TSTP Solution File: SET814+4 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SET814+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n017.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 02:16:28 EDT 2022
% Result : Theorem 4.53s 4.73s
% Output : CNFRefutation 4.53s
% 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(thI3,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
input ).
fof(thI3_0,plain,
! [A,B,C] :
( subset(A,C)
| ~ ( subset(A,B)
& subset(B,C) ) ),
inference(orientation,[status(thm)],[thI3]) ).
fof(successor,axiom,
! [A,X] :
( member(X,suc(A))
<=> member(X,union(A,singleton(A))) ),
input ).
fof(successor_0,plain,
! [A,X] :
( member(X,suc(A))
| ~ member(X,union(A,singleton(A))) ),
inference(orientation,[status(thm)],[successor]) ).
fof(successor_1,plain,
! [A,X] :
( ~ member(X,suc(A))
| member(X,union(A,singleton(A))) ),
inference(orientation,[status(thm)],[successor]) ).
fof(initial_segment,axiom,
! [X,R,A,Y] :
( member(Y,initial_segment(X,R,A))
<=> ( member(Y,A)
& apply(R,Y,X) ) ),
input ).
fof(initial_segment_0,plain,
! [A,R,X,Y] :
( member(Y,initial_segment(X,R,A))
| ~ ( member(Y,A)
& apply(R,Y,X) ) ),
inference(orientation,[status(thm)],[initial_segment]) ).
fof(initial_segment_1,plain,
! [A,R,X,Y] :
( ~ member(Y,initial_segment(X,R,A))
| ( member(Y,A)
& apply(R,Y,X) ) ),
inference(orientation,[status(thm)],[initial_segment]) ).
fof(set_member,axiom,
! [X] :
( set(X)
=> ! [Y] :
( member(Y,X)
=> set(Y) ) ),
input ).
fof(set_member_0,plain,
! [X] :
( ~ set(X)
| ! [Y] :
( member(Y,X)
=> set(Y) ) ),
inference(orientation,[status(thm)],[set_member]) ).
fof(strict_order,axiom,
! [R,E] :
( strict_order(R,E)
<=> ( ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ~ ( apply(R,X,Y)
& apply(R,Y,X) ) )
& ! [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(strict_order_0,plain,
! [E,R] :
( strict_order(R,E)
| ~ ( ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ~ ( apply(R,X,Y)
& apply(R,Y,X) ) )
& ! [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)],[strict_order]) ).
fof(strict_order_1,plain,
! [E,R] :
( ~ strict_order(R,E)
| ( ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ~ ( apply(R,X,Y)
& apply(R,Y,X) ) )
& ! [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)],[strict_order]) ).
fof(rel_member,axiom,
! [X,Y] :
( apply(member_predicate,X,Y)
<=> member(X,Y) ),
input ).
fof(rel_member_0,plain,
! [X,Y] :
( apply(member_predicate,X,Y)
| ~ member(X,Y) ),
inference(orientation,[status(thm)],[rel_member]) ).
fof(rel_member_1,plain,
! [X,Y] :
( ~ apply(member_predicate,X,Y)
| member(X,Y) ),
inference(orientation,[status(thm)],[rel_member]) ).
fof(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> ( M = X
| apply(R,M,X) ) ) ) ),
input ).
fof(least_0,plain,
! [E,M,R] :
( least(M,R,E)
| ~ ( member(M,E)
& ! [X] :
( member(X,E)
=> ( M = X
| 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)
=> ( M = X
| apply(R,M,X) ) ) ) ),
inference(orientation,[status(thm)],[least]) ).
fof(strict_well_order,axiom,
! [R,E] :
( strict_well_order(R,E)
<=> ( strict_order(R,E)
& ! [A] :
( ( subset(A,E)
& ? [X] : member(X,A) )
=> ? [Y] : least(Y,R,A) ) ) ),
input ).
fof(strict_well_order_0,plain,
! [E,R] :
( strict_well_order(R,E)
| ~ ( strict_order(R,E)
& ! [A] :
( ( subset(A,E)
& ? [X] : member(X,A) )
=> ? [Y] : least(Y,R,A) ) ) ),
inference(orientation,[status(thm)],[strict_well_order]) ).
fof(strict_well_order_1,plain,
! [E,R] :
( ~ strict_well_order(R,E)
| ( strict_order(R,E)
& ! [A] :
( ( subset(A,E)
& ? [X] : member(X,A) )
=> ? [Y] : least(Y,R,A) ) ) ),
inference(orientation,[status(thm)],[strict_well_order]) ).
fof(ordinal_number,axiom,
! [A] :
( member(A,on)
<=> ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
input ).
fof(ordinal_number_0,plain,
! [A] :
( member(A,on)
| ~ ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
inference(orientation,[status(thm)],[ordinal_number]) ).
fof(ordinal_number_1,plain,
! [A] :
( ~ member(A,on)
| ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
inference(orientation,[status(thm)],[ordinal_number]) ).
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,
! [A] :
( lhs_atom22(A)
<=> ~ member(A,on) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [A] :
( lhs_atom22(A)
| ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
inference(fold_definition,[status(thm)],[ordinal_number_1,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [A] :
( lhs_atom23(A)
<=> member(A,on) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [A] :
( lhs_atom23(A)
| ~ ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
inference(fold_definition,[status(thm)],[ordinal_number_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [R,E] :
( lhs_atom24(R,E)
<=> ~ strict_well_order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [E,R] :
( lhs_atom24(R,E)
| ( strict_order(R,E)
& ! [A] :
( ( subset(A,E)
& ? [X] : member(X,A) )
=> ? [Y] : least(Y,R,A) ) ) ),
inference(fold_definition,[status(thm)],[strict_well_order_1,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [R,E] :
( lhs_atom25(R,E)
<=> strict_well_order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [E,R] :
( lhs_atom25(R,E)
| ~ ( strict_order(R,E)
& ! [A] :
( ( subset(A,E)
& ? [X] : member(X,A) )
=> ? [Y] : least(Y,R,A) ) ) ),
inference(fold_definition,[status(thm)],[strict_well_order_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [R,M,E] :
( lhs_atom26(R,M,E)
<=> ~ least(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [E,M,R] :
( lhs_atom26(R,M,E)
| ( member(M,E)
& ! [X] :
( member(X,E)
=> ( M = X
| apply(R,M,X) ) ) ) ),
inference(fold_definition,[status(thm)],[least_1,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [R,M,E] :
( lhs_atom27(R,M,E)
<=> least(M,R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [E,M,R] :
( lhs_atom27(R,M,E)
| ~ ( member(M,E)
& ! [X] :
( member(X,E)
=> ( M = X
| apply(R,M,X) ) ) ) ),
inference(fold_definition,[status(thm)],[least_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [Y,X] :
( lhs_atom28(Y,X)
<=> ~ apply(member_predicate,X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [X,Y] :
( lhs_atom28(Y,X)
| member(X,Y) ),
inference(fold_definition,[status(thm)],[rel_member_1,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [Y,X] :
( lhs_atom29(Y,X)
<=> apply(member_predicate,X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [X,Y] :
( lhs_atom29(Y,X)
| ~ member(X,Y) ),
inference(fold_definition,[status(thm)],[rel_member_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [R,E] :
( lhs_atom30(R,E)
<=> ~ strict_order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [E,R] :
( lhs_atom30(R,E)
| ( ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ~ ( apply(R,X,Y)
& apply(R,Y,X) ) )
& ! [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)],[strict_order_1,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [R,E] :
( lhs_atom31(R,E)
<=> strict_order(R,E) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [E,R] :
( lhs_atom31(R,E)
| ~ ( ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ~ ( apply(R,X,Y)
& apply(R,Y,X) ) )
& ! [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)],[strict_order_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [X] :
( lhs_atom32(X)
<=> ~ set(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [X] :
( lhs_atom32(X)
| ! [Y] :
( member(Y,X)
=> set(Y) ) ),
inference(fold_definition,[status(thm)],[set_member_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [Y,X,R,A] :
( lhs_atom33(Y,X,R,A)
<=> ~ member(Y,initial_segment(X,R,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [A,R,X,Y] :
( lhs_atom33(Y,X,R,A)
| ( member(Y,A)
& apply(R,Y,X) ) ),
inference(fold_definition,[status(thm)],[initial_segment_1,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [Y,X,R,A] :
( lhs_atom34(Y,X,R,A)
<=> member(Y,initial_segment(X,R,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [A,R,X,Y] :
( lhs_atom34(Y,X,R,A)
| ~ ( member(Y,A)
& apply(R,Y,X) ) ),
inference(fold_definition,[status(thm)],[initial_segment_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [X,A] :
( lhs_atom35(X,A)
<=> ~ member(X,suc(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [A,X] :
( lhs_atom35(X,A)
| member(X,union(A,singleton(A))) ),
