TSTP Solution File: SET800+4 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:16:22 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(greatest_lower_bound,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
input ).
fof(greatest_lower_bound_0,plain,
! [A,E,R,X] :
( greatest_lower_bound(A,X,R,E)
| ~ ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
inference(orientation,[status(thm)],[greatest_lower_bound]) ).
fof(greatest_lower_bound_1,plain,
! [A,E,R,X] :
( ~ greatest_lower_bound(A,X,R,E)
| ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
inference(orientation,[status(thm)],[greatest_lower_bound]) ).
fof(least_upper_bound,axiom,
! [A,X,R,E] :
( least_upper_bound(A,X,R,E)
<=> ( member(A,X)
& upper_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& upper_bound(M,R,X) )
=> apply(R,A,M) ) ) ),
input ).
fof(least_upper_bound_0,plain,
! [A,E,R,X] :
( least_upper_bound(A,X,R,E)
| ~ ( member(A,X)
& upper_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& upper_bound(M,R,X) )
=> apply(R,A,M) ) ) ),
inference(orientation,[status(thm)],[least_upper_bound]) ).
fof(least_upper_bound_1,plain,
! [A,E,R,X] :
( ~ least_upper_bound(A,X,R,E)
| ( member(A,X)
& upper_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& upper_bound(M,R,X) )
=> apply(R,A,M) ) ) ),
inference(orientation,[status(thm)],[least_upper_bound]) ).
fof(min,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
input ).
fof(min_0,plain,
! [E,M,R] :
( min(M,R,E)
| ~ ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
inference(orientation,[status(thm)],[min]) ).
fof(min_1,plain,
! [E,M,R] :
( ~ min(M,R,E)
| ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
inference(orientation,[status(thm)],[min]) ).
fof(max,axiom,
! [R,E,M] :
( max(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,M,X) )
=> M = X ) ) ),
input ).
fof(max_0,plain,
! [E,M,R] :
( max(M,R,E)
| ~ ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,M,X) )
=> M = X ) ) ),
inference(orientation,[status(thm)],[max]) ).
fof(max_1,plain,
! [E,M,R] :
( ~ max(M,R,E)
| ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,M,X) )
=> M = X ) ) ),
inference(orientation,[status(thm)],[max]) ).
fof(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
input ).
fof(least_0,plain,
! [E,M,R] :
( least(M,R,E)
| ~ ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
inference(orientation,[status(thm)],[least]) ).
fof(least_1,plain,
! [E,M,R] :
( ~ least(M,R,E)
| ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
inference(orientation,[status(thm)],[least]) ).
fof(greatest,axiom,
! [R,E,M] :
( greatest(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ),
input ).
fof(greatest_0,plain,
! [E,M,R] :
( greatest(M,R,E)
| ~ ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ),
inference(orientation,[status(thm)],[greatest]) ).
fof(greatest_1,plain,
! [E,M,R] :
( ~ greatest(M,R,E)
| ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ),
inference(orientation,[status(thm)],[greatest]) ).
fof(lower_bound,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
input ).
fof(lower_bound_0,plain,
! [E,M,R] :
( lower_bound(M,R,E)
| ~ ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
inference(orientation,[status(thm)],[lower_bound]) ).
fof(lower_bound_1,plain,
! [E,M,R] :
( ~ lower_bound(M,R,E)
| ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
inference(orientation,[status(thm)],[lower_bound]) ).
fof(upper_bound,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
input ).
fof(upper_bound_0,plain,
! [E,M,R] :
( upper_bound(M,R,E)
| ~ ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
inference(orientation,[status(thm)],[upper_bound]) ).
fof(upper_bound_1,plain,
! [E,M,R] :
( ~ upper_bound(M,R,E)
| ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
inference(orientation,[status(thm)],[upper_bound]) ).
fof(total_order,axiom,
! [R,E] :
( total_order(R,E)
<=> ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
input ).
fof(total_order_0,plain,
! [E,R] :
( total_order(R,E)
| ~ ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
inference(orientation,[status(thm)],[total_order]) ).
fof(total_order_1,plain,
! [E,R] :
( ~ total_order(R,E)
| ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
inference(orientation,[status(thm)],[total_order]) ).
fof(order,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
input ).
fof(order_0,plain,
! [E,R] :
( order(R,E)
| ~ ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
inference(orientation,[status(thm)],[order]) ).
fof(order_1,plain,
! [E,R] :
( ~ order(R,E)
| ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
inference(orientation,[status(thm)],[order]) ).
fof(product,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
input ).
fof(product_0,plain,
! [A,X] :
( member(X,product(A))
| ~ ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(orientation,[status(thm)],[product]) ).
fof(product_1,plain,
! [A,X] :
( ~ member(X,product(A))
| ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(orientation,[status(thm)],[product]) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
input ).
fof(sum_0,plain,
! [A,X] :
( member(X,sum(A))
| ~ ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(orientation,[status(thm)],[sum]) ).
fof(sum_1,plain,
! [A,X] :
( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(orientation,[status(thm)],[sum]) ).
fof(unordered_pair,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = A
| X = B ) ),
input ).
fof(unordered_pair_0,plain,
! [A,B,X] :
( member(X,unordered_pair(A,B))
| ~ ( X = A
| X = B ) ),
inference(orientation,[status(thm)],[unordered_pair]) ).
fof(unordered_pair_1,plain,
! [A,B,X] :
( ~ member(X,unordered_pair(A,B))
| X = A
| X = B ),
inference(orientation,[status(thm)],[unordered_pair]) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
input ).
fof(singleton_0,plain,
! [A,X] :
( member(X,singleton(A))
| X != A ),
inference(orientation,[status(thm)],[singleton]) ).
fof(singleton_1,plain,
! [A,X] :
( ~ member(X,singleton(A))
| X = A ),
inference(orientation,[status(thm)],[singleton]) ).
fof(difference,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
input ).
fof(difference_0,plain,
! [A,B,E] :
( member(B,difference(E,A))
| ~ ( member(B,E)
& ~ member(B,A) ) ),
inference(orientation,[status(thm)],[difference]) ).
fof(difference_1,plain,
! [A,B,E] :
( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) ),
inference(orientation,[status(thm)],[difference]) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
input ).
fof(empty_set_0,plain,
! [X] :
( ~ member(X,empty_set)
| $false ),
inference(orientation,[status(thm)],[empty_set]) ).
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
input ).
fof(union_0,plain,
! [A,B,X] :
( member(X,union(A,B))
| ~ ( member(X,A)
| member(X,B) ) ),
inference(orientation,[status(thm)],[union]) ).
fof(union_1,plain,
! [A,B,X] :
( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) ),
inference(orientation,[status(thm)],[union]) ).
fof(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
input ).
fof(intersection_0,plain,
! [A,B,X] :
( member(X,intersection(A,B))
| ~ ( member(X,A)
& member(X,B) ) ),
inference(orientation,[status(thm)],[intersection]) ).
fof(intersection_1,plain,
! [A,B,X] :
( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) ),
inference(orientation,[status(thm)],[intersection]) ).
fof(power_set,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
input ).
fof(power_set_0,plain,
! [A,X] :
( member(X,power_set(A))
| ~ subset(X,A) ),
inference(orientation,[status(thm)],[power_set]) ).
fof(power_set_1,plain,
! [A,X] :
( ~ member(X,power_set(A))
| subset(X,A) ),
inference(orientation,[status(thm)],[power_set]) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
input ).
fof(equal_set_0,plain,
! [A,B] :
( equal_set(A,B)
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[equal_set]) ).
fof(equal_set_1,plain,
! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[equal_set]) ).
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
input ).
fof(subset_0,plain,
! [A,B] :
( subset(A,B)
| ~ ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(orientation,[status(thm)],[subset]) ).
fof(subset_1,plain,
! [A,B] :
( ~ subset(A,B)
| ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(orientation,[status(thm)],[subset]) ).
fof(def_lhs_atom1,axiom,
! [B,A] :
( lhs_atom1(B,A)
<=> ~ subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [A,B] :
( lhs_atom1(B,A)
| ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(fold_definition,[status(thm)],[subset_1,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [B,A] :
( lhs_atom2(B,A)
<=> subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A,B] :
( lhs_atom2(B,A)
| ~ ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(fold_definition,[status(thm)],[subset_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [B,A] :
( lhs_atom3(B,A)
<=> ~ equal_set(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A,B] :
( lhs_atom3(B,A)
| ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[equal_set_1,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [B,A] :
( lhs_atom4(B,A)
<=> equal_set(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [A,B] :
( lhs_atom4(B,A)
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[equal_set_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [X,A] :
( lhs_atom5(X,A)
<=> ~ member(X,power_set(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [A,X] :
( lhs_atom5(X,A)
| subset(X,A) ),
inference(fold_definition,[status(thm)],[power_set_1,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [X,A] :
( lhs_atom6(X,A)
<=> member(X,power_set(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [A,X] :
( lhs_atom6(X,A)
| ~ subset(X,A) ),
inference(fold_definition,[status(thm)],[power_set_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [X,B,A] :
( lhs_atom7(X,B,A)
<=> ~ member(X,intersection(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A,B,X] :
( lhs_atom7(X,B,A)
| ( member(X,A)
& member(X,B) ) ),
inference(fold_definition,[status(thm)],[intersection_1,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [X,B,A] :
( lhs_atom8(X,B,A)
<=> member(X,intersection(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A,B,X] :
( lhs_atom8(X,B,A)
| ~ ( member(X,A)
& member(X,B) ) ),
inference(fold_definition,[status(thm)],[intersection_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [X,B,A] :
( lhs_atom9(X,B,A)
<=> ~ member(X,union(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A,B,X] :
( lhs_atom9(X,B,A)
| member(X,A)
| member(X,B) ),
inference(fold_definition,[status(thm)],[union_1,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [X,B,A] :
( lhs_atom10(X,B,A)
<=> member(X,union(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A,B,X] :
( lhs_atom10(X,B,A)
| ~ ( member(X,A)
| member(X,B) ) ),
inference(fold_definition,[status(thm)],[union_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [X] :
( lhs_atom11(X)
<=> ~ member(X,empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [X] :
( lhs_atom11(X)
| $false ),
inference(fold_definition,[status(thm)],[empty_set_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [E,B,A] :
( lhs_atom12(E,B,A)
<=> ~ member(B,difference(E,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [A,B,E] :
( lhs_atom12(E,B,A)
| ( member(B,E)
& ~ member(B,A) ) ),
inference(fold_definition,[status(thm)],[difference_1,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [E,B,A] :
( lhs_atom13(E,B,A)
<=> member(B,difference(E,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [A,B,E] :
( lhs_atom13(E,B,A)
| ~ ( member(B,E)
& ~ member(B,A) ) ),
inference(fold_definition,[status(thm)],[difference_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [X,A] :
( lhs_atom14(X,A)
<=> ~ member(X,singleton(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [A,X] :
( lhs_atom14(X,A)
| X = A ),
inference(fold_definition,[status(thm)],[singleton_1,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [X,A] :
( lhs_atom15(X,A)
<=> member(X,singleton(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [A,X] :
( lhs_atom15(X,A)
| X != A ),
inference(fold_definition,[status(thm)],[singleton_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [X,B,A] :
( lhs_atom16(X,B,A)
<=> ~ member(X,unordered_pair(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [A,B,X] :
( lhs_atom16(X,B,A)
| X = A
| X = B ),
inference(fold_definition,[status(thm)],[unordered_pair_1,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [X,B,A] :
( lhs_atom17(X,B,A)
<=> member(X,unordered_pair(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [A,B,X] :
( lhs_atom17(X,B,A)
| ~ ( X = A
| X = B ) ),
inference(fold_definition,[status(thm)],[unordered_pair_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [X,A] :
( lhs_atom18(X,A)
<=> ~ member(X,sum(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [A,X] :
( lhs_atom18(X,A)
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(fold_definition,[status(thm)],[sum_1,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [X,A] :
( lhs_atom19(X,A)
<=> member(X,sum(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [A,X] :
( lhs_atom19(X,A)
| ~ ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(fold_definition,[status(thm)],[sum_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [X,A] :
( lhs_atom20(X,A)
<=> ~ member(X,product(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [A,X] :
( lhs_atom20(X,A)
| ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(fold_definition,[status(thm)],[product_1,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [X,A] :
( lhs_atom21(X,A)
<=> member(X,product(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [A,X] :
( lhs_atom21(X,A)
| ~ ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(fold_definition,[status(thm)],[product_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [R,E] :
( lhs_atom22(R,E)
<=> ~ order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [E,R] :
( lhs_atom22(R,E)
| ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
inference(fold_definition,[status(thm)],[order_1,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [R,E] :
( lhs_atom23(R,E)
<=> order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [E,R] :
( lhs_atom23(R,E)
| ~ ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
inference(fold_definition,[status(thm)],[order_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [R,E] :
( lhs_atom24(R,E)
<=> ~ total_order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [E,R] :
( lhs_atom24(R,E)
| ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
inference(fold_definition,[status(thm)],[total_order_1,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [R,E] :
( lhs_atom25(R,E)
<=> total_order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [E,R] :
( lhs_atom25(R,E)
| ~ ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ),
inference(fold_definition,[status(thm)],[total_order_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [R,M,E] :
( lhs_atom26(R,M,E)
<=> ~ upper_bound(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [E,M,R] :
( lhs_atom26(R,M,E)
| ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
inference(fold_definition,[status(thm)],[upper_bound_1,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [R,M,E] :
( lhs_atom27(R,M,E)
<=> upper_bound(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [E,M,R] :
( lhs_atom27(R,M,E)
| ~ ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
inference(fold_definition,[status(thm)],[upper_bound_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [R,M,E] :
( lhs_atom28(R,M,E)
<=> ~ lower_bound(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [E,M,R] :
( lhs_atom28(R,M,E)
| ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
inference(fold_definition,[status(thm)],[lower_bound_1,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [R,M,E] :
( lhs_atom29(R,M,E)
<=> lower_bound(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [E,M,R] :
( lhs_atom29(R,M,E)
| ~ ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
inference(fold_definition,[status(thm)],[lower_bound_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [R,M,E] :
( lhs_atom30(R,M,E)
<=> ~ greatest(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [E,M,R] :
( lhs_atom30(R,M,E)
| ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ),
inference(fold_definition,[status(thm)],[greatest_1,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [R,M,E] :
( lhs_atom31(R,M,E)
<=> greatest(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [E,M,R] :
( lhs_atom31(R,M,E)
| ~ ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ),
inference(fold_definition,[status(thm)],[greatest_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [R,M,E] :
( lhs_atom32(R,M,E)
<=> ~ least(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [E,M,R] :
( lhs_atom32(R,M,E)
| ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
inference(fold_definition,[status(thm)],[least_1,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [R,M,E] :
( lhs_atom33(R,M,E)
<=> least(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [E,M,R] :
( lhs_atom33(R,M,E)
| ~ ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
inference(fold_definition,[status(thm)],[least_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [R,M,E] :
( lhs_atom34(R,M,E)
<=> ~ max(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [E,M,R] :
( lhs_atom34(R,M,E)
| ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,M,X) )
=> M = X ) ) ),
inference(fold_definition,[status(thm)],[max_1,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [R,M,E] :
( lhs_atom35(R,M,E)
<=> max(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [E,M,R] :
( lhs_atom35(R,M,E)
| ~ ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,M,X) )
=> M = X ) ) ),
inference(fold_definition,[status(thm)],[max_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [R,M,E] :
( lhs_atom36(R,M,E)
<=> ~ min(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [E,M,R] :
( lhs_atom36(R,M,E)
| ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
inference(fold_definition,[status(thm)],[min_1,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [R,M,E] :
( lhs_atom37(R,M,E)
<=> min(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [E,M,R] :
( lhs_atom37(R,M,E)
| ~ ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
inference(fold_definition,[status(thm)],[min_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [X,R,E,A] :
( lhs_atom38(X,R,E,A)
<=> ~ least_upper_bound(A,X,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [A,E,R,X] :
( lhs_atom38(X,R,E,A)
| ( member(A,X)
& upper_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& upper_bound(M,R,X) )
=> apply(R,A,M) ) ) ),
inference(fold_definition,[status(thm)],[least_upper_bound_1,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [X,R,E,A] :
( lhs_atom39(X,R,E,A)
<=> least_upper_bound(A,X,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [A,E,R,X] :
( lhs_atom39(X,R,E,A)
| ~ ( member(A,X)
& upper_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& upper_bound(M,R,X) )
=> apply(R,A,M) ) ) ),
inference(fold_definition,[status(thm)],[least_upper_bound_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [X,R,E,A] :
( lhs_atom40(X,R,E,A)
<=> ~ greatest_lower_bound(A,X,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [A,E,R,X] :
( lhs_atom40(X,R,E,A)
| ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
inference(fold_definition,[status(thm)],[greatest_lower_bound_1,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [X,R,E,A] :
( lhs_atom41(X,R,E,A)
<=> greatest_lower_bound(A,X,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [A,E,R,X] :
( lhs_atom41(X,R,E,A)
| ~ ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
inference(fold_definition,[status(thm)],[greatest_lower_bound_0,def_lhs_atom41]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X6,X4,X2] :
( lhs_atom41(X3,X6,X4,X2)
| ~ ( member(X2,X3)
& lower_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X2) ) ) ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_1,axiom,
! [X3,X6,X4,X2] :
( lhs_atom39(X3,X6,X4,X2)
| ~ ( member(X2,X3)
& upper_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X2,X8) ) ) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_2,axiom,
! [X3,X6,X4,X2] :
( lhs_atom40(X3,X6,X4,X2)
| ( member(X2,X3)
& lower_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X2) ) ) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_3,axiom,
! [X3,X6,X4,X2] :
( lhs_atom38(X3,X6,X4,X2)
| ( member(X2,X3)
& upper_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X2,X8) ) ) ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_4,axiom,
! [X6,X8,X4] :
( lhs_atom33(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_5,axiom,
! [X6,X8,X4] :
( lhs_atom31(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_6,axiom,
! [X6,X8,X4] :
( lhs_atom29(X6,X8,X4)
| ~ ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_7,axiom,
! [X6,X8,X4] :
( lhs_atom27(X6,X8,X4)
| ~ ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_8,axiom,
! [X6,X8,X4] :
( lhs_atom37(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X3,X8) )
=> X8 = X3 ) ) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_9,axiom,
! [X6,X8,X4] :
( lhs_atom35(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X8,X3) )
=> X8 = X3 ) ) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_10,axiom,
! [X6,X4] :
( lhs_atom25(X6,X4)
| ~ ( order(X6,X4)
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( apply(X6,X3,X5)
| apply(X6,X5,X3) ) ) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_11,axiom,
! [X6,X4] :
( lhs_atom23(X6,X4)
| ~ ( ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_12,axiom,
! [X6,X4] :
( lhs_atom24(X6,X4)
| ( order(X6,X4)
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( apply(X6,X3,X5)
| apply(X6,X5,X3) ) ) ) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_13,axiom,
! [X6,X8,X4] :
( lhs_atom36(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X3,X8) )
=> X8 = X3 ) ) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_14,axiom,
! [X6,X8,X4] :
( lhs_atom34(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X8,X3) )
=> X8 = X3 ) ) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_15,axiom,
! [X6,X8,X4] :
( lhs_atom32(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_16,axiom,
! [X6,X8,X4] :
( lhs_atom30(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_17,axiom,
! [X6,X8,X4] :
( lhs_atom28(X6,X8,X4)
| ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_18,axiom,
! [X6,X8,X4] :
( lhs_atom26(X6,X8,X4)
| ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_19,axiom,
! [X3,X1,X2] :
( lhs_atom8(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_20,axiom,
! [X6,X4] :
( lhs_atom22(X6,X4)
| ( ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_21,axiom,
! [X4,X1,X2] :
( lhs_atom13(X4,X1,X2)
| ~ ( member(X1,X4)
& ~ member(X1,X2) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_22,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| member(X3,X2)
| member(X3,X1) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_23,axiom,
! [X3,X2] :
( lhs_atom21(X3,X2)
| ~ ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_24,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_25,axiom,
! [X4,X1,X2] :
( lhs_atom12(X4,X1,X2)
| ( member(X1,X4)
& ~ member(X1,X2) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_26,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ( member(X3,X2)
| member(X3,X1) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_27,axiom,
! [X3,X1,X2] :
( lhs_atom7(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_28,axiom,
! [X3,X2] :
( lhs_atom19(X3,X2)
| ~ ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_29,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_30,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| X3 = X2
| X3 = X1 ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_31,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ( X3 = X2
| X3 = X1 ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_32,axiom,
! [X3,X2] :
( lhs_atom18(X3,X2)
| ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_33,axiom,
! [X3,X2] :
( lhs_atom20(X3,X2)
| ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_34,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_35,axiom,
! [X3,X2] :
( lhs_atom6(X3,X2)
| ~ subset(X3,X2) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_36,axiom,
! [X3,X2] :
( lhs_atom5(X3,X2)
| subset(X3,X2) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_37,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_38,axiom,
! [X3,X2] :
( lhs_atom15(X3,X2)
| X3 != X2 ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_39,axiom,
! [X3,X2] :
( lhs_atom14(X3,X2)
| X3 = X2 ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_40,axiom,
! [X3] :
( lhs_atom11(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_41,plain,
! [X4,X6] :
( epred1_2(X6,X4)
<=> ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
introduced(definition) ).
fof(c_0_42,axiom,
! [X3,X6,X4,X2] :
( lhs_atom41(X3,X6,X4,X2)
| ~ ( member(X2,X3)
& lower_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X2) ) ) ),
c_0_0 ).
fof(c_0_43,axiom,
! [X3,X6,X4,X2] :
( lhs_atom39(X3,X6,X4,X2)
| ~ ( member(X2,X3)
& upper_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X2,X8) ) ) ),
c_0_1 ).
fof(c_0_44,axiom,
! [X3,X6,X4,X2] :
( lhs_atom40(X3,X6,X4,X2)
| ( member(X2,X3)
& lower_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X2) ) ) ),
c_0_2 ).
fof(c_0_45,axiom,
! [X3,X6,X4,X2] :
( lhs_atom38(X3,X6,X4,X2)
| ( member(X2,X3)
& upper_bound(X2,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X2,X8) ) ) ),
c_0_3 ).
fof(c_0_46,axiom,
! [X6,X8,X4] :
( lhs_atom33(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ) ),
c_0_4 ).
fof(c_0_47,axiom,
! [X6,X8,X4] :
( lhs_atom31(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ) ),
c_0_5 ).
fof(c_0_48,plain,
! [X4,X6] :
( epred1_2(X6,X4)
<=> ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
c_0_41 ).
fof(c_0_49,axiom,
! [X6,X8,X4] :
( lhs_atom29(X6,X8,X4)
| ~ ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
c_0_6 ).
fof(c_0_50,axiom,
! [X6,X8,X4] :
( lhs_atom27(X6,X8,X4)
| ~ ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
c_0_7 ).
fof(c_0_51,axiom,
! [X6,X8,X4] :
( lhs_atom37(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X3,X8) )
=> X8 = X3 ) ) ),
c_0_8 ).
fof(c_0_52,axiom,
! [X6,X8,X4] :
( lhs_atom35(X6,X8,X4)
| ~ ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X8,X3) )
=> X8 = X3 ) ) ),
c_0_9 ).
fof(c_0_53,axiom,
! [X6,X4] :
( lhs_atom25(X6,X4)
| ~ ( order(X6,X4)
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( apply(X6,X3,X5)
| apply(X6,X5,X3) ) ) ) ),
c_0_10 ).
fof(c_0_54,axiom,
! [X6,X4] :
( lhs_atom23(X6,X4)
| ~ ( ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& epred1_2(X6,X4) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_41,theory(equality,[symmetry])]) ).
fof(c_0_55,axiom,
! [X6,X4] :
( lhs_atom24(X6,X4)
| ( order(X6,X4)
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( apply(X6,X3,X5)
| apply(X6,X5,X3) ) ) ) ),
c_0_12 ).
fof(c_0_56,axiom,
! [X6,X8,X4] :
( lhs_atom36(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X3,X8) )
=> X8 = X3 ) ) ),
c_0_13 ).
fof(c_0_57,axiom,
! [X6,X8,X4] :
( lhs_atom34(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( ( member(X3,X4)
& apply(X6,X8,X3) )
=> X8 = X3 ) ) ),
c_0_14 ).
fof(c_0_58,axiom,
! [X6,X8,X4] :
( lhs_atom32(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ) ),
c_0_15 ).
fof(c_0_59,axiom,
! [X6,X8,X4] :
( lhs_atom30(X6,X8,X4)
| ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ) ),
c_0_16 ).
fof(c_0_60,axiom,
! [X6,X8,X4] :
( lhs_atom28(X6,X8,X4)
| ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
c_0_17 ).
fof(c_0_61,axiom,
! [X6,X8,X4] :
( lhs_atom26(X6,X8,X4)
| ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
c_0_18 ).
