiom,
! [X2] :
( lhs_atom3(X2)
| X2 = empty_set ),
c_0_9 ).
fof(c_0_28,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_29,plain,
lhs_atom9,
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_30,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_31,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_32,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_33,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_34,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_35,plain,
lhs_atom6,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_36,plain,
! [X3,X4] :
( lhs_atom2(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_18]) ).
fof(c_0_37,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| empty(X3)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_19]) ).
fof(c_0_38,plain,
! [X3,X4] :
( lhs_atom2(X3,X4)
| element(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_20]) ).
fof(c_0_39,plain,
! [X3] :
( lhs_atom5(X3)
| ~ epsilon_transitive(X3)
| ~ epsilon_connected(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_40,plain,
! [X3] :
( lhs_atom5(X3)
| ~ epsilon_transitive(X3)
| ~ epsilon_connected(X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
fof(c_0_41,plain,
! [X3] :
( ( epsilon_transitive(X3)
| lhs_atom4(X3) )
& ( epsilon_connected(X3)
| lhs_atom4(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
fof(c_0_42,plain,
! [X3] :
( ( epsilon_transitive(X3)
| lhs_atom4(X3) )
& ( epsilon_connected(X3)
| lhs_atom4(X3) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_24])]) ).
fof(c_0_43,plain,
! [X3] :
( lhs_atom3(X3)
| relation(X3) ),
inference(variable_rename,[status(thm)],[c_0_25]) ).
fof(c_0_44,plain,
! [X3] :
( lhs_atom3(X3)
| function(X3) ),
inference(variable_rename,[status(thm)],[c_0_26]) ).
fof(c_0_45,plain,
! [X3] :
( lhs_atom3(X3)
| X3 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_27]) ).
fof(c_0_46,plain,
lhs_atom10,
c_0_28 ).
fof(c_0_47,plain,
lhs_atom9,
c_0_29 ).
fof(c_0_48,plain,
lhs_atom7,
c_0_30 ).
fof(c_0_49,plain,
lhs_atom7,
c_0_31 ).
fof(c_0_50,plain,
lhs_atom6,
c_0_32 ).
fof(c_0_51,plain,
lhs_atom8,
c_0_33 ).
fof(c_0_52,plain,
lhs_atom7,
c_0_34 ).
fof(c_0_53,plain,
lhs_atom6,
c_0_35 ).
cnf(c_0_54,plain,
( lhs_atom2(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_55,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_56,plain,
( element(X1,X2)
| lhs_atom2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_57,plain,
( lhs_atom5(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_58,plain,
( lhs_atom5(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_59,plain,
( lhs_atom4(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_60,plain,
( lhs_atom4(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_61,plain,
( lhs_atom4(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_62,plain,
( lhs_atom4(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_63,plain,
( relation(X1)
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_64,plain,
( function(X1)
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_65,plain,
( X1 = empty_set
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_66,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_67,plain,
lhs_atom9,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_68,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_69,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_70,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_71,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_72,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_73,plain,
lhs_atom6,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_74,plain,
( lhs_atom2(X1,X2)
| ~ in(X1,X2) ),
c_0_54,
[final] ).
cnf(c_0_75,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom1(X2,X1) ),
c_0_55,
[final] ).
cnf(c_0_76,plain,
( element(X1,X2)
| lhs_atom2(X2,X1) ),
c_0_56,
[final] ).
cnf(c_0_77,plain,
( lhs_atom5(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_57,
[final] ).
cnf(c_0_78,plain,
( lhs_atom5(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
c_0_58,
[final] ).
cnf(c_0_79,plain,
( lhs_atom4(X1)
| epsilon_transitive(X1) ),
c_0_59,
[final] ).
cnf(c_0_80,plain,
( lhs_atom4(X1)
| epsilon_connected(X1) ),
c_0_60,
[final] ).
cnf(c_0_81,plain,
( lhs_atom4(X1)
| epsilon_transitive(X1) ),
c_0_61,
[final] ).
cnf(c_0_82,plain,
( lhs_atom4(X1)
| epsilon_connected(X1) ),
c_0_62,
[final] ).
cnf(c_0_83,plain,
( relation(X1)
| lhs_atom3(X1) ),
c_0_63,
[final] ).