inference(fold_definition,[status(thm)],[successor_1,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [X,A] :
( lhs_atom36(X,A)
<=> member(X,suc(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [A,X] :
( lhs_atom36(X,A)
| ~ member(X,union(A,singleton(A))) ),
inference(fold_definition,[status(thm)],[successor_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [C,A] :
( lhs_atom37(C,A)
<=> subset(A,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [A,B,C] :
( lhs_atom37(C,A)
| ~ ( subset(A,B)
& subset(B,C) ) ),
inference(fold_definition,[status(thm)],[thI3_0,def_lhs_atom37]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X5,X3,X6,X2] :
( lhs_atom34(X5,X3,X6,X2)
| ~ ( member(X5,X2)
& apply(X6,X5,X3) ) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_1,axiom,
! [X6,X7,X4] :
( lhs_atom27(X6,X7,X4)
| ~ ( member(X7,X4)
& ! [X3] :
( member(X3,X4)
=> ( X7 = X3
| apply(X6,X7,X3) ) ) ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_2,axiom,
! [X6,X4] :
( lhs_atom30(X6,X4)
| ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ~ ( apply(X6,X3,X5)
& apply(X6,X5,X3) ) )
& ! [X3,X5,X8] :
( ( member(X3,X4)
& member(X5,X4)
& member(X8,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X8) )
=> apply(X6,X3,X8) ) ) ) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_3,axiom,
! [X5,X3,X6,X2] :
( lhs_atom33(X5,X3,X6,X2)
| ( member(X5,X2)
& apply(X6,X5,X3) ) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_4,axiom,
! [X6,X4] :
( lhs_atom31(X6,X4)
| ~ ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ~ ( apply(X6,X3,X5)
& apply(X6,X5,X3) ) )
& ! [X3,X5,X8] :
( ( member(X3,X4)
& member(X5,X4)
& member(X8,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X8) )
=> apply(X6,X3,X8) ) ) ) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_5,axiom,
! [X6,X4] :
( lhs_atom24(X6,X4)
| ( strict_order(X6,X4)
& ! [X2] :
( ( subset(X2,X4)
& ? [X3] : member(X3,X2) )
=> ? [X5] : least(X5,X6,X2) ) ) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_6,axiom,
! [X6,X4] :
( lhs_atom25(X6,X4)
| ~ ( strict_order(X6,X4)
& ! [X2] :
( ( subset(X2,X4)
& ? [X3] : member(X3,X2) )
=> ? [X5] : least(X5,X6,X2) ) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_7,axiom,
! [X6,X7,X4] :
( lhs_atom26(X6,X7,X4)
| ( member(X7,X4)
& ! [X3] :
( member(X3,X4)
=> ( X7 = X3
| apply(X6,X7,X3) ) ) ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_8,axiom,
! [X3,X1,X2] :
( lhs_atom8(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_9,axiom,
! [X3,X2] :
( lhs_atom36(X3,X2)
| ~ member(X3,union(X2,singleton(X2))) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_10,axiom,
! [X4,X1,X2] :
( lhs_atom13(X4,X1,X2)
| ~ ( member(X1,X4)
& ~ member(X1,X2) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_11,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| member(X3,X2)
| member(X3,X1) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_12,axiom,
! [X3,X2] :
( lhs_atom21(X3,X2)
| ~ ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_13,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_14,axiom,
! [X4,X1,X2] :
( lhs_atom12(X4,X1,X2)
| ( member(X1,X4)
& ~ member(X1,X2) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_15,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ( member(X3,X2)
| member(X3,X1) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_16,axiom,
! [X3,X1,X2] :
( lhs_atom7(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_17,axiom,
! [X3,X2] :
( lhs_atom35(X3,X2)
| member(X3,union(X2,singleton(X2))) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_18,axiom,
! [X2] :
( lhs_atom23(X2)
| ~ ( set(X2)
& strict_well_order(member_predicate,X2)
& ! [X3] :
( member(X3,X2)
=> subset(X3,X2) ) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_19,axiom,
! [X9,X1,X2] :
( lhs_atom37(X9,X2)
| ~ ( subset(X2,X1)
& subset(X1,X9) ) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_20,axiom,
! [X3,X2] :
( lhs_atom19(X3,X2)
| ~ ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_21,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_22,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| X3 = X2
| X3 = X1 ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_23,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ( X3 = X2
| X3 = X1 ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_24,axiom,
! [X3,X2] :
( lhs_atom18(X3,X2)
| ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_25,axiom,
! [X3,X2] :
( lhs_atom20(X3,X2)
| ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_26,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_27,axiom,
! [X2] :
( lhs_atom22(X2)
| ( set(X2)
& strict_well_order(member_predicate,X2)
& ! [X3] :
( member(X3,X2)
=> subset(X3,X2) ) ) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_28,axiom,
! [X5,X3] :
( lhs_atom29(X5,X3)
| ~ member(X3,X5) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_29,axiom,
! [X3,X2] :
( lhs_atom6(X3,X2)
| ~ subset(X3,X2) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_30,axiom,
! [X3] :
( lhs_atom32(X3)
| ! [X5] :
( member(X5,X3)
=> set(X5) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_31,axiom,
! [X5,X3] :
( lhs_atom28(X5,X3)
| member(X3,X5) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_32,axiom,
! [X3,X2] :
( lhs_atom5(X3,X2)
| subset(X3,X2) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_33,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_34,axiom,
! [X3,X2] :
( lhs_atom15(X3,X2)
| X3 != X2 ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_35,axiom,
! [X3,X2] :
( lhs_atom14(X3,X2)
| X3 = X2 ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_36,axiom,
! [X3] :
( lhs_atom11(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_37,axiom,
! [X5,X3,X6,X2] :
( lhs_atom34(X5,X3,X6,X2)
| ~ ( member(X5,X2)
& apply(X6,X5,X3) ) ),
c_0_0 ).
fof(c_0_38,axiom,
! [X6,X7,X4] :
( lhs_atom27(X6,X7,X4)
| ~ ( member(X7,X4)
& ! [X3] :
( member(X3,X4)
=> ( X7 = X3
| apply(X6,X7,X3) ) ) ) ),
c_0_1 ).
fof(c_0_39,axiom,
! [X6,X4] :
( lhs_atom30(X6,X4)
| ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ~ ( apply(X6,X3,X5)
& apply(X6,X5,X3) ) )
& ! [X3,X5,X8] :
( ( member(X3,X4)
& member(X5,X4)
& member(X8,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X8) )
=> apply(X6,X3,X8) ) ) ) ),
c_0_2 ).
fof(c_0_40,axiom,
! [X5,X3,X6,X2] :
( lhs_atom33(X5,X3,X6,X2)
| ( member(X5,X2)
& apply(X6,X5,X3) ) ),
c_0_3 ).
fof(c_0_41,axiom,
! [X6,X4] :
( lhs_atom31(X6,X4)
| ~ ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ~ ( apply(X6,X3,X5)
& apply(X6,X5,X3) ) )
& ! [X3,X5,X8] :
( ( member(X3,X4)
& member(X5,X4)
& member(X8,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X8) )
=> apply(X6,X3,X8) ) ) ) ),
c_0_4 ).
fof(c_0_42,axiom,
! [X6,X4] :
( lhs_atom24(X6,X4)
| ( strict_order(X6,X4)
& ! [X2] :
( ( subset(X2,X4)
& ? [X3] : member(X3,X2) )
=> ? [X5] : least(X5,X6,X2) ) ) ),
c_0_5 ).
fof(c_0_43,axiom,
! [X6,X4] :
( lhs_atom25(X6,X4)
| ~ ( strict_order(X6,X4)
& ! [X2] :
( ( subset(X2,X4)
& ? [X3] : member(X3,X2) )
=> ? [X5] : least(X5,X6,X2) ) ) ),
c_0_6 ).
fof(c_0_44,axiom,
! [X6,X7,X4] :
( lhs_atom26(X6,X7,X4)
| ( member(X7,X4)
& ! [X3] :
( member(X3,X4)
=> ( X7 = X3
| apply(X6,X7,X3) ) ) ) ),
c_0_7 ).
fof(c_0_45,axiom,
! [X3,X1,X2] :
( lhs_atom8(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
c_0_8 ).
fof(c_0_46,plain,
! [X3,X2] :
( lhs_atom36(X3,X2)
| ~ member(X3,union(X2,singleton(X2))) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_47,plain,
! [X4,X1,X2] :
( lhs_atom13(X4,X1,X2)
| ~ ( member(X1,X4)
& ~ member(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_48,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| member(X3,X2)
| member(X3,X1) ),
c_0_11 ).
fof(c_0_49,axiom,
! [X3,X2] :
( lhs_atom21(X3,X2)
| ~ ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
c_0_12 ).
fof(c_0_50,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_13 ).
fof(c_0_51,plain,
! [X4,X1,X2] :
( lhs_atom12(X4,X1,X2)
| ( member(X1,X4)
& ~ member(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_52,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ( member(X3,X2)
| member(X3,X1) ) ),
c_0_15 ).
fof(c_0_53,axiom,
! [X3,X1,X2] :
( lhs_atom7(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
c_0_16 ).
fof(c_0_54,axiom,
! [X3,X2] :
( lhs_atom35(X3,X2)
| member(X3,union(X2,singleton(X2))) ),
c_0_17 ).