fof(c_0_62,axiom,
! [X3,X1,X2] :
( lhs_atom8(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
c_0_19 ).
fof(c_0_63,axiom,
! [X6,X4] :
( lhs_atom22(X6,X4)
| ( ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& epred1_2(X6,X4) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_41,theory(equality,[symmetry])]) ).
fof(c_0_64,plain,
! [X4,X1,X2] :
( lhs_atom13(X4,X1,X2)
| ~ ( member(X1,X4)
& ~ member(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_65,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| member(X3,X2)
| member(X3,X1) ),
c_0_22 ).
fof(c_0_66,axiom,
! [X3,X2] :
( lhs_atom21(X3,X2)
| ~ ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
c_0_23 ).
fof(c_0_67,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_24 ).
fof(c_0_68,plain,
! [X4,X1,X2] :
( lhs_atom12(X4,X1,X2)
| ( member(X1,X4)
& ~ member(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_69,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ( member(X3,X2)
| member(X3,X1) ) ),
c_0_26 ).
fof(c_0_70,axiom,
! [X3,X1,X2] :
( lhs_atom7(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
c_0_27 ).
fof(c_0_71,axiom,
! [X3,X2] :
( lhs_atom19(X3,X2)
| ~ ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
c_0_28 ).
fof(c_0_72,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_29 ).
fof(c_0_73,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| X3 = X2
| X3 = X1 ),
c_0_30 ).
fof(c_0_74,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ( X3 = X2
| X3 = X1 ) ),
c_0_31 ).
fof(c_0_75,axiom,
! [X3,X2] :
( lhs_atom18(X3,X2)
| ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
c_0_32 ).
fof(c_0_76,axiom,
! [X3,X2] :
( lhs_atom20(X3,X2)
| ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
c_0_33 ).
fof(c_0_77,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_34 ).
fof(c_0_78,plain,
! [X3,X2] :
( lhs_atom6(X3,X2)
| ~ subset(X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_79,axiom,
! [X3,X2] :
( lhs_atom5(X3,X2)
| subset(X3,X2) ),
c_0_36 ).
fof(c_0_80,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_37 ).
fof(c_0_81,plain,
! [X3,X2] :
( lhs_atom15(X3,X2)
| X3 != X2 ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_82,axiom,
! [X3,X2] :
( lhs_atom14(X3,X2)
| X3 = X2 ),
c_0_39 ).
fof(c_0_83,plain,
! [X3] : lhs_atom11(X3),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_84,plain,
! [X9,X10,X11,X12] :
( ( member(esk14_4(X9,X10,X11,X12),X11)
| ~ lower_bound(X12,X10,X9)
| ~ member(X12,X9)
| lhs_atom41(X9,X10,X11,X12) )
& ( lower_bound(esk14_4(X9,X10,X11,X12),X10,X9)
| ~ lower_bound(X12,X10,X9)
| ~ member(X12,X9)
| lhs_atom41(X9,X10,X11,X12) )
& ( ~ apply(X10,esk14_4(X9,X10,X11,X12),X12)
| ~ lower_bound(X12,X10,X9)
| ~ member(X12,X9)
| lhs_atom41(X9,X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
fof(c_0_85,plain,
! [X9,X10,X11,X12] :
( ( member(esk13_4(X9,X10,X11,X12),X11)
| ~ upper_bound(X12,X10,X9)
| ~ member(X12,X9)
| lhs_atom39(X9,X10,X11,X12) )
& ( upper_bound(esk13_4(X9,X10,X11,X12),X10,X9)
| ~ upper_bound(X12,X10,X9)
| ~ member(X12,X9)
| lhs_atom39(X9,X10,X11,X12) )
& ( ~ apply(X10,X12,esk13_4(X9,X10,X11,X12))
| ~ upper_bound(X12,X10,X9)
| ~ member(X12,X9)
| lhs_atom39(X9,X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
fof(c_0_86,plain,
! [X9,X10,X11,X12,X13] :
( ( member(X12,X9)
| lhs_atom40(X9,X10,X11,X12) )
& ( lower_bound(X12,X10,X9)
| lhs_atom40(X9,X10,X11,X12) )
& ( ~ member(X13,X11)
| ~ lower_bound(X13,X10,X9)
| apply(X10,X13,X12)
| lhs_atom40(X9,X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
fof(c_0_87,plain,
! [X9,X10,X11,X12,X13] :
( ( member(X12,X9)
| lhs_atom38(X9,X10,X11,X12) )
& ( upper_bound(X12,X10,X9)
| lhs_atom38(X9,X10,X11,X12) )
& ( ~ member(X13,X11)
| ~ upper_bound(X13,X10,X9)
| apply(X10,X12,X13)
| lhs_atom38(X9,X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
fof(c_0_88,plain,
! [X9,X10,X11] :
( ( member(esk10_3(X9,X10,X11),X11)
| ~ member(X10,X11)
| lhs_atom33(X9,X10,X11) )
& ( ~ apply(X9,X10,esk10_3(X9,X10,X11))
| ~ member(X10,X11)
| lhs_atom33(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
fof(c_0_89,plain,
! [X9,X10,X11] :
( ( member(esk9_3(X9,X10,X11),X11)
| ~ member(X10,X11)
| lhs_atom31(X9,X10,X11) )
& ( ~ apply(X9,esk9_3(X9,X10,X11),X10)
| ~ member(X10,X11)
| lhs_atom31(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
fof(c_0_90,plain,
! [X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ~ member(X10,X8)
| ~ member(X11,X8)
| ~ apply(X9,X10,X11)
| ~ apply(X9,X11,X10)
| X10 = X11
| ~ epred1_2(X9,X8) )
& ( ~ member(X12,X8)
| ~ member(X13,X8)
| ~ member(X14,X8)
| ~ apply(X9,X12,X13)
| ~ apply(X9,X13,X14)
| apply(X9,X12,X14)
| ~ epred1_2(X9,X8) )
& ( member(esk17_2(X15,X16),X15)
| member(esk15_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( member(esk18_2(X15,X16),X15)
| member(esk15_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( member(esk19_2(X15,X16),X15)
| member(esk15_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( apply(X16,esk17_2(X15,X16),esk18_2(X15,X16))
| member(esk15_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( apply(X16,esk18_2(X15,X16),esk19_2(X15,X16))
| member(esk15_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( ~ apply(X16,esk17_2(X15,X16),esk19_2(X15,X16))
| member(esk15_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( member(esk17_2(X15,X16),X15)
| member(esk16_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( member(esk18_2(X15,X16),X15)
| member(esk16_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( member(esk19_2(X15,X16),X15)
| member(esk16_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( apply(X16,esk17_2(X15,X16),esk18_2(X15,X16))
| member(esk16_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( apply(X16,esk18_2(X15,X16),esk19_2(X15,X16))
| member(esk16_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( ~ apply(X16,esk17_2(X15,X16),esk19_2(X15,X16))
| member(esk16_2(X15,X16),X15)
| epred1_2(X16,X15) )
& ( member(esk17_2(X15,X16),X15)
| apply(X16,esk15_2(X15,X16),esk16_2(X15,X16))
| epred1_2(X16,X15) )
& ( member(esk18_2(X15,X16),X15)
| apply(X16,esk15_2(X15,X16),esk16_2(X15,X16))
| epred1_2(X16,X15) )
& ( member(esk19_2(X15,X16),X15)
| apply(X16,esk15_2(X15,X16),esk16_2(X15,X16))
| epred1_2(X16,X15) )
& ( apply(X16,esk17_2(X15,X16),esk18_2(X15,X16))
| apply(X16,esk15_2(X15,X16),esk16_2(X15,X16))
| epred1_2(X16,X15) )
& ( apply(X16,esk18_2(X15,X16),esk19_2(X15,X16))
| apply(X16,esk15_2(X15,X16),esk16_2(X15,X16))
| epred1_2(X16,X15) )
& ( ~ apply(X16,esk17_2(X15,X16),esk19_2(X15,X16))
| apply(X16,esk15_2(X15,X16),esk16_2(X15,X16))
| epred1_2(X16,X15) )
& ( member(esk17_2(X15,X16),X15)
| apply(X16,esk16_2(X15,X16),esk15_2(X15,X16))
| epred1_2(X16,X15) )
& ( member(esk18_2(X15,X16),X15)
| apply(X16,esk16_2(X15,X16),esk15_2(X15,X16))
| epred1_2(X16,X15) )
& ( member(esk19_2(X15,X16),X15)
| apply(X16,esk16_2(X15,X16),esk15_2(X15,X16))
| epred1_2(X16,X15) )
& ( apply(X16,esk17_2(X15,X16),esk18_2(X15,X16))
| apply(X16,esk16_2(X15,X16),esk15_2(X15,X16))
| epred1_2(X16,X15) )
& ( apply(X16,esk18_2(X15,X16),esk19_2(X15,X16))
| apply(X16,esk16_2(X15,X16),esk15_2(X15,X16))
| epred1_2(X16,X15) )
& ( ~ apply(X16,esk17_2(X15,X16),esk19_2(X15,X16))
| apply(X16,esk16_2(X15,X16),esk15_2(X15,X16))
| epred1_2(X16,X15) )
& ( member(esk17_2(X15,X16),X15)
| esk15_2(X15,X16) != esk16_2(X15,X16)
| epred1_2(X16,X15) )
& ( member(esk18_2(X15,X16),X15)
| esk15_2(X15,X16) != esk16_2(X15,X16)
| epred1_2(X16,X15) )
& ( member(esk19_2(X15,X16),X15)
| esk15_2(X15,X16) != esk16_2(X15,X16)
| epred1_2(X16,X15) )
& ( apply(X16,esk17_2(X15,X16),esk18_2(X15,X16))
| esk15_2(X15,X16) != esk16_2(X15,X16)
| epred1_2(X16,X15) )
& ( apply(X16,esk18_2(X15,X16),esk19_2(X15,X16))
| esk15_2(X15,X16) != esk16_2(X15,X16)
| epred1_2(X16,X15) )
& ( ~ apply(X16,esk17_2(X15,X16),esk19_2(X15,X16))
| esk15_2(X15,X16) != esk16_2(X15,X16)
| epred1_2(X16,X15) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])])]) ).
fof(c_0_91,plain,
! [X9,X10,X11] :
( ( member(esk8_3(X9,X10,X11),X11)
| lhs_atom29(X9,X10,X11) )
& ( ~ apply(X9,X10,esk8_3(X9,X10,X11))
| lhs_atom29(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
fof(c_0_92,plain,
! [X9,X10,X11] :
( ( member(esk7_3(X9,X10,X11),X11)
| lhs_atom27(X9,X10,X11) )
& ( ~ apply(X9,esk7_3(X9,X10,X11),X10)
| lhs_atom27(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
fof(c_0_93,plain,
! [X9,X10,X11] :
( ( member(esk12_3(X9,X10,X11),X11)
| ~ member(X10,X11)
| lhs_atom37(X9,X10,X11) )
& ( apply(X9,esk12_3(X9,X10,X11),X10)
| ~ member(X10,X11)
| lhs_atom37(X9,X10,X11) )
& ( X10 != esk12_3(X9,X10,X11)
| ~ member(X10,X11)
| lhs_atom37(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).