cnf(c_0_84,plain,
( function(X1)
| lhs_atom3(X1) ),
c_0_64,
[final] ).
cnf(c_0_85,plain,
( X1 = empty_set
| lhs_atom3(X1) ),
c_0_65,
[final] ).
cnf(c_0_86,plain,
lhs_atom10,
c_0_66,
[final] ).
cnf(c_0_87,plain,
lhs_atom9,
c_0_67,
[final] ).
cnf(c_0_88,plain,
lhs_atom7,
c_0_68,
[final] ).
cnf(c_0_89,plain,
lhs_atom7,
c_0_69,
[final] ).
cnf(c_0_90,plain,
lhs_atom6,
c_0_70,
[final] ).
cnf(c_0_91,plain,
lhs_atom8,
c_0_71,
[final] ).
cnf(c_0_92,plain,
lhs_atom7,
c_0_72,
[final] ).
cnf(c_0_93,plain,
lhs_atom6,
c_0_73,
[final] ).
% End CNF derivation
cnf(c_0_74_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_74,def_lhs_atom2]) ).
cnf(c_0_75_0,axiom,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(unfold_definition,[status(thm)],[c_0_75,def_lhs_atom1]) ).
cnf(c_0_76_0,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_76,def_lhs_atom2]) ).
cnf(c_0_77_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_77,def_lhs_atom5]) ).
cnf(c_0_78_0,axiom,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_78,def_lhs_atom5]) ).
cnf(c_0_79_0,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_79,def_lhs_atom4]) ).
cnf(c_0_80_0,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(unfold_definition,[status(thm)],[c_0_80,def_lhs_atom4]) ).
cnf(c_0_81_0,axiom,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(unfold_definition,[status(thm)],[c_0_81,def_lhs_atom4]) ).
cnf(c_0_82_0,axiom,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(unfold_definition,[status(thm)],[c_0_82,def_lhs_atom4]) ).
cnf(c_0_83_0,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(unfold_definition,[status(thm)],[c_0_83,def_lhs_atom3]) ).
cnf(c_0_84_0,axiom,
( ~ empty(X1)
| function(X1) ),
inference(unfold_definition,[status(thm)],[c_0_84,def_lhs_atom3]) ).
cnf(c_0_85_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_85,def_lhs_atom3]) ).
cnf(c_0_86_0,axiom,
epsilon_transitive(empty_set),
inference(unfold_definition,[status(thm)],[c_0_86,def_lhs_atom10]) ).
cnf(c_0_87_0,axiom,
epsilon_connected(empty_set),
inference(unfold_definition,[status(thm)],[c_0_87,def_lhs_atom9]) ).
cnf(c_0_88_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_88,def_lhs_atom7]) ).
cnf(c_0_89_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_89,def_lhs_atom7]) ).
cnf(c_0_90_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_90,def_lhs_atom6]) ).
cnf(c_0_91_0,axiom,
relation_empty_yielding(empty_set),
inference(unfold_definition,[status(thm)],[c_0_91,def_lhs_atom8]) ).
cnf(c_0_92_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_92,def_lhs_atom7]) ).
cnf(c_0_93_0,axiom,
relation(empty_set),
inference(unfold_definition,[status(thm)],[c_0_93,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] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_1_002,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_2_003,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_3_004,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_4_005,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_5_006,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_6_007,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('<stdin>',rc1_ordinal1) ).
fof(c_0_7_008,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_8_009,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_9_010,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_10_011,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('<stdin>',rc4_funct_1) ).
fof(c_0_11_012,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('<stdin>',rc5_funct_1) ).
fof(c_0_12_013,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_13_014,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_14_015,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_15_016,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_0 ).
fof(c_0_16_017,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_1 ).
fof(c_0_17_018,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_2 ).
fof(c_0_18_019,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_3 ).
fof(c_0_19_020,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_20_021,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_21_022,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
c_0_6 ).
fof(c_0_22_023,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_7 ).
fof(c_0_23_024,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_8 ).
fof(c_0_24_025,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_9 ).
fof(c_0_25_026,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
c_0_10 ).
fof(c_0_26_027,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
c_0_11 ).
fof(c_0_27_028,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_12 ).
fof(c_0_28_029,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_13 ).