fof(c_0_55,axiom,
! [X2] :
( lhs_atom23(X2)
| ~ ( set(X2)
& strict_well_order(member_predicate,X2)
& ! [X3] :
( member(X3,X2)
=> subset(X3,X2) ) ) ),
c_0_18 ).
fof(c_0_56,axiom,
! [X9,X1,X2] :
( lhs_atom37(X9,X2)
| ~ ( subset(X2,X1)
& subset(X1,X9) ) ),
c_0_19 ).
fof(c_0_57,axiom,
! [X3,X2] :
( lhs_atom19(X3,X2)
| ~ ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
c_0_20 ).
fof(c_0_58,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_21 ).
fof(c_0_59,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| X3 = X2
| X3 = X1 ),
c_0_22 ).
fof(c_0_60,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ( X3 = X2
| X3 = X1 ) ),
c_0_23 ).
fof(c_0_61,axiom,
! [X3,X2] :
( lhs_atom18(X3,X2)
| ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
c_0_24 ).
fof(c_0_62,axiom,
! [X3,X2] :
( lhs_atom20(X3,X2)
| ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
c_0_25 ).
fof(c_0_63,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_26 ).
fof(c_0_64,axiom,
! [X2] :
( lhs_atom22(X2)
| ( set(X2)
& strict_well_order(member_predicate,X2)
& ! [X3] :
( member(X3,X2)
=> subset(X3,X2) ) ) ),
c_0_27 ).
fof(c_0_65,plain,
! [X5,X3] :
( lhs_atom29(X5,X3)
| ~ member(X3,X5) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_66,plain,
! [X3,X2] :
( lhs_atom6(X3,X2)
| ~ subset(X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_67,axiom,
! [X3] :
( lhs_atom32(X3)
| ! [X5] :
( member(X5,X3)
=> set(X5) ) ),
c_0_30 ).
fof(c_0_68,axiom,
! [X5,X3] :
( lhs_atom28(X5,X3)
| member(X3,X5) ),
c_0_31 ).
fof(c_0_69,axiom,
! [X3,X2] :
( lhs_atom5(X3,X2)
| subset(X3,X2) ),
c_0_32 ).
fof(c_0_70,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_33 ).
fof(c_0_71,plain,
! [X3,X2] :
( lhs_atom15(X3,X2)
| X3 != X2 ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_72,axiom,
! [X3,X2] :
( lhs_atom14(X3,X2)
| X3 = X2 ),
c_0_35 ).
fof(c_0_73,plain,
! [X3] : lhs_atom11(X3),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_74,plain,
! [X7,X8,X9,X10] :
( lhs_atom34(X7,X8,X9,X10)
| ~ member(X7,X10)
| ~ apply(X9,X7,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])]) ).
fof(c_0_75,plain,
! [X8,X9,X10] :
( ( member(esk8_3(X8,X9,X10),X10)
| ~ member(X9,X10)
| lhs_atom27(X8,X9,X10) )
& ( X9 != esk8_3(X8,X9,X10)
| ~ member(X9,X10)
| lhs_atom27(X8,X9,X10) )
& ( ~ apply(X8,X9,esk8_3(X8,X9,X10))
| ~ member(X9,X10)
| lhs_atom27(X8,X9,X10) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
fof(c_0_76,plain,
! [X9,X10,X11,X12,X13,X14,X15] :
( ( ~ member(X11,X10)
| ~ member(X12,X10)
| ~ apply(X9,X11,X12)
| ~ apply(X9,X12,X11)
| lhs_atom30(X9,X10) )
& ( ~ member(X13,X10)
| ~ member(X14,X10)
| ~ member(X15,X10)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15)
| lhs_atom30(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
fof(c_0_77,plain,
! [X7,X8,X9,X10] :
( ( member(X7,X10)
| lhs_atom33(X7,X8,X9,X10) )
& ( apply(X9,X7,X8)
| lhs_atom33(X7,X8,X9,X10) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
fof(c_0_78,plain,
! [X9,X10] :
( ( member(esk11_2(X9,X10),X10)
| member(esk9_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( member(esk12_2(X9,X10),X10)
| member(esk9_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( member(esk13_2(X9,X10),X10)
| member(esk9_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( apply(X9,esk11_2(X9,X10),esk12_2(X9,X10))
| member(esk9_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( apply(X9,esk12_2(X9,X10),esk13_2(X9,X10))
| member(esk9_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( ~ apply(X9,esk11_2(X9,X10),esk13_2(X9,X10))
| member(esk9_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( member(esk11_2(X9,X10),X10)
| member(esk10_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( member(esk12_2(X9,X10),X10)
| member(esk10_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( member(esk13_2(X9,X10),X10)
| member(esk10_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( apply(X9,esk11_2(X9,X10),esk12_2(X9,X10))
| member(esk10_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( apply(X9,esk12_2(X9,X10),esk13_2(X9,X10))
| member(esk10_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( ~ apply(X9,esk11_2(X9,X10),esk13_2(X9,X10))
| member(esk10_2(X9,X10),X10)
| lhs_atom31(X9,X10) )
& ( member(esk11_2(X9,X10),X10)
| apply(X9,esk9_2(X9,X10),esk10_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( member(esk12_2(X9,X10),X10)
| apply(X9,esk9_2(X9,X10),esk10_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( member(esk13_2(X9,X10),X10)
| apply(X9,esk9_2(X9,X10),esk10_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( apply(X9,esk11_2(X9,X10),esk12_2(X9,X10))
| apply(X9,esk9_2(X9,X10),esk10_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( apply(X9,esk12_2(X9,X10),esk13_2(X9,X10))
| apply(X9,esk9_2(X9,X10),esk10_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( ~ apply(X9,esk11_2(X9,X10),esk13_2(X9,X10))
| apply(X9,esk9_2(X9,X10),esk10_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( member(esk11_2(X9,X10),X10)
| apply(X9,esk10_2(X9,X10),esk9_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( member(esk12_2(X9,X10),X10)
| apply(X9,esk10_2(X9,X10),esk9_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( member(esk13_2(X9,X10),X10)
| apply(X9,esk10_2(X9,X10),esk9_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( apply(X9,esk11_2(X9,X10),esk12_2(X9,X10))
| apply(X9,esk10_2(X9,X10),esk9_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( apply(X9,esk12_2(X9,X10),esk13_2(X9,X10))
| apply(X9,esk10_2(X9,X10),esk9_2(X9,X10))
| lhs_atom31(X9,X10) )
& ( ~ apply(X9,esk11_2(X9,X10),esk13_2(X9,X10))
| apply(X9,esk10_2(X9,X10),esk9_2(X9,X10))
| lhs_atom31(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_79,plain,
! [X7,X8,X9,X10] :
( ( strict_order(X7,X8)
| lhs_atom24(X7,X8) )
& ( ~ subset(X9,X8)
| ~ member(X10,X9)
| least(esk5_3(X7,X8,X9),X7,X9)
| lhs_atom24(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])]) ).
fof(c_0_80,plain,
! [X7,X8,X11] :
( ( subset(esk6_2(X7,X8),X8)
| ~ strict_order(X7,X8)
| lhs_atom25(X7,X8) )
& ( member(esk7_2(X7,X8),esk6_2(X7,X8))
| ~ strict_order(X7,X8)
| lhs_atom25(X7,X8) )
& ( ~ least(X11,X7,esk6_2(X7,X8))
| ~ strict_order(X7,X8)
| lhs_atom25(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])]) ).
fof(c_0_81,plain,
! [X8,X9,X10,X11] :
( ( member(X9,X10)
| lhs_atom26(X8,X9,X10) )
& ( ~ member(X11,X10)
| X9 = X11
| apply(X8,X9,X11)
| lhs_atom26(X8,X9,X10) ) ),
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_82,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_45])]) ).
fof(c_0_83,plain,
! [X4,X5] :
( lhs_atom36(X4,X5)
| ~ member(X4,union(X5,singleton(X5))) ),
inference(variable_rename,[status(thm)],[c_0_46]) ).
fof(c_0_84,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_47])]) ).
fof(c_0_85,plain,
! [X4,X5,X6] :
( lhs_atom9(X4,X5,X6)
| member(X4,X6)
| member(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_48]) ).
fof(c_0_86,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_49])])])]) ).
fof(c_0_87,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_50])])])]) ).
fof(c_0_88,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_51])]) ).
fof(c_0_89,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_52])])]) ).
fof(c_0_90,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_53])]) ).
fof(c_0_91,plain,
! [X4,X5] :
( lhs_atom35(X4,X5)
| member(X4,union(X5,singleton(X5))) ),
inference(variable_rename,[status(thm)],[c_0_54]) ).
fof(c_0_92,plain,
! [X4] :
( ( member(esk4_1(X4),X4)
| ~ strict_well_order(member_predicate,X4)
| ~ set(X4)
| lhs_atom23(X4) )
& ( ~ subset(esk4_1(X4),X4)
| ~ strict_well_order(member_predicate,X4)
| ~ set(X4)
| lhs_atom23(X4) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_93,plain,
! [X10,X11,X12] :
( lhs_atom37(X10,X12)
| ~ subset(X12,X11)
| ~ subset(X11,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])]) ).