fof(c_0_94,plain,
! [X9,X10,X11] :
( ( member(esk11_3(X9,X10,X11),X11)
| ~ member(X10,X11)
| lhs_atom35(X9,X10,X11) )
& ( apply(X9,X10,esk11_3(X9,X10,X11))
| ~ member(X10,X11)
| lhs_atom35(X9,X10,X11) )
& ( X10 != esk11_3(X9,X10,X11)
| ~ member(X10,X11)
| lhs_atom35(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
fof(c_0_95,plain,
! [X7,X8] :
( ( member(esk5_2(X7,X8),X8)
| ~ order(X7,X8)
| lhs_atom25(X7,X8) )
& ( member(esk6_2(X7,X8),X8)
| ~ order(X7,X8)
| lhs_atom25(X7,X8) )
& ( ~ apply(X7,esk5_2(X7,X8),esk6_2(X7,X8))
| ~ order(X7,X8)
| lhs_atom25(X7,X8) )
& ( ~ apply(X7,esk6_2(X7,X8),esk5_2(X7,X8))
| ~ order(X7,X8)
| lhs_atom25(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
fof(c_0_96,plain,
! [X7,X8] :
( ( member(esk4_2(X7,X8),X8)
| ~ epred1_2(X7,X8)
| lhs_atom23(X7,X8) )
& ( ~ apply(X7,esk4_2(X7,X8),esk4_2(X7,X8))
| ~ epred1_2(X7,X8)
| lhs_atom23(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
fof(c_0_97,plain,
! [X7,X8,X9,X10] :
( ( order(X7,X8)
| lhs_atom24(X7,X8) )
& ( ~ member(X9,X8)
| ~ member(X10,X8)
| apply(X7,X9,X10)
| apply(X7,X10,X9)
| lhs_atom24(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_98,plain,
! [X9,X10,X11,X12] :
( ( member(X10,X11)
| lhs_atom36(X9,X10,X11) )
& ( ~ member(X12,X11)
| ~ apply(X9,X12,X10)
| X10 = X12
| lhs_atom36(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
fof(c_0_99,plain,
! [X9,X10,X11,X12] :
( ( member(X10,X11)
| lhs_atom34(X9,X10,X11) )
& ( ~ member(X12,X11)
| ~ apply(X9,X10,X12)
| X10 = X12
| lhs_atom34(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
fof(c_0_100,plain,
! [X9,X10,X11,X12] :
( ( member(X10,X11)
| lhs_atom32(X9,X10,X11) )
& ( ~ member(X12,X11)
| apply(X9,X10,X12)
| lhs_atom32(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
fof(c_0_101,plain,
! [X9,X10,X11,X12] :
( ( member(X10,X11)
| lhs_atom30(X9,X10,X11) )
& ( ~ member(X12,X11)
| apply(X9,X12,X10)
| lhs_atom30(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
fof(c_0_102,plain,
! [X9,X10,X11,X12] :
( lhs_atom28(X9,X10,X11)
| ~ member(X12,X11)
| apply(X9,X10,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
fof(c_0_103,plain,
! [X9,X10,X11,X12] :
( lhs_atom26(X9,X10,X11)
| ~ member(X12,X11)
| apply(X9,X12,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])]) ).
fof(c_0_104,plain,
! [X4,X5,X6] :
( lhs_atom8(X4,X5,X6)
| ~ member(X4,X6)
| ~ member(X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])]) ).
fof(c_0_105,plain,
! [X7,X8,X9] :
( ( ~ member(X9,X8)
| apply(X7,X9,X9)
| lhs_atom22(X7,X8) )
& ( epred1_2(X7,X8)
| lhs_atom22(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])]) ).
fof(c_0_106,plain,
! [X5,X6,X7] :
( lhs_atom13(X5,X6,X7)
| ~ member(X6,X5)
| member(X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])]) ).
fof(c_0_107,plain,
! [X4,X5,X6] :
( lhs_atom9(X4,X5,X6)
| member(X4,X6)
| member(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_108,plain,
! [X6,X7] :
( ( member(esk3_2(X6,X7),X7)
| lhs_atom21(X6,X7) )
& ( ~ member(X6,esk3_2(X6,X7))
| lhs_atom21(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])]) ).
fof(c_0_109,plain,
! [X4,X5] :
( ( member(esk1_2(X4,X5),X5)
| lhs_atom2(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X4)
| lhs_atom2(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
fof(c_0_110,plain,
! [X5,X6,X7] :
( ( member(X6,X5)
| lhs_atom12(X5,X6,X7) )
& ( ~ member(X6,X7)
| lhs_atom12(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])]) ).
fof(c_0_111,plain,
! [X4,X5,X6] :
( ( ~ member(X4,X6)
| lhs_atom10(X4,X5,X6) )
& ( ~ member(X4,X5)
| lhs_atom10(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])]) ).
fof(c_0_112,plain,
! [X4,X5,X6] :
( ( member(X4,X6)
| lhs_atom7(X4,X5,X6) )
& ( member(X4,X5)
| lhs_atom7(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_70])]) ).
fof(c_0_113,plain,
! [X6,X7,X8] :
( lhs_atom19(X6,X7)
| ~ member(X8,X7)
| ~ member(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])]) ).
fof(c_0_114,plain,
! [X3,X4] :
( lhs_atom4(X3,X4)
| ~ subset(X4,X3)
| ~ subset(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])]) ).
fof(c_0_115,plain,
! [X4,X5,X6] :
( lhs_atom16(X4,X5,X6)
| X4 = X6
| X4 = X5 ),
inference(variable_rename,[status(thm)],[c_0_73]) ).
fof(c_0_116,plain,
! [X4,X5,X6] :
( ( X4 != X6
| lhs_atom17(X4,X5,X6) )
& ( X4 != X5
| lhs_atom17(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])]) ).
fof(c_0_117,plain,
! [X6,X7] :
( ( member(esk2_2(X6,X7),X7)
| lhs_atom18(X6,X7) )
& ( member(X6,esk2_2(X6,X7))
| lhs_atom18(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_75])])]) ).
fof(c_0_118,plain,
! [X6,X7,X8] :
( lhs_atom20(X6,X7)
| ~ member(X8,X7)
| member(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
fof(c_0_119,plain,
! [X4,X5,X6] :
( lhs_atom1(X4,X5)
| ~ member(X6,X5)
| member(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
fof(c_0_120,plain,
! [X4,X5] :
( lhs_atom6(X4,X5)
| ~ subset(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_78]) ).
fof(c_0_121,plain,
! [X4,X5] :
( lhs_atom5(X4,X5)
| subset(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_79]) ).
fof(c_0_122,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom3(X3,X4) )
& ( subset(X3,X4)
| lhs_atom3(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_80])]) ).
fof(c_0_123,plain,
! [X4,X5] :
( lhs_atom15(X4,X5)
| X4 != X5 ),
inference(variable_rename,[status(thm)],[c_0_81]) ).
fof(c_0_124,plain,
! [X4,X5] :
( lhs_atom14(X4,X5)
| X4 = X5 ),
inference(variable_rename,[status(thm)],[c_0_82]) ).
fof(c_0_125,plain,
! [X4] : lhs_atom11(X4),
inference(variable_rename,[status(thm)],[c_0_83]) ).
cnf(c_0_126,plain,
( lhs_atom41(X1,X2,X3,X4)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1)
| ~ apply(X2,esk14_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_127,plain,
( lhs_atom39(X1,X2,X3,X4)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1)
| ~ apply(X2,X4,esk13_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_128,plain,
( lhs_atom41(X1,X2,X3,X4)
| lower_bound(esk14_4(X1,X2,X3,X4),X2,X1)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_129,plain,
( lhs_atom39(X1,X2,X3,X4)
| upper_bound(esk13_4(X1,X2,X3,X4),X2,X1)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_130,plain,
( lhs_atom41(X1,X2,X3,X4)
| member(esk14_4(X1,X2,X3,X4),X3)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_131,plain,
( lhs_atom39(X1,X2,X3,X4)
| member(esk13_4(X1,X2,X3,X4),X3)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_132,plain,
( lhs_atom40(X1,X2,X3,X4)
| apply(X2,X5,X4)
| ~ lower_bound(X5,X2,X1)
| ~ member(X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_133,plain,
( lhs_atom38(X1,X2,X3,X4)
| apply(X2,X4,X5)
| ~ upper_bound(X5,X2,X1)
| ~ member(X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_134,plain,
( lhs_atom33(X1,X2,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,esk10_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_135,plain,
( lhs_atom31(X1,X2,X3)
| ~ member(X2,X3)
| ~ apply(X1,esk9_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_136,plain,
( apply(X1,X3,X4)
| ~ epred1_2(X1,X2)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_137,plain,
( lhs_atom29(X1,X2,X3)
| ~ apply(X1,X2,esk8_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_138,plain,
( lhs_atom27(X1,X2,X3)
| ~ apply(X1,esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_139,plain,
( lhs_atom40(X1,X2,X3,X4)
| lower_bound(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_140,plain,
( lhs_atom38(X1,X2,X3,X4)
| upper_bound(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_141,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_142,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_143,plain,
( lhs_atom40(X1,X2,X3,X4)
| member(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_144,plain,
( lhs_atom38(X1,X2,X3,X4)
| member(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_145,plain,
( X3 = X4
| ~ epred1_2(X1,X2)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X4,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_146,plain,
( lhs_atom37(X1,X2,X3)
| apply(X1,esk12_3(X1,X2,X3),X2)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_147,plain,
( lhs_atom35(X1,X2,X3)
| apply(X1,X2,esk11_3(X1,X2,X3))
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_148,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_149,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_150,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_151,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_152,plain,
( epred1_2(X1,X2)
| esk15_2(X2,X1) != esk16_2(X2,X1)
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_153,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_154,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_155,plain,
( lhs_atom25(X1,X2)
| ~ order(X1,X2)
| ~ apply(X1,esk5_2(X1,X2),esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_156,plain,
( lhs_atom25(X1,X2)
| ~ order(X1,X2)
| ~ apply(X1,esk6_2(X1,X2),esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_157,plain,
( lhs_atom23(X1,X2)
| ~ epred1_2(X1,X2)
| ~ apply(X1,esk4_2(X1,X2),esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_158,plain,
( lhs_atom37(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_159,plain,
( lhs_atom35(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_160,plain,
( lhs_atom33(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_161,plain,
( lhs_atom31(X1,X2,X3)
| member(esk9_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_162,plain,
( lhs_atom29(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_163,plain,
( lhs_atom27(X1,X2,X3)
| member(esk7_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_164,plain,
( lhs_atom24(X1,X2)
| apply(X1,X3,X4)
| apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_165,plain,
( lhs_atom36(X1,X2,X3)
| X2 = X4
| ~ apply(X1,X4,X2)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_166,plain,
( lhs_atom34(X1,X2,X3)
| X2 = X4
| ~ apply(X1,X2,X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_167,plain,
( epred1_2(X1,X2)
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1))
| esk15_2(X2,X1) != esk16_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_168,plain,
( epred1_2(X1,X2)
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1))
| esk15_2(X2,X1) != esk16_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_169,plain,
( lhs_atom37(X1,X2,X3)
| ~ member(X2,X3)
| X2 != esk12_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_170,plain,
( lhs_atom35(X1,X2,X3)
| ~ member(X2,X3)
| X2 != esk11_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_171,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_172,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_173,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_174,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_175,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| member(esk17_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_176,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| member(esk18_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_177,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| member(esk19_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_178,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| member(esk17_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_179,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| member(esk18_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_180,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| member(esk19_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_181,plain,
( lhs_atom32(X1,X2,X3)
| apply(X1,X2,X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_182,plain,
( lhs_atom30(X1,X2,X3)
| apply(X1,X4,X2)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_183,plain,
( apply(X1,X2,X3)
| lhs_atom28(X1,X2,X4)
| ~ member(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_184,plain,
( apply(X1,X2,X3)
| lhs_atom26(X1,X3,X4)
| ~ member(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_185,plain,
( lhs_atom8(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_186,plain,
( epred1_2(X1,X2)
| member(esk17_2(X2,X1),X2)
| esk15_2(X2,X1) != esk16_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_187,plain,
( epred1_2(X1,X2)
| member(esk18_2(X2,X1),X2)
| esk15_2(X2,X1) != esk16_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_188,plain,
( epred1_2(X1,X2)
| member(esk19_2(X2,X1),X2)
| esk15_2(X2,X1) != esk16_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_189,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| member(esk17_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_190,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_191,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| member(esk19_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_192,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| member(esk17_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_193,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_194,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| member(esk19_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_195,plain,
( lhs_atom22(X1,X2)
| apply(X1,X3,X3)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_196,plain,
( member(X1,X2)
| lhs_atom13(X3,X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_197,plain,
( member(X1,X2)
| member(X1,X3)
| lhs_atom9(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_198,plain,
( lhs_atom21(X1,X2)
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_199,plain,
( lhs_atom2(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_200,plain,
( lhs_atom25(X1,X2)
| member(esk5_2(X1,X2),X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_201,plain,
( lhs_atom25(X1,X2)
| member(esk6_2(X1,X2),X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_202,plain,
( lhs_atom23(X1,X2)
| member(esk4_2(X1,X2),X2)
| ~ epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_203,plain,
( lhs_atom12(X1,X2,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_204,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_205,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_206,plain,
( lhs_atom36(X1,X2,X3)
| member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_207,plain,
( lhs_atom34(X1,X2,X3)
| member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_208,plain,
( lhs_atom32(X1,X2,X3)
| member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_209,plain,
( lhs_atom30(X1,X2,X3)
| member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_210,plain,
( lhs_atom12(X1,X2,X3)
| member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_211,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_212,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_213,plain,
( lhs_atom19(X1,X3)
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_214,plain,
( lhs_atom4(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_215,plain,
( X1 = X2
| X1 = X3
| lhs_atom16(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_216,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_217,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_218,plain,
( lhs_atom21(X1,X2)
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_219,plain,
( lhs_atom18(X1,X2)
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_220,plain,
( lhs_atom18(X1,X2)
| member(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_221,plain,
( lhs_atom2(X1,X2)
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_222,plain,
( member(X1,X2)
| lhs_atom20(X1,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_223,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_224,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_225,plain,
( lhs_atom24(X1,X2)
| order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_226,plain,
( lhs_atom22(X1,X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_227,plain,
( subset(X1,X2)
| lhs_atom5(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_228,plain,
( lhs_atom3(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_229,plain,
( lhs_atom3(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_230,plain,
( lhs_atom15(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_231,plain,
( X1 = X2
| lhs_atom14(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_232,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_233,plain,
( lhs_atom41(X1,X2,X3,X4)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1)
| ~ apply(X2,esk14_4(X1,X2,X3,X4),X4) ),
c_0_126,
[final] ).