fof(c_0_29_030,axiom,
? [X1] : empty(X1),
c_0_14 ).
fof(c_0_30_031,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
fof(c_0_31_032,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_16])])]) ).
fof(c_0_32_033,plain,
! [X3] : element(esk12_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
fof(c_0_33_034,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_18])])])]) ).
fof(c_0_34_035,plain,
( ~ empty(esk4_0)
& relation(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
fof(c_0_35_036,plain,
~ empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_20])]) ).
fof(c_0_36_037,plain,
( epsilon_transitive(esk11_0)
& epsilon_connected(esk11_0)
& ordinal(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])]) ).
fof(c_0_37_038,plain,
( relation(esk10_0)
& function(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_22])]) ).
fof(c_0_38_039,plain,
( relation(esk9_0)
& empty(esk9_0)
& function(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
fof(c_0_39_040,plain,
( relation(esk8_0)
& function(esk8_0)
& one_to_one(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_24])]) ).
fof(c_0_40_041,plain,
( relation(esk7_0)
& relation_empty_yielding(esk7_0)
& function(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_25])]) ).
fof(c_0_41_042,plain,
( relation(esk6_0)
& relation_non_empty(esk6_0)
& function(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
fof(c_0_42_043,plain,
( empty(esk5_0)
& relation(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_43_044,plain,
( relation(esk3_0)
& relation_empty_yielding(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_44_045,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_45_046,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46_047,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47_048,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_48_049,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_49_050,plain,
element(esk12_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_50_051,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_51_052,plain,
~ empty(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_52_053,plain,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_53_054,plain,
epsilon_transitive(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_54_055,plain,
epsilon_connected(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_55_056,plain,
ordinal(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_56_057,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_57_058,plain,
function(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_58_059,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_59_060,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_60_061,plain,
function(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_61_062,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_62_063,plain,
function(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_63_064,plain,
one_to_one(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_64_065,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_65_066,plain,
relation_empty_yielding(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_66_067,plain,
function(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_67_068,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_68_069,plain,
relation_non_empty(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_69_070,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_70_071,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_71_072,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_72_073,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_73_074,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_74_075,plain,
relation_empty_yielding(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_75_076,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_76_077,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_45,
[final] ).
cnf(c_0_77_078,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_46,
[final] ).
cnf(c_0_78_079,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_47,
[final] ).
cnf(c_0_79_080,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_48,
[final] ).
cnf(c_0_80_081,plain,
element(esk12_1(X1),X1),
c_0_49,
[final] ).
cnf(c_0_81_082,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_50,
[final] ).
cnf(c_0_82_083,plain,
~ empty(esk4_0),
c_0_51,
[final] ).
cnf(c_0_83_084,plain,
~ empty(esk1_0),
c_0_52,
[final] ).
cnf(c_0_84_085,plain,
epsilon_transitive(esk11_0),
c_0_53,
[final] ).
cnf(c_0_85_086,plain,
epsilon_connected(esk11_0),
c_0_54,
[final] ).
cnf(c_0_86_087,plain,
ordinal(esk11_0),
c_0_55,
[final] ).
cnf(c_0_87_088,plain,
relation(esk10_0),
c_0_56,
[final] ).
cnf(c_0_88_089,plain,
function(esk10_0),
c_0_57,
[final] ).
cnf(c_0_89_090,plain,
relation(esk9_0),
c_0_58,
[final] ).
cnf(c_0_90_091,plain,
empty(esk9_0),
c_0_59,
[final] ).
cnf(c_0_91_092,plain,
function(esk9_0),
c_0_60,
[final] ).
cnf(c_0_92_093,plain,
relation(esk8_0),
c_0_61,
[final] ).
cnf(c_0_93_094,plain,
function(esk8_0),
c_0_62,
[final] ).
cnf(c_0_94,plain,
one_to_one(esk8_0),
c_0_63,
[final] ).
cnf(c_0_95,plain,
relation(esk7_0),
c_0_64,
[final] ).
cnf(c_0_96,plain,
relation_empty_yielding(esk7_0),
c_0_65,
[final] ).
cnf(c_0_97,plain,
function(esk7_0),
c_0_66,
[final] ).