fof(c_0_94,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_57])])]) ).
fof(c_0_95,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_58])]) ).
fof(c_0_96,plain,
! [X4,X5,X6] :
( lhs_atom16(X4,X5,X6)
| X4 = X6
| X4 = X5 ),
inference(variable_rename,[status(thm)],[c_0_59]) ).
fof(c_0_97,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_60])])]) ).
fof(c_0_98,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_61])])]) ).
fof(c_0_99,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_62])])]) ).
fof(c_0_100,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_63])])]) ).
fof(c_0_101,plain,
! [X4,X5] :
( ( set(X4)
| lhs_atom22(X4) )
& ( strict_well_order(member_predicate,X4)
| lhs_atom22(X4) )
& ( ~ member(X5,X4)
| subset(X5,X4)
| lhs_atom22(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
fof(c_0_102,plain,
! [X6,X7] :
( lhs_atom29(X6,X7)
| ~ member(X7,X6) ),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_103,plain,
! [X4,X5] :
( lhs_atom6(X4,X5)
| ~ subset(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_104,plain,
! [X6,X7] :
( lhs_atom32(X6)
| ~ member(X7,X6)
| set(X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
fof(c_0_105,plain,
! [X6,X7] :
( lhs_atom28(X6,X7)
| member(X7,X6) ),
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_106,plain,
! [X4,X5] :
( lhs_atom5(X4,X5)
| subset(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_107,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_70])]) ).
fof(c_0_108,plain,
! [X4,X5] :
( lhs_atom15(X4,X5)
| X4 != X5 ),
inference(variable_rename,[status(thm)],[c_0_71]) ).
fof(c_0_109,plain,
! [X4,X5] :
( lhs_atom14(X4,X5)
| X4 = X5 ),
inference(variable_rename,[status(thm)],[c_0_72]) ).
fof(c_0_110,plain,
! [X4] : lhs_atom11(X4),
inference(variable_rename,[status(thm)],[c_0_73]) ).
cnf(c_0_111,plain,
( lhs_atom34(X2,X3,X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_112,plain,
( lhs_atom27(X1,X2,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,esk8_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_113,plain,
( lhs_atom30(X1,X2)
| apply(X1,X3,X4)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_114,plain,
( lhs_atom33(X1,X2,X3,X4)
| apply(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_115,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_116,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_117,plain,
( lhs_atom33(X1,X2,X3,X4)
| member(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_118,plain,
( lhs_atom30(X1,X2)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_119,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_120,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_121,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_122,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_123,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_124,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_125,plain,
( lhs_atom24(X1,X2)
| least(esk5_3(X1,X2,X3),X1,X3)
| ~ member(X4,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_126,plain,
( lhs_atom27(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_127,plain,
( lhs_atom27(X1,X2,X3)
| ~ member(X2,X3)
| X2 != esk8_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_128,plain,
( lhs_atom25(X1,X2)
| ~ strict_order(X1,X2)
| ~ least(X3,X1,esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_129,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_130,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_131,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_132,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_133,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| member(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_134,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| member(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_135,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| member(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_136,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_137,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_138,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_139,plain,
( lhs_atom26(X1,X2,X3)
| apply(X1,X2,X4)
| X2 = X4
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_140,plain,
( lhs_atom25(X1,X2)
| member(esk7_2(X1,X2),esk6_2(X1,X2))
| ~ strict_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_141,plain,
( lhs_atom8(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_142,plain,
( lhs_atom36(X1,X2)
| ~ member(X1,union(X2,singleton(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_143,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_144,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| member(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_145,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| member(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_146,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_147,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| member(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_148,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| member(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_149,plain,
( member(X1,X2)
| lhs_atom13(X3,X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_150,plain,
( member(X1,X2)
| member(X1,X3)
| lhs_atom9(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_151,plain,
( lhs_atom21(X1,X2)
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_152,plain,
( lhs_atom2(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_153,plain,
( lhs_atom25(X1,X2)
| subset(esk6_2(X1,X2),X2)
| ~ strict_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_154,plain,
( lhs_atom12(X1,X2,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_155,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_156,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_157,plain,
( lhs_atom26(X1,X2,X3)
| member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_158,plain,
( lhs_atom12(X1,X2,X3)
| member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_159,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_160,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_161,plain,
( member(X1,union(X2,singleton(X2)))
| lhs_atom35(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_162,plain,
( lhs_atom23(X1)
| ~ set(X1)
| ~ strict_well_order(member_predicate,X1)
| ~ subset(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_163,plain,
( lhs_atom37(X2,X3)
| ~ subset(X1,X2)
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_164,plain,
( lhs_atom19(X1,X3)
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_165,plain,
( lhs_atom4(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_166,plain,
( X1 = X2
| X1 = X3
| lhs_atom16(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_167,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_168,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_169,plain,
( lhs_atom21(X1,X2)
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_170,plain,
( lhs_atom18(X1,X2)
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_171,plain,
( lhs_atom18(X1,X2)
| member(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_172,plain,
( lhs_atom2(X1,X2)
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_173,plain,
( lhs_atom23(X1)
| member(esk4_1(X1),X1)
| ~ set(X1)
| ~ strict_well_order(member_predicate,X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_174,plain,
( member(X1,X2)
| lhs_atom20(X1,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_175,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_176,plain,
( lhs_atom22(X1)
| subset(X2,X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_177,plain,
( lhs_atom29(X2,X1)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_178,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_179,plain,
( set(X1)
| lhs_atom32(X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_180,plain,
( member(X1,X2)
| lhs_atom28(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_181,plain,
( lhs_atom24(X1,X2)
| strict_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_182,plain,
( subset(X1,X2)
| lhs_atom5(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_183,plain,
( lhs_atom3(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_184,plain,
( lhs_atom3(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_185,plain,
( lhs_atom15(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_186,plain,
( lhs_atom22(X1)
| strict_well_order(member_predicate,X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_187,plain,
( X1 = X2
| lhs_atom14(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_188,plain,
( lhs_atom22(X1)
| set(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_189,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_190,plain,
( lhs_atom34(X2,X3,X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X2,X4) ),
c_0_111,
[final] ).
cnf(c_0_191,plain,
( lhs_atom27(X1,X2,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,esk8_3(X1,X2,X3)) ),
c_0_112,
[final] ).
cnf(c_0_192,plain,
( lhs_atom30(X1,X2)
| apply(X1,X3,X4)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
c_0_113,
[final] ).
cnf(c_0_193,plain,
( lhs_atom33(X1,X2,X3,X4)
| apply(X3,X1,X2) ),
c_0_114,
[final] ).
cnf(c_0_194,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
c_0_115,
[final] ).
cnf(c_0_195,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
c_0_116,
[final] ).
cnf(c_0_196,plain,
( lhs_atom33(X1,X2,X3,X4)
| member(X1,X4) ),
c_0_117,
[final] ).
cnf(c_0_197,plain,
( lhs_atom30(X1,X2)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
c_0_118,
[final] ).
cnf(c_0_198,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
c_0_119,
[final] ).
cnf(c_0_199,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
c_0_120,
[final] ).
cnf(c_0_200,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
c_0_121,
[final] ).
cnf(c_0_201,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
c_0_122,
[final] ).
cnf(c_0_202,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
c_0_123,
[final] ).
cnf(c_0_203,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| ~ apply(X1,esk11_2(X1,X2),esk13_2(X1,X2)) ),
c_0_124,
[final] ).
cnf(c_0_204,plain,
( lhs_atom24(X1,X2)
| least(esk5_3(X1,X2,X3),X1,X3)
| ~ member(X4,X3)
| ~ subset(X3,X2) ),
c_0_125,
[final] ).
cnf(c_0_205,plain,
( lhs_atom27(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
c_0_126,
[final] ).
cnf(c_0_206,plain,
( lhs_atom27(X1,X2,X3)
| ~ member(X2,X3)
| esk8_3(X1,X2,X3) != X2 ),
c_0_127,
[final] ).
cnf(c_0_207,plain,
( lhs_atom25(X1,X2)
| ~ strict_order(X1,X2)
| ~ least(X3,X1,esk6_2(X1,X2)) ),
c_0_128,
[final] ).
cnf(c_0_208,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
c_0_129,
[final] ).
cnf(c_0_209,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
c_0_130,
[final] ).
cnf(c_0_210,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| apply(X1,esk11_2(X1,X2),esk12_2(X1,X2)) ),
c_0_131,
[final] ).
cnf(c_0_211,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| apply(X1,esk12_2(X1,X2),esk13_2(X1,X2)) ),
c_0_132,
[final] ).
cnf(c_0_212,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| member(esk11_2(X1,X2),X2) ),
c_0_133,
[final] ).
cnf(c_0_213,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| member(esk12_2(X1,X2),X2) ),
c_0_134,
[final] ).
cnf(c_0_214,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk9_2(X1,X2),esk10_2(X1,X2))
| member(esk13_2(X1,X2),X2) ),
c_0_135,
[final] ).