cnf(c_0_234,plain,
( lhs_atom39(X1,X2,X3,X4)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1)
| ~ apply(X2,X4,esk13_4(X1,X2,X3,X4)) ),
c_0_127,
[final] ).
cnf(c_0_235,plain,
( lhs_atom41(X1,X2,X3,X4)
| lower_bound(esk14_4(X1,X2,X3,X4),X2,X1)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1) ),
c_0_128,
[final] ).
cnf(c_0_236,plain,
( lhs_atom39(X1,X2,X3,X4)
| upper_bound(esk13_4(X1,X2,X3,X4),X2,X1)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1) ),
c_0_129,
[final] ).
cnf(c_0_237,plain,
( lhs_atom41(X1,X2,X3,X4)
| member(esk14_4(X1,X2,X3,X4),X3)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1) ),
c_0_130,
[final] ).
cnf(c_0_238,plain,
( lhs_atom39(X1,X2,X3,X4)
| member(esk13_4(X1,X2,X3,X4),X3)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1) ),
c_0_131,
[final] ).
cnf(c_0_239,plain,
( lhs_atom40(X1,X2,X3,X4)
| apply(X2,X5,X4)
| ~ lower_bound(X5,X2,X1)
| ~ member(X5,X3) ),
c_0_132,
[final] ).
cnf(c_0_240,plain,
( lhs_atom38(X1,X2,X3,X4)
| apply(X2,X4,X5)
| ~ upper_bound(X5,X2,X1)
| ~ member(X5,X3) ),
c_0_133,
[final] ).
cnf(c_0_241,plain,
( lhs_atom33(X1,X2,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,esk10_3(X1,X2,X3)) ),
c_0_134,
[final] ).
cnf(c_0_242,plain,
( lhs_atom31(X1,X2,X3)
| ~ member(X2,X3)
| ~ apply(X1,esk9_3(X1,X2,X3),X2) ),
c_0_135,
[final] ).
cnf(c_0_243,plain,
( apply(X1,X3,X4)
| ~ epred1_2(X1,X2)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
c_0_136,
[final] ).
cnf(c_0_244,plain,
( lhs_atom29(X1,X2,X3)
| ~ apply(X1,X2,esk8_3(X1,X2,X3)) ),
c_0_137,
[final] ).
cnf(c_0_245,plain,
( lhs_atom27(X1,X2,X3)
| ~ apply(X1,esk7_3(X1,X2,X3),X2) ),
c_0_138,
[final] ).
cnf(c_0_246,plain,
( lhs_atom40(X1,X2,X3,X4)
| lower_bound(X4,X2,X1) ),
c_0_139,
[final] ).
cnf(c_0_247,plain,
( lhs_atom38(X1,X2,X3,X4)
| upper_bound(X4,X2,X1) ),
c_0_140,
[final] ).
cnf(c_0_248,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
c_0_141,
[final] ).
cnf(c_0_249,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
c_0_142,
[final] ).
cnf(c_0_250,plain,
( lhs_atom40(X1,X2,X3,X4)
| member(X4,X1) ),
c_0_143,
[final] ).
cnf(c_0_251,plain,
( lhs_atom38(X1,X2,X3,X4)
| member(X4,X1) ),
c_0_144,
[final] ).
cnf(c_0_252,plain,
( X3 = X4
| ~ epred1_2(X1,X2)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X4,X2)
| ~ member(X3,X2) ),
c_0_145,
[final] ).
cnf(c_0_253,plain,
( lhs_atom37(X1,X2,X3)
| apply(X1,esk12_3(X1,X2,X3),X2)
| ~ member(X2,X3) ),
c_0_146,
[final] ).
cnf(c_0_254,plain,
( lhs_atom35(X1,X2,X3)
| apply(X1,X2,esk11_3(X1,X2,X3))
| ~ member(X2,X3) ),
c_0_147,
[final] ).
cnf(c_0_255,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
c_0_148,
[final] ).
cnf(c_0_256,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
c_0_149,
[final] ).
cnf(c_0_257,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
c_0_150,
[final] ).
cnf(c_0_258,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
c_0_151,
[final] ).
cnf(c_0_259,plain,
( epred1_2(X1,X2)
| esk16_2(X2,X1) != esk15_2(X2,X1)
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
c_0_152,
[final] ).
cnf(c_0_260,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
c_0_153,
[final] ).
cnf(c_0_261,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| ~ apply(X1,esk17_2(X2,X1),esk19_2(X2,X1)) ),
c_0_154,
[final] ).
cnf(c_0_262,plain,
( lhs_atom25(X1,X2)
| ~ order(X1,X2)
| ~ apply(X1,esk5_2(X1,X2),esk6_2(X1,X2)) ),
c_0_155,
[final] ).
cnf(c_0_263,plain,
( lhs_atom25(X1,X2)
| ~ order(X1,X2)
| ~ apply(X1,esk6_2(X1,X2),esk5_2(X1,X2)) ),
c_0_156,
[final] ).
cnf(c_0_264,plain,
( lhs_atom23(X1,X2)
| ~ epred1_2(X1,X2)
| ~ apply(X1,esk4_2(X1,X2),esk4_2(X1,X2)) ),
c_0_157,
[final] ).
cnf(c_0_265,plain,
( lhs_atom37(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
c_0_158,
[final] ).
cnf(c_0_266,plain,
( lhs_atom35(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
c_0_159,
[final] ).
cnf(c_0_267,plain,
( lhs_atom33(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
c_0_160,
[final] ).
cnf(c_0_268,plain,
( lhs_atom31(X1,X2,X3)
| member(esk9_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
c_0_161,
[final] ).
cnf(c_0_269,plain,
( lhs_atom29(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X3) ),
c_0_162,
[final] ).
cnf(c_0_270,plain,
( lhs_atom27(X1,X2,X3)
| member(esk7_3(X1,X2,X3),X3) ),
c_0_163,
[final] ).
cnf(c_0_271,plain,
( lhs_atom24(X1,X2)
| apply(X1,X3,X4)
| apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
c_0_164,
[final] ).
cnf(c_0_272,plain,
( lhs_atom36(X1,X2,X3)
| X2 = X4
| ~ apply(X1,X4,X2)
| ~ member(X4,X3) ),
c_0_165,
[final] ).
cnf(c_0_273,plain,
( lhs_atom34(X1,X2,X3)
| X2 = X4
| ~ apply(X1,X2,X4)
| ~ member(X4,X3) ),
c_0_166,
[final] ).
cnf(c_0_274,plain,
( epred1_2(X1,X2)
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1))
| esk16_2(X2,X1) != esk15_2(X2,X1) ),
c_0_167,
[final] ).
cnf(c_0_275,plain,
( epred1_2(X1,X2)
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1))
| esk16_2(X2,X1) != esk15_2(X2,X1) ),
c_0_168,
[final] ).
cnf(c_0_276,plain,
( lhs_atom37(X1,X2,X3)
| ~ member(X2,X3)
| esk12_3(X1,X2,X3) != X2 ),
c_0_169,
[final] ).
cnf(c_0_277,plain,
( lhs_atom35(X1,X2,X3)
| ~ member(X2,X3)
| esk11_3(X1,X2,X3) != X2 ),
c_0_170,
[final] ).
cnf(c_0_278,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
c_0_171,
[final] ).
cnf(c_0_279,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
c_0_172,
[final] ).
cnf(c_0_280,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| apply(X1,esk17_2(X2,X1),esk18_2(X2,X1)) ),
c_0_173,
[final] ).
cnf(c_0_281,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| apply(X1,esk18_2(X2,X1),esk19_2(X2,X1)) ),
c_0_174,
[final] ).
cnf(c_0_282,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| member(esk17_2(X2,X1),X2) ),
c_0_175,
[final] ).
cnf(c_0_283,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| member(esk18_2(X2,X1),X2) ),
c_0_176,
[final] ).
cnf(c_0_284,plain,
( epred1_2(X1,X2)
| apply(X1,esk15_2(X2,X1),esk16_2(X2,X1))
| member(esk19_2(X2,X1),X2) ),
c_0_177,
[final] ).
cnf(c_0_285,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| member(esk17_2(X2,X1),X2) ),
c_0_178,
[final] ).
cnf(c_0_286,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| member(esk18_2(X2,X1),X2) ),
c_0_179,
[final] ).
cnf(c_0_287,plain,
( epred1_2(X1,X2)
| apply(X1,esk16_2(X2,X1),esk15_2(X2,X1))
| member(esk19_2(X2,X1),X2) ),
c_0_180,
[final] ).
cnf(c_0_288,plain,
( lhs_atom32(X1,X2,X3)
| apply(X1,X2,X4)
| ~ member(X4,X3) ),
c_0_181,
[final] ).
cnf(c_0_289,plain,
( lhs_atom30(X1,X2,X3)
| apply(X1,X4,X2)
| ~ member(X4,X3) ),
c_0_182,
[final] ).
cnf(c_0_290,plain,
( apply(X1,X2,X3)
| lhs_atom28(X1,X2,X4)
| ~ member(X3,X4) ),
c_0_183,
[final] ).
cnf(c_0_291,plain,
( apply(X1,X2,X3)
| lhs_atom26(X1,X3,X4)
| ~ member(X2,X4) ),
c_0_184,
[final] ).
cnf(c_0_292,plain,
( lhs_atom8(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
c_0_185,
[final] ).
cnf(c_0_293,plain,
( epred1_2(X1,X2)
| member(esk17_2(X2,X1),X2)
| esk16_2(X2,X1) != esk15_2(X2,X1) ),
c_0_186,
[final] ).
cnf(c_0_294,plain,
( epred1_2(X1,X2)
| member(esk18_2(X2,X1),X2)
| esk16_2(X2,X1) != esk15_2(X2,X1) ),
c_0_187,
[final] ).
cnf(c_0_295,plain,
( epred1_2(X1,X2)
| member(esk19_2(X2,X1),X2)
| esk16_2(X2,X1) != esk15_2(X2,X1) ),
c_0_188,
[final] ).
cnf(c_0_296,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| member(esk17_2(X2,X1),X2) ),
c_0_189,
[final] ).
cnf(c_0_297,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2) ),
c_0_190,
[final] ).
cnf(c_0_298,plain,
( epred1_2(X1,X2)
| member(esk15_2(X2,X1),X2)
| member(esk19_2(X2,X1),X2) ),
c_0_191,
[final] ).
cnf(c_0_299,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| member(esk17_2(X2,X1),X2) ),
c_0_192,
[final] ).
cnf(c_0_300,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2) ),
c_0_193,
[final] ).
cnf(c_0_301,plain,
( epred1_2(X1,X2)
| member(esk16_2(X2,X1),X2)
| member(esk19_2(X2,X1),X2) ),
c_0_194,
[final] ).
cnf(c_0_302,plain,
( lhs_atom22(X1,X2)
| apply(X1,X3,X3)
| ~ member(X3,X2) ),
c_0_195,
[final] ).
cnf(c_0_303,plain,
( member(X1,X2)
| lhs_atom13(X3,X1,X2)
| ~ member(X1,X3) ),
c_0_196,
[final] ).
cnf(c_0_304,plain,
( member(X1,X2)
| member(X1,X3)
| lhs_atom9(X1,X2,X3) ),
c_0_197,
[final] ).
cnf(c_0_305,plain,
( lhs_atom21(X1,X2)
| ~ member(X1,esk3_2(X1,X2)) ),
c_0_198,
[final] ).
cnf(c_0_306,plain,
( lhs_atom2(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
c_0_199,
[final] ).
cnf(c_0_307,plain,
( lhs_atom25(X1,X2)
| member(esk5_2(X1,X2),X2)
| ~ order(X1,X2) ),
c_0_200,
[final] ).