cnf(c_0_98,plain,
relation(esk6_0),
c_0_67,
[final] ).
cnf(c_0_99,plain,
relation_non_empty(esk6_0),
c_0_68,
[final] ).
cnf(c_0_100,plain,
function(esk6_0),
c_0_69,
[final] ).
cnf(c_0_101,plain,
empty(esk5_0),
c_0_70,
[final] ).
cnf(c_0_102,plain,
relation(esk5_0),
c_0_71,
[final] ).
cnf(c_0_103,plain,
relation(esk4_0),
c_0_72,
[final] ).
cnf(c_0_104,plain,
relation(esk3_0),
c_0_73,
[final] ).
cnf(c_0_105,plain,
relation_empty_yielding(esk3_0),
c_0_74,
[final] ).
cnf(c_0_106,plain,
empty(esk2_0),
c_0_75,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_76_1,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_76]) ).
cnf(c_0_76_2,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_76]) ).
cnf(c_0_77_1,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_77]) ).
cnf(c_0_77_2,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_77]) ).
cnf(c_0_77_3,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_77]) ).
cnf(c_0_77_4,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_77]) ).
cnf(c_0_78_1,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_78]) ).
cnf(c_0_78_2,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_78]) ).
cnf(c_0_78_3,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_78]) ).
cnf(c_0_78_4,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_78]) ).
cnf(c_0_79_1,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_79]) ).
cnf(c_0_79_2,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_79]) ).
cnf(c_0_79_3,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_79]) ).
cnf(c_0_79_4,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_79]) ).
cnf(c_0_81_1,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_81]) ).
cnf(c_0_81_2,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_81]) ).
cnf(c_0_81_3,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_81]) ).
cnf(c_0_82_1,axiom,
~ empty(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_82]) ).
cnf(c_0_83_1,axiom,
~ empty(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_83]) ).
cnf(c_0_80_1,axiom,
element(sk2_esk12_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_80]) ).
cnf(c_0_84_1,axiom,
epsilon_transitive(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_84]) ).
cnf(c_0_85_1,axiom,
epsilon_connected(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_85]) ).
cnf(c_0_86_1,axiom,
ordinal(sk2_esk11_0),
inference(literals_permutation,[status(thm)],[c_0_86]) ).
cnf(c_0_87_1,axiom,
relation(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_87]) ).
cnf(c_0_88_1,axiom,
function(sk2_esk10_0),
inference(literals_permutation,[status(thm)],[c_0_88]) ).
cnf(c_0_89_1,axiom,
relation(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_89]) ).
cnf(c_0_90_1,axiom,
empty(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_90]) ).
cnf(c_0_91_1,axiom,
function(sk2_esk9_0),
inference(literals_permutation,[status(thm)],[c_0_91]) ).
cnf(c_0_92_1,axiom,
relation(sk2_esk8_0),
inference(literals_permutation,[status(thm)],[c_0_92]) ).
cnf(c_0_93_1,axiom,
function(sk2_esk8_0),
inference(literals_permutation,[status(thm)],[c_0_93]) ).
cnf(c_0_94_0,axiom,
one_to_one(sk2_esk8_0),
inference(literals_permutation,[status(thm)],[c_0_94]) ).
cnf(c_0_95_0,axiom,
relation(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_95]) ).
cnf(c_0_96_0,axiom,
relation_empty_yielding(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_96]) ).
cnf(c_0_97_0,axiom,
function(sk2_esk7_0),
inference(literals_permutation,[status(thm)],[c_0_97]) ).
cnf(c_0_98_0,axiom,
relation(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_98]) ).
cnf(c_0_99_0,axiom,
relation_non_empty(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_99]) ).
cnf(c_0_100_0,axiom,
function(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_100]) ).
cnf(c_0_101_0,axiom,
empty(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_101]) ).
cnf(c_0_102_0,axiom,
relation(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_102]) ).
cnf(c_0_103_0,axiom,
relation(sk2_esk4_0),
inference(literals_permutation,[status(thm)],[c_0_103]) ).
cnf(c_0_104_0,axiom,
relation(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_104]) ).
cnf(c_0_105_0,axiom,
relation_empty_yielding(sk2_esk3_0),
inference(literals_permutation,[status(thm)],[c_0_105]) ).