cnf(c_0_215,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk11_2(X1,X2),X2) ),
c_0_136,
[final] ).
cnf(c_0_216,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk12_2(X1,X2),X2) ),
c_0_137,
[final] ).
cnf(c_0_217,plain,
( lhs_atom31(X1,X2)
| apply(X1,esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk13_2(X1,X2),X2) ),
c_0_138,
[final] ).
cnf(c_0_218,plain,
( lhs_atom26(X1,X2,X3)
| apply(X1,X2,X4)
| X2 = X4
| ~ member(X4,X3) ),
c_0_139,
[final] ).
cnf(c_0_219,plain,
( lhs_atom25(X1,X2)
| member(esk7_2(X1,X2),esk6_2(X1,X2))
| ~ strict_order(X1,X2) ),
c_0_140,
[final] ).
cnf(c_0_220,plain,
( lhs_atom8(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
c_0_141,
[final] ).
cnf(c_0_221,plain,
( lhs_atom36(X1,X2)
| ~ member(X1,union(X2,singleton(X2))) ),
c_0_142,
[final] ).
cnf(c_0_222,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2) ),
c_0_143,
[final] ).
cnf(c_0_223,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| member(esk12_2(X1,X2),X2) ),
c_0_144,
[final] ).
cnf(c_0_224,plain,
( lhs_atom31(X1,X2)
| member(esk9_2(X1,X2),X2)
| member(esk13_2(X1,X2),X2) ),
c_0_145,
[final] ).
cnf(c_0_225,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2) ),
c_0_146,
[final] ).
cnf(c_0_226,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| member(esk12_2(X1,X2),X2) ),
c_0_147,
[final] ).
cnf(c_0_227,plain,
( lhs_atom31(X1,X2)
| member(esk10_2(X1,X2),X2)
| member(esk13_2(X1,X2),X2) ),
c_0_148,
[final] ).
cnf(c_0_228,plain,
( member(X1,X2)
| lhs_atom13(X3,X1,X2)
| ~ member(X1,X3) ),
c_0_149,
[final] ).
cnf(c_0_229,plain,
( member(X1,X2)
| member(X1,X3)
| lhs_atom9(X1,X2,X3) ),
c_0_150,
[final] ).
cnf(c_0_230,plain,
( lhs_atom21(X1,X2)
| ~ member(X1,esk3_2(X1,X2)) ),
c_0_151,
[final] ).
cnf(c_0_231,plain,
( lhs_atom2(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
c_0_152,
[final] ).
cnf(c_0_232,plain,
( lhs_atom25(X1,X2)
| subset(esk6_2(X1,X2),X2)
| ~ strict_order(X1,X2) ),
c_0_153,
[final] ).
cnf(c_0_233,plain,
( lhs_atom12(X1,X2,X3)
| ~ member(X2,X3) ),
c_0_154,
[final] ).
cnf(c_0_234,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X3) ),
c_0_155,
[final] ).
cnf(c_0_235,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X2) ),
c_0_156,
[final] ).
cnf(c_0_236,plain,
( lhs_atom26(X1,X2,X3)
| member(X2,X3) ),
c_0_157,
[final] ).
cnf(c_0_237,plain,
( lhs_atom12(X1,X2,X3)
| member(X2,X1) ),
c_0_158,
[final] ).
cnf(c_0_238,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X3) ),
c_0_159,
[final] ).
cnf(c_0_239,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X2) ),
c_0_160,
[final] ).
cnf(c_0_240,plain,
( member(X1,union(X2,singleton(X2)))
| lhs_atom35(X1,X2) ),
c_0_161,
[final] ).
cnf(c_0_241,plain,
( lhs_atom23(X1)
| ~ set(X1)
| ~ strict_well_order(member_predicate,X1)
| ~ subset(esk4_1(X1),X1) ),
c_0_162,
[final] ).
cnf(c_0_242,plain,
( lhs_atom37(X2,X3)
| ~ subset(X1,X2)
| ~ subset(X3,X1) ),
c_0_163,
[final] ).
cnf(c_0_243,plain,
( lhs_atom19(X1,X3)
| ~ member(X1,X2)
| ~ member(X2,X3) ),
c_0_164,
[final] ).
cnf(c_0_244,plain,
( lhs_atom4(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_165,
[final] ).
cnf(c_0_245,plain,
( X1 = X2
| X1 = X3
| lhs_atom16(X1,X2,X3) ),
c_0_166,
[final] ).
cnf(c_0_246,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X3 ),
c_0_167,
[final] ).
cnf(c_0_247,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X2 ),
c_0_168,
[final] ).
cnf(c_0_248,plain,
( lhs_atom21(X1,X2)
| member(esk3_2(X1,X2),X2) ),
c_0_169,
[final] ).
cnf(c_0_249,plain,
( lhs_atom18(X1,X2)
| member(esk2_2(X1,X2),X2) ),
c_0_170,
[final] ).
cnf(c_0_250,plain,
( lhs_atom18(X1,X2)
| member(X1,esk2_2(X1,X2)) ),
c_0_171,
[final] ).
cnf(c_0_251,plain,
( lhs_atom2(X1,X2)
| member(esk1_2(X1,X2),X2) ),
c_0_172,
[final] ).
cnf(c_0_252,plain,
( lhs_atom23(X1)
| member(esk4_1(X1),X1)
| ~ set(X1)
| ~ strict_well_order(member_predicate,X1) ),
c_0_173,
[final] ).
cnf(c_0_253,plain,
( member(X1,X2)
| lhs_atom20(X1,X3)
| ~ member(X2,X3) ),
c_0_174,
[final] ).
cnf(c_0_254,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
c_0_175,
[final] ).
cnf(c_0_255,plain,
( lhs_atom22(X1)
| subset(X2,X1)
| ~ member(X2,X1) ),
c_0_176,
[final] ).
cnf(c_0_256,plain,
( lhs_atom29(X2,X1)
| ~ member(X1,X2) ),
c_0_177,
[final] ).
cnf(c_0_257,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2) ),
c_0_178,
[final] ).
cnf(c_0_258,plain,
( set(X1)
| lhs_atom32(X2)
| ~ member(X1,X2) ),
c_0_179,
[final] ).
cnf(c_0_259,plain,
( member(X1,X2)
| lhs_atom28(X2,X1) ),
c_0_180,
[final] ).
cnf(c_0_260,plain,
( lhs_atom24(X1,X2)
| strict_order(X1,X2) ),
c_0_181,
[final] ).
cnf(c_0_261,plain,
( subset(X1,X2)
| lhs_atom5(X1,X2) ),
c_0_182,
[final] ).
cnf(c_0_262,plain,
( lhs_atom3(X1,X2)
| subset(X2,X1) ),
c_0_183,
[final] ).
cnf(c_0_263,plain,
( lhs_atom3(X1,X2)
| subset(X1,X2) ),
c_0_184,
[final] ).
cnf(c_0_264,plain,
( lhs_atom15(X1,X2)
| X1 != X2 ),
c_0_185,
[final] ).
cnf(c_0_265,plain,
( lhs_atom22(X1)
| strict_well_order(member_predicate,X1) ),
c_0_186,
[final] ).
cnf(c_0_266,plain,
( X1 = X2
| lhs_atom14(X1,X2) ),
c_0_187,
[final] ).
cnf(c_0_267,plain,
( lhs_atom22(X1)
| set(X1) ),
c_0_188,
[final] ).
cnf(c_0_268,plain,
lhs_atom11(X1),
c_0_189,
[final] ).
% End CNF derivation
cnf(c_0_190_0,axiom,
( member(X2,initial_segment(X3,X1,X4))
| ~ apply(X1,X2,X3)
| ~ member(X2,X4) ),
inference(unfold_definition,[status(thm)],[c_0_190,def_lhs_atom34]) ).
cnf(c_0_191_0,axiom,
( least(X2,X1,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,sk1_esk8_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_191,def_lhs_atom27]) ).
cnf(c_0_192_0,axiom,
( ~ strict_order(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_192,def_lhs_atom30]) ).
cnf(c_0_193_0,axiom,
( ~ member(X1,initial_segment(X2,X3,X4))
| apply(X3,X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_193,def_lhs_atom33]) ).
cnf(c_0_194_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk9_2(X1,X2),sk1_esk10_2(X1,X2))
| ~ apply(X1,sk1_esk11_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_194,def_lhs_atom31]) ).
cnf(c_0_195_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk10_2(X1,X2),sk1_esk9_2(X1,X2))
| ~ apply(X1,sk1_esk11_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_195,def_lhs_atom31]) ).
cnf(c_0_196_0,axiom,
( ~ member(X1,initial_segment(X2,X3,X4))
| member(X1,X4) ),
inference(unfold_definition,[status(thm)],[c_0_196,def_lhs_atom33]) ).
cnf(c_0_197_0,axiom,
( ~ strict_order(X1,X2)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_197,def_lhs_atom30]) ).