cnf(c_0_308,plain,
( lhs_atom25(X1,X2)
| member(esk6_2(X1,X2),X2)
| ~ order(X1,X2) ),
c_0_201,
[final] ).
cnf(c_0_309,plain,
( lhs_atom23(X1,X2)
| member(esk4_2(X1,X2),X2)
| ~ epred1_2(X1,X2) ),
c_0_202,
[final] ).
cnf(c_0_310,plain,
( lhs_atom12(X1,X2,X3)
| ~ member(X2,X3) ),
c_0_203,
[final] ).
cnf(c_0_311,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X3) ),
c_0_204,
[final] ).
cnf(c_0_312,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X2) ),
c_0_205,
[final] ).
cnf(c_0_313,plain,
( lhs_atom36(X1,X2,X3)
| member(X2,X3) ),
c_0_206,
[final] ).
cnf(c_0_314,plain,
( lhs_atom34(X1,X2,X3)
| member(X2,X3) ),
c_0_207,
[final] ).
cnf(c_0_315,plain,
( lhs_atom32(X1,X2,X3)
| member(X2,X3) ),
c_0_208,
[final] ).
cnf(c_0_316,plain,
( lhs_atom30(X1,X2,X3)
| member(X2,X3) ),
c_0_209,
[final] ).
cnf(c_0_317,plain,
( lhs_atom12(X1,X2,X3)
| member(X2,X1) ),
c_0_210,
[final] ).
cnf(c_0_318,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X3) ),
c_0_211,
[final] ).
cnf(c_0_319,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X2) ),
c_0_212,
[final] ).
cnf(c_0_320,plain,
( lhs_atom19(X1,X3)
| ~ member(X1,X2)
| ~ member(X2,X3) ),
c_0_213,
[final] ).
cnf(c_0_321,plain,
( lhs_atom4(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_214,
[final] ).
cnf(c_0_322,plain,
( X1 = X2
| X1 = X3
| lhs_atom16(X1,X2,X3) ),
c_0_215,
[final] ).
cnf(c_0_323,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X3 ),
c_0_216,
[final] ).
cnf(c_0_324,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X2 ),
c_0_217,
[final] ).
cnf(c_0_325,plain,
( lhs_atom21(X1,X2)
| member(esk3_2(X1,X2),X2) ),
c_0_218,
[final] ).
cnf(c_0_326,plain,
( lhs_atom18(X1,X2)
| member(esk2_2(X1,X2),X2) ),
c_0_219,
[final] ).
cnf(c_0_327,plain,
( lhs_atom18(X1,X2)
| member(X1,esk2_2(X1,X2)) ),
c_0_220,
[final] ).
cnf(c_0_328,plain,
( lhs_atom2(X1,X2)
| member(esk1_2(X1,X2),X2) ),
c_0_221,
[final] ).
cnf(c_0_329,plain,
( member(X1,X2)
| lhs_atom20(X1,X3)
| ~ member(X2,X3) ),
c_0_222,
[final] ).
cnf(c_0_330,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
c_0_223,
[final] ).
cnf(c_0_331,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2) ),
c_0_224,
[final] ).
cnf(c_0_332,plain,
( lhs_atom24(X1,X2)
| order(X1,X2) ),
c_0_225,
[final] ).
cnf(c_0_333,plain,
( lhs_atom22(X1,X2)
| epred1_2(X1,X2) ),
c_0_226,
[final] ).
cnf(c_0_334,plain,
( subset(X1,X2)
| lhs_atom5(X1,X2) ),
c_0_227,
[final] ).
cnf(c_0_335,plain,
( lhs_atom3(X1,X2)
| subset(X2,X1) ),
c_0_228,
[final] ).
cnf(c_0_336,plain,
( lhs_atom3(X1,X2)
| subset(X1,X2) ),
c_0_229,
[final] ).
cnf(c_0_337,plain,
( lhs_atom15(X1,X2)
| X1 != X2 ),
c_0_230,
[final] ).
cnf(c_0_338,plain,
( X1 = X2
| lhs_atom14(X1,X2) ),
c_0_231,
[final] ).
cnf(c_0_339,plain,
lhs_atom11(X1),
c_0_232,
[final] ).
% End CNF derivation
cnf(c_0_233_0,axiom,
( greatest_lower_bound(X4,X1,X2,X3)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1)
| ~ apply(X2,sk1_esk14_4(X1,X2,X3,X4),X4) ),
inference(unfold_definition,[status(thm)],[c_0_233,def_lhs_atom41]) ).
cnf(c_0_234_0,axiom,
( least_upper_bound(X4,X1,X2,X3)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1)
| ~ apply(X2,X4,sk1_esk13_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_234,def_lhs_atom39]) ).
cnf(c_0_235_0,axiom,
( greatest_lower_bound(X4,X1,X2,X3)
| lower_bound(sk1_esk14_4(X1,X2,X3,X4),X2,X1)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_235,def_lhs_atom41]) ).
cnf(c_0_236_0,axiom,
( least_upper_bound(X4,X1,X2,X3)
| upper_bound(sk1_esk13_4(X1,X2,X3,X4),X2,X1)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_236,def_lhs_atom39]) ).
cnf(c_0_237_0,axiom,
( greatest_lower_bound(X4,X1,X2,X3)
| member(sk1_esk14_4(X1,X2,X3,X4),X3)
| ~ member(X4,X1)
| ~ lower_bound(X4,X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_237,def_lhs_atom41]) ).
cnf(c_0_238_0,axiom,
( least_upper_bound(X4,X1,X2,X3)
| member(sk1_esk13_4(X1,X2,X3,X4),X3)
| ~ member(X4,X1)
| ~ upper_bound(X4,X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_238,def_lhs_atom39]) ).
cnf(c_0_239_0,axiom,
( ~ greatest_lower_bound(X4,X1,X2,X3)
| apply(X2,X5,X4)
| ~ lower_bound(X5,X2,X1)
| ~ member(X5,X3) ),
inference(unfold_definition,[status(thm)],[c_0_239,def_lhs_atom40]) ).
cnf(c_0_240_0,axiom,
( ~ least_upper_bound(X4,X1,X2,X3)
| apply(X2,X4,X5)
| ~ upper_bound(X5,X2,X1)
| ~ member(X5,X3) ),
inference(unfold_definition,[status(thm)],[c_0_240,def_lhs_atom38]) ).
cnf(c_0_241_0,axiom,
( least(X2,X1,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,sk1_esk10_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_241,def_lhs_atom33]) ).
cnf(c_0_242_0,axiom,
( greatest(X2,X1,X3)
| ~ member(X2,X3)
| ~ apply(X1,sk1_esk9_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_242,def_lhs_atom31]) ).
cnf(c_0_243_0,axiom,
( ~ epred1_2(X1,X2)
| apply(X1,X3,X4)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_243,def_epred1_2]) ).
cnf(c_0_244_0,axiom,
( lower_bound(X2,X1,X3)
| ~ apply(X1,X2,sk1_esk8_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_244,def_lhs_atom29]) ).
cnf(c_0_245_0,axiom,
( upper_bound(X2,X1,X3)
| ~ apply(X1,sk1_esk7_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_245,def_lhs_atom27]) ).
cnf(c_0_246_0,axiom,
( ~ greatest_lower_bound(X4,X1,X2,X3)
| lower_bound(X4,X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_246,def_lhs_atom40]) ).
cnf(c_0_247_0,axiom,
( ~ least_upper_bound(X4,X1,X2,X3)
| upper_bound(X4,X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_247,def_lhs_atom38]) ).
cnf(c_0_248_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk15_2(X2,X1),sk1_esk16_2(X2,X1))
| ~ apply(X1,sk1_esk17_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_248,def_epred1_2]) ).
cnf(c_0_249_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk16_2(X2,X1),sk1_esk15_2(X2,X1))
| ~ apply(X1,sk1_esk17_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_249,def_epred1_2]) ).
cnf(c_0_250_0,axiom,
( ~ greatest_lower_bound(X4,X1,X2,X3)
| member(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_250,def_lhs_atom40]) ).
cnf(c_0_251_0,axiom,
( ~ least_upper_bound(X4,X1,X2,X3)
| member(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_251,def_lhs_atom38]) ).
cnf(c_0_252_0,axiom,
( ~ epred1_2(X1,X2)
| X3 = X4
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X4,X2)
| ~ member(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_252,def_epred1_2]) ).
cnf(c_0_253_0,axiom,
( min(X2,X1,X3)
| apply(X1,sk1_esk12_3(X1,X2,X3),X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_253,def_lhs_atom37]) ).
cnf(c_0_254_0,axiom,
( max(X2,X1,X3)
| apply(X1,X2,sk1_esk11_3(X1,X2,X3))
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_254,def_lhs_atom35]) ).
cnf(c_0_255_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk15_2(X2,X1),sk1_esk16_2(X2,X1))
| apply(X1,sk1_esk17_2(X2,X1),sk1_esk18_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_255,def_epred1_2]) ).
cnf(c_0_256_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk15_2(X2,X1),sk1_esk16_2(X2,X1))
| apply(X1,sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_256,def_epred1_2]) ).
cnf(c_0_257_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk16_2(X2,X1),sk1_esk15_2(X2,X1))
| apply(X1,sk1_esk17_2(X2,X1),sk1_esk18_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_257,def_epred1_2]) ).
cnf(c_0_258_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk16_2(X2,X1),sk1_esk15_2(X2,X1))
| apply(X1,sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_258,def_epred1_2]) ).
cnf(c_0_259_0,axiom,
( epred1_2(X1,X2)
| sk1_esk16_2(X2,X1) != sk1_esk15_2(X2,X1)
| ~ apply(X1,sk1_esk17_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_259,def_epred1_2]) ).
cnf(c_0_260_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk15_2(X2,X1),X2)
| ~ apply(X1,sk1_esk17_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_260,def_epred1_2]) ).
cnf(c_0_261_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk16_2(X2,X1),X2)
| ~ apply(X1,sk1_esk17_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_261,def_epred1_2]) ).
cnf(c_0_262_0,axiom,
( total_order(X1,X2)
| ~ order(X1,X2)
| ~ apply(X1,sk1_esk5_2(X1,X2),sk1_esk6_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_262,def_lhs_atom25]) ).
cnf(c_0_263_0,axiom,
( total_order(X1,X2)
| ~ order(X1,X2)
| ~ apply(X1,sk1_esk6_2(X1,X2),sk1_esk5_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_263,def_lhs_atom25]) ).
cnf(c_0_264_0,axiom,
( order(X1,X2)
| ~ epred1_2(X1,X2)
| ~ apply(X1,sk1_esk4_2(X1,X2),sk1_esk4_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_264,def_lhs_atom23]) ).
cnf(c_0_265_0,axiom,
( min(X2,X1,X3)
| member(sk1_esk12_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_265,def_lhs_atom37]) ).
cnf(c_0_266_0,axiom,
( max(X2,X1,X3)
| member(sk1_esk11_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_266,def_lhs_atom35]) ).
cnf(c_0_267_0,axiom,
( least(X2,X1,X3)
| member(sk1_esk10_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_267,def_lhs_atom33]) ).
cnf(c_0_268_0,axiom,
( greatest(X2,X1,X3)
| member(sk1_esk9_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_268,def_lhs_atom31]) ).
cnf(c_0_269_0,axiom,
( lower_bound(X2,X1,X3)
| member(sk1_esk8_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_269,def_lhs_atom29]) ).
cnf(c_0_270_0,axiom,
( upper_bound(X2,X1,X3)
| member(sk1_esk7_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_270,def_lhs_atom27]) ).
cnf(c_0_271_0,axiom,
( ~ total_order(X1,X2)
| apply(X1,X3,X4)
| apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_271,def_lhs_atom24]) ).
cnf(c_0_272_0,axiom,
( ~ min(X2,X1,X3)
| X2 = X4
| ~ apply(X1,X4,X2)
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_272,def_lhs_atom36]) ).
cnf(c_0_273_0,axiom,
( ~ max(X2,X1,X3)
| X2 = X4
| ~ apply(X1,X2,X4)
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_273,def_lhs_atom34]) ).
cnf(c_0_274_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk17_2(X2,X1),sk1_esk18_2(X2,X1))
| sk1_esk16_2(X2,X1) != sk1_esk15_2(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_274,def_epred1_2]) ).
cnf(c_0_275_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1))
| sk1_esk16_2(X2,X1) != sk1_esk15_2(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_275,def_epred1_2]) ).