cnf(c_0_106_0,axiom,
empty(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_106]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_095,conjecture,
ordinal(empty_set),
file('<stdin>',t27_ordinal1) ).
fof(c_0_1_096,negated_conjecture,
~ ordinal(empty_set),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_2_097,negated_conjecture,
~ ordinal(empty_set),
c_0_1 ).
cnf(c_0_3_098,negated_conjecture,
~ ordinal(empty_set),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_099,negated_conjecture,
~ ordinal(empty_set),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_49,plain,
epsilon_connected(empty_set),
file('/export/starexec/sandbox2/tmp/iprover_modulo_16b789.p',c_0_87_0) ).
cnf(c_50,plain,
epsilon_transitive(empty_set),
file('/export/starexec/sandbox2/tmp/iprover_modulo_16b789.p',c_0_86_0) ).
cnf(c_59,plain,
( ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0)
| ordinal(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_16b789.p',c_0_77_0) ).
cnf(c_66,plain,
( ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set)
| ordinal(empty_set) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_63,negated_conjecture,
~ ordinal(empty_set),
file('/export/starexec/sandbox2/tmp/iprover_modulo_16b789.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_49,c_50,c_66,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM395+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : iprover_modulo %s %d
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 02:03:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.12/0.40 % Orienting using strategy Equiv(ClausalAll)
% 0.12/0.40 % FOF problem with conjecture
% 0.12/0.40 % 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_e25697.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_16b789.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_2c7123 | grep -v "SZS"
% 0.19/0.42
% 0.19/0.42 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.42
% 0.19/0.42 %
% 0.19/0.42 % ------ iProver source info
% 0.19/0.42
% 0.19/0.42 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.42 % git: non_committed_changes: true
% 0.19/0.42 % git: last_make_outside_of_git: true
% 0.19/0.42
% 0.19/0.42 %
% 0.19/0.42 % ------ Input Options
% 0.19/0.42
% 0.19/0.42 % --out_options all
% 0.19/0.42 % --tptp_safe_out true
% 0.19/0.42 % --problem_path ""
% 0.19/0.42 % --include_path ""
% 0.19/0.42 % --clausifier .//eprover
% 0.19/0.42 % --clausifier_options --tstp-format
% 0.19/0.42 % --stdin false
% 0.19/0.42 % --dbg_backtrace false
% 0.19/0.42 % --dbg_dump_prop_clauses false
% 0.19/0.42 % --dbg_dump_prop_clauses_file -
% 0.19/0.42 % --dbg_out_stat false
% 0.19/0.42
% 0.19/0.42 % ------ General Options
% 0.19/0.42
% 0.19/0.42 % --fof false
% 0.19/0.42 % --time_out_real 150.
% 0.19/0.42 % --time_out_prep_mult 0.2
% 0.19/0.42 % --time_out_virtual -1.
% 0.19/0.42 % --schedule none
% 0.19/0.42 % --ground_splitting input
% 0.19/0.42 % --splitting_nvd 16
% 0.19/0.42 % --non_eq_to_eq false
% 0.19/0.42 % --prep_gs_sim true
% 0.19/0.42 % --prep_unflatten false
% 0.19/0.42 % --prep_res_sim true
% 0.19/0.42 % --prep_upred true
% 0.19/0.42 % --res_sim_input true