cnf(c_0_198_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk9_2(X1,X2),sk1_esk10_2(X1,X2))
| apply(X1,sk1_esk11_2(X1,X2),sk1_esk12_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_198,def_lhs_atom31]) ).
cnf(c_0_199_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk9_2(X1,X2),sk1_esk10_2(X1,X2))
| apply(X1,sk1_esk12_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_199,def_lhs_atom31]) ).
cnf(c_0_200_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk10_2(X1,X2),sk1_esk9_2(X1,X2))
| apply(X1,sk1_esk11_2(X1,X2),sk1_esk12_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_200,def_lhs_atom31]) ).
cnf(c_0_201_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk10_2(X1,X2),sk1_esk9_2(X1,X2))
| apply(X1,sk1_esk12_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_201,def_lhs_atom31]) ).
cnf(c_0_202_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk9_2(X1,X2),X2)
| ~ apply(X1,sk1_esk11_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_202,def_lhs_atom31]) ).
cnf(c_0_203_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk10_2(X1,X2),X2)
| ~ apply(X1,sk1_esk11_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_203,def_lhs_atom31]) ).
cnf(c_0_204_0,axiom,
( ~ strict_well_order(X1,X2)
| least(sk1_esk5_3(X1,X2,X3),X1,X3)
| ~ member(X4,X3)
| ~ subset(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_204,def_lhs_atom24]) ).
cnf(c_0_205_0,axiom,
( least(X2,X1,X3)
| member(sk1_esk8_3(X1,X2,X3),X3)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_205,def_lhs_atom27]) ).
cnf(c_0_206_0,axiom,
( least(X2,X1,X3)
| ~ member(X2,X3)
| sk1_esk8_3(X1,X2,X3) != X2 ),
inference(unfold_definition,[status(thm)],[c_0_206,def_lhs_atom27]) ).
cnf(c_0_207_0,axiom,
( strict_well_order(X1,X2)
| ~ strict_order(X1,X2)
| ~ least(X3,X1,sk1_esk6_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_207,def_lhs_atom25]) ).
cnf(c_0_208_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk9_2(X1,X2),X2)
| apply(X1,sk1_esk11_2(X1,X2),sk1_esk12_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_208,def_lhs_atom31]) ).
cnf(c_0_209_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk9_2(X1,X2),X2)
| apply(X1,sk1_esk12_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_209,def_lhs_atom31]) ).
cnf(c_0_210_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk10_2(X1,X2),X2)
| apply(X1,sk1_esk11_2(X1,X2),sk1_esk12_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_210,def_lhs_atom31]) ).
cnf(c_0_211_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk10_2(X1,X2),X2)
| apply(X1,sk1_esk12_2(X1,X2),sk1_esk13_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_211,def_lhs_atom31]) ).
cnf(c_0_212_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk9_2(X1,X2),sk1_esk10_2(X1,X2))
| member(sk1_esk11_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_212,def_lhs_atom31]) ).
cnf(c_0_213_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk9_2(X1,X2),sk1_esk10_2(X1,X2))
| member(sk1_esk12_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_213,def_lhs_atom31]) ).
cnf(c_0_214_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk9_2(X1,X2),sk1_esk10_2(X1,X2))
| member(sk1_esk13_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_214,def_lhs_atom31]) ).
cnf(c_0_215_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk10_2(X1,X2),sk1_esk9_2(X1,X2))
| member(sk1_esk11_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_215,def_lhs_atom31]) ).
cnf(c_0_216_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk10_2(X1,X2),sk1_esk9_2(X1,X2))
| member(sk1_esk12_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_216,def_lhs_atom31]) ).
cnf(c_0_217_0,axiom,
( strict_order(X1,X2)
| apply(X1,sk1_esk10_2(X1,X2),sk1_esk9_2(X1,X2))
| member(sk1_esk13_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_217,def_lhs_atom31]) ).
cnf(c_0_218_0,axiom,
( ~ least(X2,X1,X3)
| apply(X1,X2,X4)
| X2 = X4
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_218,def_lhs_atom26]) ).
cnf(c_0_219_0,axiom,
( strict_well_order(X1,X2)
| member(sk1_esk7_2(X1,X2),sk1_esk6_2(X1,X2))
| ~ strict_order(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_219,def_lhs_atom25]) ).
cnf(c_0_220_0,axiom,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_220,def_lhs_atom8]) ).
cnf(c_0_221_0,axiom,
( member(X1,suc(X2))
| ~ member(X1,union(X2,singleton(X2))) ),
inference(unfold_definition,[status(thm)],[c_0_221,def_lhs_atom36]) ).
cnf(c_0_222_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk9_2(X1,X2),X2)
| member(sk1_esk11_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_222,def_lhs_atom31]) ).
cnf(c_0_223_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk9_2(X1,X2),X2)
| member(sk1_esk12_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_223,def_lhs_atom31]) ).
cnf(c_0_224_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk9_2(X1,X2),X2)
| member(sk1_esk13_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_224,def_lhs_atom31]) ).
cnf(c_0_225_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk10_2(X1,X2),X2)
| member(sk1_esk11_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_225,def_lhs_atom31]) ).
cnf(c_0_226_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk10_2(X1,X2),X2)
| member(sk1_esk12_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_226,def_lhs_atom31]) ).
cnf(c_0_227_0,axiom,
( strict_order(X1,X2)
| member(sk1_esk10_2(X1,X2),X2)
| member(sk1_esk13_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_227,def_lhs_atom31]) ).
cnf(c_0_228_0,axiom,
( member(X1,difference(X3,X2))
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_228,def_lhs_atom13]) ).
cnf(c_0_229_0,axiom,
( ~ member(X1,union(X3,X2))
| member(X1,X2)
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_229,def_lhs_atom9]) ).
cnf(c_0_230_0,axiom,
( member(X1,product(X2))
| ~ member(X1,sk1_esk3_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_230,def_lhs_atom21]) ).
cnf(c_0_231_0,axiom,
( subset(X2,X1)
| ~ member(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_231,def_lhs_atom2]) ).
cnf(c_0_232_0,axiom,
( strict_well_order(X1,X2)
| subset(sk1_esk6_2(X1,X2),X2)
| ~ strict_order(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_232,def_lhs_atom25]) ).
cnf(c_0_233_0,axiom,
( ~ member(X2,difference(X1,X3))
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_233,def_lhs_atom12]) ).
cnf(c_0_234_0,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_234,def_lhs_atom10]) ).
cnf(c_0_235_0,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_235,def_lhs_atom10]) ).
cnf(c_0_236_0,axiom,
( ~ least(X2,X1,X3)
| member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_236,def_lhs_atom26]) ).
cnf(c_0_237_0,axiom,
( ~ member(X2,difference(X1,X3))
| member(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_237,def_lhs_atom12]) ).
cnf(c_0_238_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_238,def_lhs_atom7]) ).
cnf(c_0_239_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_239,def_lhs_atom7]) ).
cnf(c_0_240_0,axiom,
( ~ member(X1,suc(X2))
| member(X1,union(X2,singleton(X2))) ),
inference(unfold_definition,[status(thm)],[c_0_240,def_lhs_atom35]) ).
cnf(c_0_241_0,axiom,
( member(X1,on)
| ~ set(X1)
| ~ strict_well_order(member_predicate,X1)
| ~ subset(sk1_esk4_1(X1),X1) ),
inference(unfold_definition,[status(thm)],[c_0_241,def_lhs_atom23]) ).
cnf(c_0_242_0,axiom,
( subset(X3,X2)
| ~ subset(X1,X2)
| ~ subset(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_242,def_lhs_atom37]) ).
cnf(c_0_243_0,axiom,
( member(X1,sum(X3))
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_243,def_lhs_atom19]) ).
cnf(c_0_244_0,axiom,
( equal_set(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_244,def_lhs_atom4]) ).
cnf(c_0_245_0,axiom,
( ~ member(X1,unordered_pair(X3,X2))
| X1 = X2
| X1 = X3 ),
inference(unfold_definition,[status(thm)],[c_0_245,def_lhs_atom16]) ).
cnf(c_0_246_0,axiom,
( member(X1,unordered_pair(X3,X2))
| X1 != X3 ),
inference(unfold_definition,[status(thm)],[c_0_246,def_lhs_atom17]) ).
cnf(c_0_247_0,axiom,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_247,def_lhs_atom17]) ).
cnf(c_0_248_0,axiom,
( member(X1,product(X2))
| member(sk1_esk3_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_248,def_lhs_atom21]) ).
cnf(c_0_249_0,axiom,
( ~ member(X1,sum(X2))
| member(sk1_esk2_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_249,def_lhs_atom18]) ).
cnf(c_0_250_0,axiom,
( ~ member(X1,sum(X2))
| member(X1,sk1_esk2_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_250,def_lhs_atom18]) ).
cnf(c_0_251_0,axiom,
( subset(X2,X1)
| member(sk1_esk1_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_251,def_lhs_atom2]) ).
cnf(c_0_252_0,axiom,
( member(X1,on)
| member(sk1_esk4_1(X1),X1)
| ~ set(X1)
| ~ strict_well_order(member_predicate,X1) ),
inference(unfold_definition,[status(thm)],[c_0_252,def_lhs_atom23]) ).