cnf(c_0_276_0,axiom,
( min(X2,X1,X3)
| ~ member(X2,X3)
| sk1_esk12_3(X1,X2,X3) != X2 ),
inference(unfold_definition,[status(thm)],[c_0_276,def_lhs_atom37]) ).
cnf(c_0_277_0,axiom,
( max(X2,X1,X3)
| ~ member(X2,X3)
| sk1_esk11_3(X1,X2,X3) != X2 ),
inference(unfold_definition,[status(thm)],[c_0_277,def_lhs_atom35]) ).
cnf(c_0_278_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk15_2(X2,X1),X2)
| apply(X1,sk1_esk17_2(X2,X1),sk1_esk18_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_278,def_epred1_2]) ).
cnf(c_0_279_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk15_2(X2,X1),X2)
| apply(X1,sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_279,def_epred1_2]) ).
cnf(c_0_280_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk16_2(X2,X1),X2)
| apply(X1,sk1_esk17_2(X2,X1),sk1_esk18_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_280,def_epred1_2]) ).
cnf(c_0_281_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk16_2(X2,X1),X2)
| apply(X1,sk1_esk18_2(X2,X1),sk1_esk19_2(X2,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_281,def_epred1_2]) ).
cnf(c_0_282_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk15_2(X2,X1),sk1_esk16_2(X2,X1))
| member(sk1_esk17_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_282,def_epred1_2]) ).
cnf(c_0_283_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk15_2(X2,X1),sk1_esk16_2(X2,X1))
| member(sk1_esk18_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_283,def_epred1_2]) ).
cnf(c_0_284_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk15_2(X2,X1),sk1_esk16_2(X2,X1))
| member(sk1_esk19_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_284,def_epred1_2]) ).
cnf(c_0_285_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk16_2(X2,X1),sk1_esk15_2(X2,X1))
| member(sk1_esk17_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_285,def_epred1_2]) ).
cnf(c_0_286_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk16_2(X2,X1),sk1_esk15_2(X2,X1))
| member(sk1_esk18_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_286,def_epred1_2]) ).
cnf(c_0_287_0,axiom,
( epred1_2(X1,X2)
| apply(X1,sk1_esk16_2(X2,X1),sk1_esk15_2(X2,X1))
| member(sk1_esk19_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_287,def_epred1_2]) ).
cnf(c_0_288_0,axiom,
( ~ least(X2,X1,X3)
| apply(X1,X2,X4)
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_288,def_lhs_atom32]) ).
cnf(c_0_289_0,axiom,
( ~ greatest(X2,X1,X3)
| apply(X1,X4,X2)
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_289,def_lhs_atom30]) ).
cnf(c_0_290_0,axiom,
( ~ lower_bound(X2,X1,X4)
| apply(X1,X2,X3)
| ~ member(X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_290,def_lhs_atom28]) ).
cnf(c_0_291_0,axiom,
( ~ upper_bound(X3,X1,X4)
| apply(X1,X2,X3)
| ~ member(X2,X4) ),
inference(unfold_definition,[status(thm)],[c_0_291,def_lhs_atom26]) ).
cnf(c_0_292_0,axiom,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_292,def_lhs_atom8]) ).
cnf(c_0_293_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk17_2(X2,X1),X2)
| sk1_esk16_2(X2,X1) != sk1_esk15_2(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_293,def_epred1_2]) ).
cnf(c_0_294_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk18_2(X2,X1),X2)
| sk1_esk16_2(X2,X1) != sk1_esk15_2(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_294,def_epred1_2]) ).
cnf(c_0_295_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk19_2(X2,X1),X2)
| sk1_esk16_2(X2,X1) != sk1_esk15_2(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_295,def_epred1_2]) ).
cnf(c_0_296_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk15_2(X2,X1),X2)
| member(sk1_esk17_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_296,def_epred1_2]) ).
cnf(c_0_297_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk15_2(X2,X1),X2)
| member(sk1_esk18_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_297,def_epred1_2]) ).
cnf(c_0_298_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk15_2(X2,X1),X2)
| member(sk1_esk19_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_298,def_epred1_2]) ).
cnf(c_0_299_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk16_2(X2,X1),X2)
| member(sk1_esk17_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_299,def_epred1_2]) ).
cnf(c_0_300_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk16_2(X2,X1),X2)
| member(sk1_esk18_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_300,def_epred1_2]) ).
cnf(c_0_301_0,axiom,
( epred1_2(X1,X2)
| member(sk1_esk16_2(X2,X1),X2)
| member(sk1_esk19_2(X2,X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_301,def_epred1_2]) ).
cnf(c_0_302_0,axiom,
( ~ order(X1,X2)
| apply(X1,X3,X3)
| ~ member(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_302,def_lhs_atom22]) ).
cnf(c_0_303_0,axiom,
( member(X1,difference(X3,X2))
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_303,def_lhs_atom13]) ).
cnf(c_0_304_0,axiom,
( ~ member(X1,union(X3,X2))
| member(X1,X2)
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_304,def_lhs_atom9]) ).
cnf(c_0_305_0,axiom,
( member(X1,product(X2))
| ~ member(X1,sk1_esk3_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_305,def_lhs_atom21]) ).
cnf(c_0_306_0,axiom,
( subset(X2,X1)
| ~ member(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_306,def_lhs_atom2]) ).
cnf(c_0_307_0,axiom,
( total_order(X1,X2)
| member(sk1_esk5_2(X1,X2),X2)
| ~ order(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_307,def_lhs_atom25]) ).
cnf(c_0_308_0,axiom,
( total_order(X1,X2)
| member(sk1_esk6_2(X1,X2),X2)
| ~ order(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_308,def_lhs_atom25]) ).
cnf(c_0_309_0,axiom,
( order(X1,X2)
| member(sk1_esk4_2(X1,X2),X2)
| ~ epred1_2(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_309,def_lhs_atom23]) ).
cnf(c_0_310_0,axiom,
( ~ member(X2,difference(X1,X3))
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_310,def_lhs_atom12]) ).
cnf(c_0_311_0,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_311,def_lhs_atom10]) ).
cnf(c_0_312_0,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_312,def_lhs_atom10]) ).
cnf(c_0_313_0,axiom,
( ~ min(X2,X1,X3)
| member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_313,def_lhs_atom36]) ).
cnf(c_0_314_0,axiom,
( ~ max(X2,X1,X3)
| member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_314,def_lhs_atom34]) ).
cnf(c_0_315_0,axiom,
( ~ least(X2,X1,X3)
| member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_315,def_lhs_atom32]) ).
cnf(c_0_316_0,axiom,
( ~ greatest(X2,X1,X3)
| member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_316,def_lhs_atom30]) ).
cnf(c_0_317_0,axiom,
( ~ member(X2,difference(X1,X3))
| member(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_317,def_lhs_atom12]) ).
cnf(c_0_318_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_318,def_lhs_atom7]) ).
cnf(c_0_319_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_319,def_lhs_atom7]) ).
cnf(c_0_320_0,axiom,
( member(X1,sum(X3))
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_320,def_lhs_atom19]) ).
cnf(c_0_321_0,axiom,
( equal_set(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_321,def_lhs_atom4]) ).
cnf(c_0_322_0,axiom,
( ~ member(X1,unordered_pair(X3,X2))
| X1 = X2
| X1 = X3 ),
inference(unfold_definition,[status(thm)],[c_0_322,def_lhs_atom16]) ).
cnf(c_0_323_0,axiom,
( member(X1,unordered_pair(X3,X2))
| X1 != X3 ),
inference(unfold_definition,[status(thm)],[c_0_323,def_lhs_atom17]) ).
cnf(c_0_324_0,axiom,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_324,def_lhs_atom17]) ).
cnf(c_0_325_0,axiom,
( member(X1,product(X2))
| member(sk1_esk3_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_325,def_lhs_atom21]) ).
cnf(c_0_326_0,axiom,
( ~ member(X1,sum(X2))
| member(sk1_esk2_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_326,def_lhs_atom18]) ).
cnf(c_0_327_0,axiom,
( ~ member(X1,sum(X2))
| member(X1,sk1_esk2_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_327,def_lhs_atom18]) ).
cnf(c_0_328_0,axiom,
( subset(X2,X1)
| member(sk1_esk1_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_328,def_lhs_atom2]) ).
cnf(c_0_329_0,axiom,
( ~ member(X1,product(X3))
| member(X1,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_329,def_lhs_atom20]) ).
cnf(c_0_330_0,axiom,
( ~ subset(X3,X2)
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_330,def_lhs_atom1]) ).
cnf(c_0_331_0,axiom,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_331,def_lhs_atom6]) ).
cnf(c_0_332_0,axiom,
( ~ total_order(X1,X2)
| order(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_332,def_lhs_atom24]) ).
cnf(c_0_333_0,axiom,
( ~ order(X1,X2)
| epred1_2(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_333,def_lhs_atom22]) ).
cnf(c_0_334_0,axiom,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_334,def_lhs_atom5]) ).
cnf(c_0_335_0,axiom,
( ~ equal_set(X2,X1)
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_335,def_lhs_atom3]) ).
cnf(c_0_336_0,axiom,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_336,def_lhs_atom3]) ).
cnf(c_0_337_0,axiom,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_337,def_lhs_atom15]) ).
cnf(c_0_338_0,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(unfold_definition,[status(thm)],[c_0_338,def_lhs_atom14]) ).
cnf(c_0_339_0,axiom,
~ member(X1,empty_set),
inference(unfold_definition,[status(thm)],[c_0_339,def_lhs_atom11]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X3,X4] :
( ( subset(X3,X2)
& subset(X4,X2)
& subset(X3,X4) )
=> ! [X5,X6] :
( ( greatest_lower_bound(X5,X3,X1,X2)
& greatest_lower_bound(X6,X4,X1,X2) )
=> apply(X1,X6,X5) ) ) ),
file('<stdin>',thIV12) ).
fof(c_0_1_002,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X3,X4] :
( ( subset(X3,X2)
& subset(X4,X2)
& subset(X3,X4) )
=> ! [X5,X6] :
( ( greatest_lower_bound(X5,X3,X1,X2)
& greatest_lower_bound(X6,X4,X1,X2) )
=> apply(X1,X6,X5) ) ) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_003,negated_conjecture,
( order(esk1_0,esk2_0)
& subset(esk3_0,esk2_0)
& subset(esk4_0,esk2_0)
& subset(esk3_0,esk4_0)
& greatest_lower_bound(esk5_0,esk3_0,esk1_0,esk2_0)
& greatest_lower_bound(esk6_0,esk4_0,esk1_0,esk2_0)
& ~ apply(esk1_0,esk6_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_004,negated_conjecture,
greatest_lower_bound(esk5_0,esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
greatest_lower_bound(esk6_0,esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_006,negated_conjecture,
~ apply(esk1_0,esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_007,negated_conjecture,
order(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7_008,negated_conjecture,
subset(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8_009,negated_conjecture,
subset(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9_010,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10_011,negated_conjecture,
greatest_lower_bound(esk5_0,esk3_0,esk1_0,esk2_0),
c_0_3,
[final] ).
cnf(c_0_11_012,negated_conjecture,
greatest_lower_bound(esk6_0,esk4_0,esk1_0,esk2_0),
c_0_4,
[final] ).
cnf(c_0_12_013,negated_conjecture,
~ apply(esk1_0,esk6_0,esk5_0),
c_0_5,
[final] ).
cnf(c_0_13_014,negated_conjecture,
order(esk1_0,esk2_0),
c_0_6,
[final] ).
cnf(c_0_14_015,negated_conjecture,
subset(esk3_0,esk2_0),
c_0_7,
[final] ).
cnf(c_0_15_016,negated_conjecture,
subset(esk4_0,esk2_0),
c_0_8,
[final] ).
cnf(c_0_16_017,negated_conjecture,
subset(esk3_0,esk4_0),
c_0_9,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_109,negated_conjecture,
greatest_lower_bound(sk3_esk6_0,sk3_esk4_0,sk3_esk1_0,sk3_esk2_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_11) ).
cnf(c_217,negated_conjecture,
greatest_lower_bound(sk3_esk6_0,sk3_esk4_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_109]) ).
cnf(c_243,negated_conjecture,
greatest_lower_bound(sk3_esk6_0,sk3_esk4_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_217]) ).
cnf(c_252,negated_conjecture,
greatest_lower_bound(sk3_esk6_0,sk3_esk4_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_243]) ).
cnf(c_259,negated_conjecture,
greatest_lower_bound(sk3_esk6_0,sk3_esk4_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_252]) ).