% 0.19/0.42 % --clause_weak_htbl true
% 0.19/0.42 % --gc_record_bc_elim false
% 0.19/0.42 % --symbol_type_check false
% 0.19/0.42 % --clausify_out false
% 0.19/0.42 % --large_theory_mode false
% 0.19/0.42 % --prep_sem_filter none
% 0.19/0.42 % --prep_sem_filter_out false
% 0.19/0.42 % --preprocessed_out false
% 0.19/0.42 % --sub_typing false
% 0.19/0.42 % --brand_transform false
% 0.19/0.42 % --pure_diseq_elim true
% 0.19/0.42 % --min_unsat_core false
% 0.19/0.42 % --pred_elim true
% 0.19/0.42 % --add_important_lit false
% 0.19/0.42 % --soft_assumptions false
% 0.19/0.42 % --reset_solvers false
% 0.19/0.42 % --bc_imp_inh []
% 0.19/0.42 % --conj_cone_tolerance 1.5
% 0.19/0.42 % --prolific_symb_bound 500
% 0.19/0.42 % --lt_threshold 2000
% 0.19/0.42
% 0.19/0.42 % ------ SAT Options
% 0.19/0.42
% 0.19/0.42 % --sat_mode false
% 0.19/0.42 % --sat_fm_restart_options ""
% 0.19/0.42 % --sat_gr_def false
% 0.19/0.42 % --sat_epr_types true
% 0.19/0.42 % --sat_non_cyclic_types false
% 0.19/0.42 % --sat_finite_models false
% 0.19/0.42 % --sat_fm_lemmas false
% 0.19/0.42 % --sat_fm_prep false
% 0.19/0.42 % --sat_fm_uc_incr true
% 0.19/0.42 % --sat_out_model small
% 0.19/0.42 % --sat_out_clauses false
% 0.19/0.42
% 0.19/0.42 % ------ QBF Options
% 0.19/0.42
% 0.19/0.42 % --qbf_mode false
% 0.19/0.42 % --qbf_elim_univ true
% 0.19/0.42 % --qbf_sk_in true
% 0.19/0.42 % --qbf_pred_elim true
% 0.19/0.42 % --qbf_split 32
% 0.19/0.42
% 0.19/0.42 % ------ BMC1 Options
% 0.19/0.42
% 0.19/0.42 % --bmc1_incremental false
% 0.19/0.42 % --bmc1_axioms reachable_all
% 0.19/0.42 % --bmc1_min_bound 0
% 0.19/0.42 % --bmc1_max_bound -1
% 0.19/0.42 % --bmc1_max_bound_default -1
% 0.19/0.42 % --bmc1_symbol_reachability true
% 0.19/0.42 % --bmc1_property_lemmas false
% 0.19/0.42 % --bmc1_k_induction false
% 0.19/0.42 % --bmc1_non_equiv_states false
% 0.19/0.42 % --bmc1_deadlock false
% 0.19/0.42 % --bmc1_ucm false
% 0.19/0.42 % --bmc1_add_unsat_core none
% 0.19/0.42 % --bmc1_unsat_core_children false
% 0.19/0.42 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.42 % --bmc1_out_stat full
% 0.19/0.42 % --bmc1_ground_init false
% 0.19/0.42 % --bmc1_pre_inst_next_state false
% 0.19/0.42 % --bmc1_pre_inst_state false
% 0.19/0.42 % --bmc1_pre_inst_reach_state false
% 0.19/0.42 % --bmc1_out_unsat_core false
% 0.19/0.42 % --bmc1_aig_witness_out false
% 0.19/0.42 % --bmc1_verbose false
% 0.19/0.42 % --bmc1_dump_clauses_tptp false
% 0.19/0.42 % --bmc1_dump_unsat_core_tptp false
% 0.19/0.42 % --bmc1_dump_file -
% 0.19/0.42 % --bmc1_ucm_expand_uc_limit 128
% 0.19/0.42 % --bmc1_ucm_n_expand_iterations 6
% 0.19/0.42 % --bmc1_ucm_extend_mode 1
% 0.19/0.42 % --bmc1_ucm_init_mode 2
% 0.19/0.42 % --bmc1_ucm_cone_mode none
% 0.19/0.42 % --bmc1_ucm_reduced_relation_type 0
% 0.19/0.42 % --bmc1_ucm_relax_model 4
% 0.19/0.42 % --bmc1_ucm_full_tr_after_sat true
% 0.19/0.42 % --bmc1_ucm_expand_neg_assumptions false
% 0.19/0.42 % --bmc1_ucm_layered_model none
% 0.19/0.42 % --bmc1_ucm_max_lemma_size 10
% 0.19/0.42
% 0.19/0.42 % ------ AIG Options
% 0.19/0.42
% 0.19/0.42 % --aig_mode false
% 0.19/0.42