cnf(c_0_253_0,axiom,
( ~ member(X1,product(X3))
| member(X1,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_253,def_lhs_atom20]) ).
cnf(c_0_254_0,axiom,
( ~ subset(X3,X2)
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_254,def_lhs_atom1]) ).
cnf(c_0_255_0,axiom,
( ~ member(X1,on)
| subset(X2,X1)
| ~ member(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_255,def_lhs_atom22]) ).
cnf(c_0_256_0,axiom,
( apply(member_predicate,X1,X2)
| ~ member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_256,def_lhs_atom29]) ).
cnf(c_0_257_0,axiom,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_257,def_lhs_atom6]) ).
cnf(c_0_258_0,axiom,
( ~ set(X2)
| set(X1)
| ~ member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_258,def_lhs_atom32]) ).
cnf(c_0_259_0,axiom,
( ~ apply(member_predicate,X1,X2)
| member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_259,def_lhs_atom28]) ).
cnf(c_0_260_0,axiom,
( ~ strict_well_order(X1,X2)
| strict_order(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_260,def_lhs_atom24]) ).
cnf(c_0_261_0,axiom,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_261,def_lhs_atom5]) ).
cnf(c_0_262_0,axiom,
( ~ equal_set(X2,X1)
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_262,def_lhs_atom3]) ).
cnf(c_0_263_0,axiom,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_263,def_lhs_atom3]) ).
cnf(c_0_264_0,axiom,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_264,def_lhs_atom15]) ).
cnf(c_0_265_0,axiom,
( ~ member(X1,on)
| strict_well_order(member_predicate,X1) ),
inference(unfold_definition,[status(thm)],[c_0_265,def_lhs_atom22]) ).
cnf(c_0_266_0,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(unfold_definition,[status(thm)],[c_0_266,def_lhs_atom14]) ).
cnf(c_0_267_0,axiom,
( ~ member(X1,on)
| set(X1) ),
inference(unfold_definition,[status(thm)],[c_0_267,def_lhs_atom22]) ).
cnf(c_0_268_0,axiom,
~ member(X1,empty_set),
inference(unfold_definition,[status(thm)],[c_0_268,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] :
( member(X1,on)
=> subset(sum(X1),X1) ),
file('<stdin>',thV14) ).
fof(c_0_1_002,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_003,negated_conjecture,
( member(esk1_0,on)
& ~ subset(sum(esk1_0),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_004,negated_conjecture,
~ subset(sum(esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
member(esk1_0,on),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_006,negated_conjecture,
~ subset(sum(esk1_0),esk1_0),
c_0_3,
[final] ).
cnf(c_0_6_007,negated_conjecture,
member(esk1_0,on),
c_0_4,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_14,plain,
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_254_0) ).
cnf(c_178,plain,
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(X1,X2) ),
inference(copy,[status(esa)],[c_14]) ).
cnf(c_29595,plain,
( ~ member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0))
| member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),X0)
| ~ subset(sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0),X0) ),
inference(instantiation,[status(thm)],[c_178]) ).
cnf(c_112517,plain,
( ~ member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0))
| member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0)
| ~ subset(sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_29595]) ).
cnf(c_13,plain,
( ~ member(X0,X1)
| subset(X0,X1)
| ~ member(X1,on) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_255_0) ).
cnf(c_177,plain,
( ~ member(X0,X1)
| subset(X0,X1)
| ~ member(X1,on) ),
inference(copy,[status(esa)],[c_13]) ).
cnf(c_29526,plain,
( ~ member(sk3_esk1_0,on)
| ~ member(X0,sk3_esk1_0)
| subset(X0,sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_177]) ).
cnf(c_30792,plain,
( ~ member(sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0)
| ~ member(sk3_esk1_0,on)
| subset(sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_29526]) ).
cnf(c_19,plain,
( member(sk1_esk2_2(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_249_0) ).
cnf(c_183,plain,
( member(sk1_esk2_2(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(copy,[status(esa)],[c_19]) ).
cnf(c_29437,plain,
( ~ member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sum(sk3_esk1_0))
| member(sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_183]) ).
cnf(c_18,plain,
( member(X0,sk1_esk2_2(X0,X1))
| ~ member(X0,sum(X1)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_250_0) ).
cnf(c_182,plain,
( member(X0,sk1_esk2_2(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(copy,[status(esa)],[c_18]) ).
cnf(c_29438,plain,
( ~ member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sum(sk3_esk1_0))
| member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk1_esk2_2(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0)) ),
inference(instantiation,[status(thm)],[c_182]) ).
cnf(c_37,plain,
( ~ member(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_231_0) ).
cnf(c_201,plain,
( ~ member(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
inference(copy,[status(esa)],[c_37]) ).
cnf(c_29319,plain,
( ~ member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sk3_esk1_0)
| subset(sum(sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_201]) ).
cnf(c_17,plain,
( member(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_251_0) ).
cnf(c_181,plain,
( member(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
inference(copy,[status(esa)],[c_17]) ).
cnf(c_29299,plain,
( member(sk1_esk1_2(sk3_esk1_0,sum(sk3_esk1_0)),sum(sk3_esk1_0))
| subset(sum(sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_181]) ).
cnf(c_79,negated_conjecture,
~ subset(sum(sk3_esk1_0),sk3_esk1_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_5) ).
cnf(c_80,negated_conjecture,
member(sk3_esk1_0,on),
file('/export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p',c_0_6) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_112517,c_30792,c_29437,c_29438,c_29319,c_29299,c_79,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET814+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 13:47:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.21/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.42 % FOF problem with conjecture
% 0.21/0.42 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_647154.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_08c3ce.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_d32e74 | grep -v "SZS"
% 0.21/0.44
% 0.21/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.44
% 0.21/0.44 %
% 0.21/0.44 % ------ iProver source info
% 0.21/0.44
% 0.21/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.44 % git: non_committed_changes: true
% 0.21/0.44 % git: last_make_outside_of_git: true
% 0.21/0.44
% 0.21/0.44 %
% 0.21/0.44 % ------ Input Options
% 0.21/0.44
% 0.21/0.44 % --out_options all
% 0.21/0.44 % --tptp_safe_out true
% 0.21/0.44 % --problem_path ""
% 0.21/0.44 % --include_path ""
% 0.21/0.44 % --clausifier .//eprover
% 0.21/0.44 % --clausifier_options --tstp-format
% 0.21/0.44 % --stdin false
% 0.21/0.44 % --dbg_backtrace false
% 0.21/0.44 % --dbg_dump_prop_clauses false
% 0.21/0.44 % --dbg_dump_prop_clauses_file -
% 0.21/0.44 % --dbg_out_stat false
% 0.21/0.44
% 0.21/0.44 % ------ General Options
% 0.21/0.44
% 0.21/0.44 % --fof false
% 0.21/0.44 % --time_out_real 150.
% 0.21/0.44 % --time_out_prep_mult 0.2
% 0.21/0.44 % --time_out_virtual -1.