cnf(c_598,negated_conjecture,
greatest_lower_bound(sk3_esk6_0,sk3_esk4_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_259]) ).
cnf(c_93,plain,
( lower_bound(X0,X1,X2)
| ~ greatest_lower_bound(X0,X2,X1,X3) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_246_0) ).
cnf(c_562,plain,
( lower_bound(X0,X1,X2)
| ~ greatest_lower_bound(X0,X2,X1,X3) ),
inference(copy,[status(esa)],[c_93]) ).
cnf(c_636,plain,
lower_bound(sk3_esk6_0,sk3_esk1_0,sk3_esk4_0),
inference(resolution,[status(thm)],[c_598,c_562]) ).
cnf(c_637,plain,
lower_bound(sk3_esk6_0,sk3_esk1_0,sk3_esk4_0),
inference(rewriting,[status(thm)],[c_636]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| apply(X2,X3,X0)
| ~ lower_bound(X3,X2,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_290_0) ).
cnf(c_474,plain,
( ~ member(X0,X1)
| apply(X2,X3,X0)
| ~ lower_bound(X3,X2,X1) ),
inference(copy,[status(esa)],[c_49]) ).
cnf(c_656,plain,
( ~ member(X0,sk3_esk4_0)
| apply(sk3_esk1_0,sk3_esk6_0,X0) ),
inference(resolution,[status(thm)],[c_637,c_474]) ).
cnf(c_657,plain,
( ~ member(X0,sk3_esk4_0)
| apply(sk3_esk1_0,sk3_esk6_0,X0) ),
inference(rewriting,[status(thm)],[c_656]) ).
cnf(c_107,negated_conjecture,
~ apply(sk3_esk1_0,sk3_esk6_0,sk3_esk5_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_12) ).
cnf(c_213,negated_conjecture,
~ apply(sk3_esk1_0,sk3_esk6_0,sk3_esk5_0),
inference(copy,[status(esa)],[c_107]) ).
cnf(c_241,negated_conjecture,
~ apply(sk3_esk1_0,sk3_esk6_0,sk3_esk5_0),
inference(copy,[status(esa)],[c_213]) ).
cnf(c_254,negated_conjecture,
~ apply(sk3_esk1_0,sk3_esk6_0,sk3_esk5_0),
inference(copy,[status(esa)],[c_241]) ).
cnf(c_257,negated_conjecture,
~ apply(sk3_esk1_0,sk3_esk6_0,sk3_esk5_0),
inference(copy,[status(esa)],[c_254]) ).
cnf(c_594,negated_conjecture,
~ apply(sk3_esk1_0,sk3_esk6_0,sk3_esk5_0),
inference(copy,[status(esa)],[c_257]) ).
cnf(c_716,plain,
~ member(sk3_esk5_0,sk3_esk4_0),
inference(resolution,[status(thm)],[c_657,c_594]) ).
cnf(c_717,plain,
~ member(sk3_esk5_0,sk3_esk4_0),
inference(rewriting,[status(thm)],[c_716]) ).
cnf(c_113,negated_conjecture,
subset(sk3_esk3_0,sk3_esk4_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_16) ).
cnf(c_225,negated_conjecture,
subset(sk3_esk3_0,sk3_esk4_0),
inference(copy,[status(esa)],[c_113]) ).
cnf(c_247,negated_conjecture,
subset(sk3_esk3_0,sk3_esk4_0),
inference(copy,[status(esa)],[c_225]) ).
cnf(c_248,negated_conjecture,
subset(sk3_esk3_0,sk3_esk4_0),
inference(copy,[status(esa)],[c_247]) ).
cnf(c_256,negated_conjecture,
subset(sk3_esk3_0,sk3_esk4_0),
inference(copy,[status(esa)],[c_248]) ).
cnf(c_592,negated_conjecture,
subset(sk3_esk3_0,sk3_esk4_0),
inference(copy,[status(esa)],[c_256]) ).
cnf(c_9,plain,
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_330_0) ).
cnf(c_394,plain,
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(X1,X2) ),
inference(copy,[status(esa)],[c_9]) ).
cnf(c_610,plain,
( ~ member(X0,sk3_esk3_0)
| member(X0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_592,c_394]) ).
cnf(c_611,plain,
( ~ member(X0,sk3_esk3_0)
| member(X0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_610]) ).
cnf(c_720,plain,
~ member(sk3_esk5_0,sk3_esk3_0),
inference(resolution,[status(thm)],[c_717,c_611]) ).
cnf(c_721,plain,
~ member(sk3_esk5_0,sk3_esk3_0),
inference(rewriting,[status(thm)],[c_720]) ).
cnf(c_108,negated_conjecture,
greatest_lower_bound(sk3_esk5_0,sk3_esk3_0,sk3_esk1_0,sk3_esk2_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_10) ).
cnf(c_215,negated_conjecture,
greatest_lower_bound(sk3_esk5_0,sk3_esk3_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_108]) ).
cnf(c_242,negated_conjecture,
greatest_lower_bound(sk3_esk5_0,sk3_esk3_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_215]) ).
cnf(c_253,negated_conjecture,
greatest_lower_bound(sk3_esk5_0,sk3_esk3_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_242]) ).
cnf(c_258,negated_conjecture,
greatest_lower_bound(sk3_esk5_0,sk3_esk3_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_253]) ).
cnf(c_596,negated_conjecture,
greatest_lower_bound(sk3_esk5_0,sk3_esk3_0,sk3_esk1_0,sk3_esk2_0),
inference(copy,[status(esa)],[c_258]) ).
cnf(c_89,plain,
( member(X0,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p',c_0_250_0) ).
cnf(c_554,plain,
( member(X0,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(copy,[status(esa)],[c_89]) ).
cnf(c_626,plain,
member(sk3_esk5_0,sk3_esk3_0),
inference(resolution,[status(thm)],[c_596,c_554]) ).
cnf(c_627,plain,
member(sk3_esk5_0,sk3_esk3_0),
inference(rewriting,[status(thm)],[c_626]) ).
cnf(c_723,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_721,c_627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n014.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 : Sat Jul 9 23:24:50 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/sandbox2/tmp/iprover_proof_c886e4.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_fc9839.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_769186 | grep -v "SZS"
% 0.20/0.43
% 0.20/0.43 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.43
% 0.20/0.43 %
% 0.20/0.43 % ------ iProver source info
% 0.20/0.43
% 0.20/0.43 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.43 % git: non_committed_changes: true
% 0.20/0.43 % git: last_make_outside_of_git: true
% 0.20/0.43
% 0.20/0.43 %
% 0.20/0.43 % ------ Input Options
% 0.20/0.43
% 0.20/0.43 % --out_options all
% 0.20/0.43 % --tptp_safe_out true
% 0.20/0.43 % --problem_path ""
% 0.20/0.43 % --include_path ""
% 0.20/0.43 % --clausifier .//eprover
% 0.20/0.43 % --clausifier_options --tstp-format
% 0.20/0.43 % --stdin false
% 0.20/0.43 % --dbg_backtrace false
% 0.20/0.43 % --dbg_dump_prop_clauses false
% 0.20/0.43 % --dbg_dump_prop_clauses_file -
% 0.20/0.43 % --dbg_out_stat false
% 0.20/0.43
% 0.20/0.43 % ------ General Options
% 0.20/0.43
% 0.20/0.43 % --fof false
% 0.20/0.43 % --time_out_real 150.
% 0.20/0.43 % --time_out_prep_mult 0.2
% 0.20/0.43 % --time_out_virtual -1.
% 0.20/0.43 % --schedule none
% 0.20/0.43 % --ground_splitting input
% 0.20/0.43 % --splitting_nvd 16
% 0.20/0.43 % --non_eq_to_eq false
% 0.20/0.43 % --prep_gs_sim true
% 0.20/0.43 % --prep_unflatten false
% 0.20/0.43 % --prep_res_sim true
% 0.20/0.43 % --prep_upred true
% 0.20/0.43 % --res_sim_input true
% 0.20/0.43 % --clause_weak_htbl true
% 0.20/0.43 % --gc_record_bc_elim false
% 0.20/0.43 % --symbol_type_check false
% 0.20/0.43 % --clausify_out false
% 0.20/0.43 % --large_theory_mode false
% 0.20/0.43 % --prep_sem_filter none
% 0.20/0.43 % --prep_sem_filter_out false
% 0.20/0.43 % --preprocessed_out false
% 0.20/0.43 % --sub_typing false
% 0.20/0.43 % --brand_transform false
% 0.20/0.43 % --pure_diseq_elim true
% 0.20/0.43 % --min_unsat_core false
% 0.20/0.43 % --pred_elim true
% 0.20/0.43 % --add_important_lit false
% 0.20/0.43 % --soft_assumptions false
% 0.20/0.43 % --reset_solvers false
% 0.20/0.43 % --bc_imp_inh []
% 0.20/0.43 % --conj_cone_tolerance 1.5
% 0.20/0.43 % --prolific_symb_bound 500
% 0.20/0.43 % --lt_threshold 2000
% 0.20/0.43
% 0.20/0.43 % ------ SAT Options
% 0.20/0.43
% 0.20/0.43 % --sat_mode false
% 0.20/0.43 % --sat_fm_restart_options ""
% 0.20/0.43 % --sat_gr_def false
% 0.20/0.43 % --sat_epr_types true
% 0.20/0.43 % --sat_non_cyclic_types false
% 0.20/0.43 % --sat_finite_models false
% 0.20/0.43 % --sat_fm_lemmas false
% 0.20/0.43 % --sat_fm_prep false
% 0.20/0.43 % --sat_fm_uc_incr true
% 0.20/0.43 % --sat_out_model small
% 0.20/0.43 % --sat_out_clauses false
% 0.20/0.43
% 0.20/0.43 % ------ QBF Options
% 0.20/0.43
% 0.20/0.43 % --qbf_mode false
% 0.20/0.43 % --qbf_elim_univ true
% 0.20/0.43 % --qbf_sk_in true
% 0.20/0.43 % --qbf_pred_elim true
% 0.20/0.43 % --qbf_split 32
% 0.20/0.43
% 0.20/0.43 % ------ BMC1 Options
% 0.20/0.43
% 0.20/0.43 % --bmc1_incremental false
% 0.20/0.43 % --bmc1_axioms reachable_all
% 0.20/0.43 % --bmc1_min_bound 0
% 0.20/0.43 % --bmc1_max_bound -1
% 0.20/0.43 % --bmc1_max_bound_default -1
% 0.20/0.43 % --bmc1_symbol_reachability true
% 0.20/0.43 % --bmc1_property_lemmas false
% 0.20/0.43 % --bmc1_k_induction false
% 0.20/0.43 % --bmc1_non_equiv_states false
% 0.20/0.43 % --bmc1_deadlock false
% 0.20/0.43 % --bmc1_ucm false
% 0.20/0.43 % --bmc1_add_unsat_core none
% 0.20/0.43 % --bmc1_unsat_core_children false
% 0.20/0.43 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.43 % --bmc1_out_stat full
% 0.20/0.43 % --bmc1_ground_init false
% 0.20/0.43 % --bmc1_pre_inst_next_state false
% 0.20/0.43 % --bmc1_pre_inst_state false
% 0.20/0.43 % --bmc1_pre_inst_reach_state false
% 0.20/0.43 % --bmc1_out_unsat_core false
% 0.20/0.43 % --bmc1_aig_witness_out false
% 0.20/0.43 % --bmc1_verbose false
% 0.20/0.43 % --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/sandbox2/tmp/iprover_proof_c886e4.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/sandbox2/tmp/iprover_proof_c886e4.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: 114
% 0.20/0.45 % num_of_input_neg_conjectures: 7
% 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: 14
% 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: 0.005
% 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: 0.036
% 0.20/0.45 % num_of_symbols: 74
% 0.20/0.45 % num_of_terms: 612
% 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: 21
% 0.20/0.45 % prop_num_of_clauses: 213
% 0.20/0.45 % prop_preprocess_simplified: 285
% 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: 114
% 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: 114
% 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: 221
% 0.20/0.45 % res_num_in_passive: 8
% 0.20/0.45 % res_num_in_active: 129
% 0.20/0.45 % res_num_of_loops: 23
% 0.20/0.45 % res_forward_subset_subsumed: 1
% 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: 1
% 0.20/0.45 % res_backward_subsumption_resolution: 0
% 0.20/0.45 % res_clause_to_clause_subsumption: 22
% 0.20/0.45 % res_orphan_elimination: 0
% 0.20/0.45 % res_tautology_del: 0
% 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
%------------------------------------------------------------------------------