% 0.19/0.42 % ------ Instantiation Options
% 0.19/0.42
% 0.19/0.42 % --instantiation_flag true
% 0.19/0.42 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.19/0.42 % --inst_solver_per_active 750
% 0.19/0.42 % --inst_solver_calls_frac 0.5
% 0.19/0.42 % --inst_passive_queue_type priority_queues
% 0.19/0.42 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.19/0.42 % --inst_passive_queues_freq [25;2]
% 0.19/0.42 % --inst_dismatching true
% 0.19/0.42 % --inst_eager_unprocessed_to_passive true
% 0.19/0.42 % --inst_prop_sim_given true
% 0.19/0.42 % --inst_prop_sim_new false
% 0.19/0.42 % --inst_orphan_elimination true
% 0.19/0.42 % --inst_learning_loop_flag true
% 0.19/0.42 % --inst_learning_start 3000
% 0.19/0.42 % --inst_learning_factor 2
% 0.19/0.42 % --inst_start_prop_sim_after_learn 3
% 0.19/0.42 % --inst_sel_renew solver
% 0.19/0.42 % --inst_lit_activity_flag true
% 0.19/0.42 % --inst_out_proof true
% 0.19/0.42
% 0.19/0.42 % ------ Resolution Options
% 0.19/0.42
% 0.19/0.42 % --resolution_flag true
% 0.19/0.42 % --res_lit_sel kbo_max
% 0.19/0.42 % --res_to_prop_solver none
% 0.19/0.42 % --res_prop_simpl_new false
% 0.19/0.42 % --res_prop_simpl_given false
% 0.19/0.42 % --res_passive_queue_type priority_queues
% 0.19/0.42 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.19/0.42 % --res_passive_queues_freq [15;5]
% 0.19/0.42 % --res_forward_subs full
% 0.19/0.42 % --res_backward_subs full
% 0.19/0.42 % --res_forward_subs_resolution true
% 0.19/0.42 % --res_backward_subs_resolution true
% 0.19/0.42 % --res_orphan_elimination false
% 0.19/0.42 % --res_time_limit 1000.
% 0.19/0.42 % --res_out_proof true
% 0.19/0.42 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e25697.s
% 0.19/0.42 % --modulo true
% 0.19/0.42
% 0.19/0.42 % ------ Combination Options
% 0.19/0.42
% 0.19/0.42 % --comb_res_mult 1000
% 0.19/0.42 % --comb_inst_mult 300
% 0.19/0.42 % ------
% 0.19/0.42
% 0.19/0.42 % ------ Parsing...% successful
% 0.19/0.42
% 0.19/0.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 % ------ Statistics
% 0.19/0.42
% 0.19/0.42 % ------ General
% 0.19/0.42
% 0.19/0.42 % num_of_input_clauses: 64
% 0.19/0.42 % num_of_input_neg_conjectures: 1
% 0.19/0.42 % num_of_splits: 0
% 0.19/0.42 % num_of_split_atoms: 0
% 0.19/0.42 % num_of_sem_filtered_clauses: 0
% 0.19/0.42 % num_of_subtypes: 0
% 0.19/0.42 % monotx_restored_types: 0
% 0.19/0.42 % sat_num_of_epr_types: 0
% 0.19/0.42 % sat_num_of_non_cyclic_types: 0
% 0.19/0.42 % sat_guarded_non_collapsed_types: 0
% 0.19/0.42 % is_epr: 0
% 0.19/0.42 % is_horn: 0
% 0.19/0.42 % has_eq: 0
% 0.19/0.42 % num_pure_diseq_elim: 0
% 0.19/0.42 % simp_replaced_by: 0
% 0.19/0.42 % res_preprocessed: 0
% 0.19/0.42 % prep_upred: 0
% 0.19/0.42 % prep_unflattend: 0
% 0.19/0.42 % pred_elim_cands: 0
% 0.19/0.42 % pred_elim: 0
% 0.19/0.42 % pred_elim_cl: 0
% 0.19/0.42 % pred_elim_cycles: 0
% 0.19/0.42 % forced_gc_time: 0
% 0.19/0.42 % gc_basic_clause_elim: 0
% 0.19/0.42 % parsing_time: 0.001
% 0.19/0.42 % sem_filter_time: 0.
% 0.19/0.42 % pred_elim_time: 0.
% 0.19/0.42 % out_proof_time: 0.
% 0.19/0.42 % monotx_time: 0.
% 0.19/0.42 % subtype_inf_time: 0.
% 0.19/0.42 % unif_index_cands_time: 0.
% 0.19/0.42 % unif_index_add_time: 0.
% 0.19/0.42 % total_time: 0.018
% 0.19/0.42 % num_of_symbols: 49
% 0.19/0.42 % num_of_terms: 98
% 0.19/0.42
% 0.19/0.42 % ------ Propositional Solver
% 0.19/0.42
% 0.19/0.42 % prop_solver_calls: 0
% 0.19/0.42 % prop_fast_solver_calls: 1
% 0.19/0.42 % prop_num_of_clauses: 53
% 0.19/0.42 % prop_preprocess_simplified: 44
% 0.19/0.42 % prop_fo_subsumed: 0
% 0.19/0.42 % prop_solver_time: 0.
% 0.19/0.42 % prop_fast_solver_time: 0.
% 0.19/0.42 % prop_unsat_core_time: 0.
% 0.19/0.42
% 0.19/0.42 % ------ QBF
% 0.19/0.42
% 0.19/0.42 % qbf_q_res: 0
% 0.19/0.42 % qbf_num_tautologies: 0
% 0.19/0.42 % qbf_prep_cycles: 0
% 0.19/0.42
% 0.19/0.42 % ------ BMC1
% 0.19/0.42
% 0.19/0.42 % bmc1_current_bound: -1
% 0.19/0.42 % bmc1_last_solved_bound: -1
% 0.19/0.42 % bmc1_unsat_core_size: -1
% 0.19/0.42 % bmc1_unsat_core_parents_size: -1
% 0.19/0.42 % bmc1_merge_next_fun: 0
% 0.19/0.42 % bmc1_unsat_core_clauses_time: 0.
% 0.19/0.42
% 0.19/0.42 % ------ Instantiation
% 0.19/0.42
% 0.19/0.42 % inst_num_of_clauses: undef
% 0.19/0.42 % inst_num_in_passive: undef
% 0.19/0.42 % inst_num_in_active: 0
% 0.19/0.42 % inst_num_in_unprocessed: 0
% 0.19/0.42 % inst_num_of_loops: 0
% 0.19/0.42 % inst_num_of_learning_restarts: 0
% 0.19/0.42 % inst_num_moves_active_passive: 0
% 0.19/0.42 % inst_lit_activity: 0
% 0.19/0.42 % inst_lit_activity_moves: 0
% 0.19/0.42 % inst_num_tautologies: 0
% 0.19/0.42 % inst_num_prop_implied: 0
% 0.19/0.42 % inst_num_existing_simplified: 0
% 0.19/0.42 % inst_num_eq_res_simplified: 0
% 0.19/0.42 % inst_num_child_elim: 0
% 0.19/0.42 % inst_num_of_dismatching_blockings: 0
% 0.19/0.42 % inst_num_of_non_proper_insts: 0
% 0.19/0.42 % inst_num_of_duplicates: 0
% 0.19/0.42 % inst_inst_num_from_inst_to_res: 0
% 0.19/0.42 % inst_dismatching_checking_time: 0.
% 0.19/0.42
% 0.19/0.42 % ------ Resolution
% 0.19/0.42
% 0.19/0.42 % res_num_of_clauses: undef
% 0.19/0.42 % res_num_in_passive: undef
% 0.19/0.42 % res_num_in_active: 0
% 0.19/0.42 % res_num_of_loops: 0
% 0.19/0.42 % res_forward_subset_subsumed: 0
% 0.19/0.42 % res_backward_subset_subsumed: 0
% 0.19/0.42 % res_forward_subsumed: 0
% 0.19/0.42 % res_backward_subsumed: 0
% 0.19/0.42 % res_forward_subsumption_resolution: 0
% 0.19/0.42 % res_backward_subsumption_resolution: 0
% 0.19/0.42 % res_clause_to_clause_subsumption: 0
% 0.19/0.42 % res_orphan_elimination: 0
% 0.19/0.42 % res_tautology_del: 0
% 0.19/0.42 % res_num_eq_res_simplified: 0
% 0.19/0.42 % res_num_sel_changes: 0
% 0.19/0.42 % res_moves_from_active_to_pass: 0
% 0.19/0.42
% 0.19/0.42 % Status Unsatisfiable
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------