% 0.21/0.44 % --schedule none
% 0.21/0.44 % --ground_splitting input
% 0.21/0.44 % --splitting_nvd 16
% 0.21/0.44 % --non_eq_to_eq false
% 0.21/0.44 % --prep_gs_sim true
% 0.21/0.44 % --prep_unflatten false
% 0.21/0.44 % --prep_res_sim true
% 0.21/0.44 % --prep_upred true
% 0.21/0.44 % --res_sim_input true
% 0.21/0.44 % --clause_weak_htbl true
% 0.21/0.44 % --gc_record_bc_elim false
% 0.21/0.44 % --symbol_type_check false
% 0.21/0.44 % --clausify_out false
% 0.21/0.44 % --large_theory_mode false
% 0.21/0.44 % --prep_sem_filter none
% 0.21/0.44 % --prep_sem_filter_out false
% 0.21/0.44 % --preprocessed_out false
% 0.21/0.44 % --sub_typing false
% 0.21/0.44 % --brand_transform false
% 0.21/0.44 % --pure_diseq_elim true
% 0.21/0.44 % --min_unsat_core false
% 0.21/0.44 % --pred_elim true
% 0.21/0.44 % --add_important_lit false
% 0.21/0.44 % --soft_assumptions false
% 0.21/0.44 % --reset_solvers false
% 0.21/0.44 % --bc_imp_inh []
% 0.21/0.44 % --conj_cone_tolerance 1.5
% 0.21/0.44 % --prolific_symb_bound 500
% 0.21/0.44 % --lt_threshold 2000
% 0.21/0.44
% 0.21/0.44 % ------ SAT Options
% 0.21/0.44
% 0.21/0.44 % --sat_mode false
% 0.21/0.44 % --sat_fm_restart_options ""
% 0.21/0.44 % --sat_gr_def false
% 0.21/0.44 % --sat_epr_types true
% 0.21/0.44 % --sat_non_cyclic_types false
% 0.21/0.44 % --sat_finite_models false
% 0.21/0.44 % --sat_fm_lemmas false
% 0.21/0.44 % --sat_fm_prep false
% 0.21/0.44 % --sat_fm_uc_incr true
% 0.21/0.44 % --sat_out_model small
% 0.21/0.44 % --sat_out_clauses false
% 0.21/0.44
% 0.21/0.44 % ------ QBF Options
% 0.21/0.44
% 0.21/0.44 % --qbf_mode false
% 0.21/0.44 % --qbf_elim_univ true
% 0.21/0.44 % --qbf_sk_in true
% 0.21/0.44 % --qbf_pred_elim true
% 0.21/0.44 % --qbf_split 32
% 0.21/0.44
% 0.21/0.44 % ------ BMC1 Options
% 0.21/0.44
% 0.21/0.44 % --bmc1_incremental false
% 0.21/0.44 % --bmc1_axioms reachable_all
% 0.21/0.44 % --bmc1_min_bound 0
% 0.21/0.44 % --bmc1_max_bound -1
% 0.21/0.44 % --bmc1_max_bound_default -1
% 0.21/0.44 % --bmc1_symbol_reachability true
% 0.21/0.44 % --bmc1_property_lemmas false
% 0.21/0.44 % --bmc1_k_induction false
% 0.21/0.44 % --bmc1_non_equiv_states false
% 0.21/0.44 % --bmc1_deadlock false
% 0.21/0.44 % --bmc1_ucm false
% 0.21/0.44 % --bmc1_add_unsat_core none
% 0.21/0.44 % --bmc1_unsat_core_children false
% 0.21/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.44 % --bmc1_out_stat full
% 0.21/0.44 % --bmc1_ground_init false
% 0.21/0.44 % --bmc1_pre_inst_next_state false
% 0.21/0.44 % --bmc1_pre_inst_state false
% 0.21/0.44 % --bmc1_pre_inst_reach_state false
% 0.21/0.44 % --bmc1_out_unsat_core false
% 0.21/0.44 % --bmc1_aig_witness_out false
% 0.21/0.44 % --bmc1_verbose false
% 0.21/0.44 % --bmc1_dump_clauses_tptp false
% 0.21/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.46 % --bmc1_dump_file -
% 0.21/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.46 % --bmc1_ucm_extend_mode 1
% 0.21/0.46 % --bmc1_ucm_init_mode 2
% 0.21/0.46 % --bmc1_ucm_cone_mode none
% 0.21/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.46 % --bmc1_ucm_relax_model 4
% 0.21/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.46 % --bmc1_ucm_layered_model none
% 0.21/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.46
% 0.21/0.46 % ------ AIG Options
% 0.21/0.46
% 0.21/0.46 % --aig_mode false
% 0.21/0.46
% 0.21/0.46 % ------ Instantiation Options
% 0.21/0.46
% 0.21/0.46 % --instantiation_flag true
% 0.21/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.46 % --inst_solver_per_active 750
% 0.21/0.46 % --inst_solver_calls_frac 0.5
% 0.21/0.46 % --inst_passive_queue_type priority_queues
% 0.21/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.46 % --inst_passive_queues_freq [25;2]
% 0.21/0.46 % --inst_dismatching true
% 0.21/0.46 % --inst_eager_unprocessed_to_passive true
% 0.21/0.46 % --inst_prop_sim_given true
% 0.21/0.46 % --inst_prop_sim_new false
% 0.21/0.46 % --inst_orphan_elimination true
% 0.21/0.46 % --inst_learning_loop_flag true
% 0.21/0.46 % --inst_learning_start 3000
% 0.21/0.46 % --inst_learning_factor 2
% 0.21/0.46 % --inst_start_prop_sim_after_learn 3
% 0.21/0.46 % --inst_sel_renew solver
% 0.21/0.46 % --inst_lit_activity_flag true
% 0.21/0.46 % --inst_out_proof true
% 0.21/0.46
% 0.21/0.46 % ------ Resolution Options
% 0.21/0.46
% 0.21/0.46 % --resolution_flag true
% 0.21/0.46 % --res_lit_sel kbo_max
% 0.21/0.46 % --res_to_prop_solver none
% 0.21/0.46 % --res_prop_simpl_new false
% 0.21/0.46 % --res_prop_simpl_given false
% 0.21/0.46 % --res_passive_queue_type priority_queues
% 0.21/0.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.21/0.46 % --res_passive_queues_freq [15;5]
% 0.21/0.46 % --res_forward_subs full
% 0.21/0.46 % --res_backward_subs full
% 0.21/0.46 % --res_forward_subs_resolution true
% 0.21/0.46 % --res_backward_subs_resolution true
% 0.21/0.46 % --res_orphan_elimination false
% 0.21/0.46 % --res_time_limit 1000.
% 0.21/0.46 % --res_out_proof true
% 0.21/0.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_647154.s
% 0.21/0.46 % --modulo true
% 0.21/0.46
% 0.21/0.46 % ------ Combination Options
% 0.21/0.46
% 0.21/0.46 % --comb_res_mult 1000
% 0.21/0.46 % --comb_inst_mult 300
% 0.21/0.46 % ------
% 0.21/0.46
% 0.21/0.46 % ------ Parsing...% successful
% 0.21/0.46
% 0.21/0.46 % ------ 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 %
% 0.21/0.46
% 0.21/0.46 % ------ Proving...
% 0.21/0.46 % ------ Problem Properties
% 0.21/0.46
% 0.21/0.46 %
% 0.21/0.46 % EPR false
% 0.21/0.46 % Horn false
% 0.21/0.46 % Has equality true
% 0.21/0.46
% 0.21/0.46 % % ------ Input Options Time Limit: Unbounded
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % % ------ Current options:
% 0.21/0.46
% 0.21/0.46 % ------ Input Options
% 0.21/0.46
% 0.21/0.46 % --out_options all
% 0.21/0.46 % --tptp_safe_out true
% 0.21/0.46 % --problem_path ""
% 0.21/0.46 % --include_path ""
% 0.21/0.46 % --clausifier .//eprover
% 0.21/0.46 % --clausifier_options --tstp-format
% 0.21/0.46 % --stdin false
% 0.21/0.46 % --dbg_backtrace false
% 0.21/0.46 % --dbg_dump_prop_clauses false
% 0.21/0.46 % --dbg_dump_prop_clauses_file -
% 0.21/0.46 % --dbg_out_stat false
% 0.21/0.46
% 0.21/0.46 % ------ General Options
% 0.21/0.46
% 0.21/0.46 % --fof false
% 0.21/0.46 % --time_out_real 150.
% 0.21/0.46 % --time_out_prep_mult 0.2
% 0.21/0.46 % --time_out_virtual -1.
% 0.21/0.46 % --schedule none
% 0.21/0.46 % --ground_splitting input
% 0.21/0.46 % --splitting_nvd 16
% 0.21/0.46 % --non_eq_to_eq false
% 0.21/0.46 % --prep_gs_sim true
% 0.21/0.46 % --prep_unflatten false
% 0.21/0.46 % --prep_res_sim true
% 0.21/0.46 % --prep_upred true
% 0.21/0.46 % --res_sim_input true
% 0.21/0.46 % --clause_weak_htbl true
% 0.21/0.46 % --gc_record_bc_elim false
% 0.21/0.46 % --symbol_type_check false
% 0.21/0.46 % --clausify_out false
% 0.21/0.46 % --large_theory_mode false
% 0.21/0.46 % --prep_sem_filter none
% 0.21/0.46 % --prep_sem_filter_out false
% 0.21/0.46 % --preprocessed_out false
% 0.21/0.46 % --sub_typing false
% 0.21/0.46 % --brand_transform false
% 0.21/0.46 % --pure_diseq_elim true
% 0.21/0.46 % --min_unsat_core false
% 0.21/0.46 % --pred_elim true
% 0.21/0.46 % --add_important_lit false
% 0.21/0.46 % --soft_assumptions false
% 0.21/0.46 % --reset_solvers false
% 0.21/0.46 % --bc_imp_inh []
% 0.21/0.46 % --conj_cone_tolerance 1.5
% 0.21/0.46 % --prolific_symb_bound 500
% 0.21/0.46 % --lt_threshold 2000
% 0.21/0.46
% 0.21/0.46 % ------ SAT Options
% 0.21/0.46
% 0.21/0.46 % --sat_mode false
% 0.21/0.46 % --sat_fm_restart_options ""
% 0.21/0.46 % --sat_gr_def false
% 0.21/0.46 % --sat_epr_types true
% 0.21/0.46 % --sat_non_cyclic_types false
% 0.21/0.46 % --sat_finite_models false
% 0.21/0.46 % --sat_fm_lemmas false
% 0.21/0.46 % --sat_fm_prep false
% 0.21/0.46 % --sat_fm_uc_incr true
% 0.21/0.46 % --sat_out_model small
% 0.21/0.46 % --sat_out_clauses false
% 0.21/0.46
% 0.21/0.46 % ------ QBF Options
% 0.21/0.46
% 0.21/0.46 % --qbf_mode false
% 0.21/0.46 % --qbf_elim_univ true
% 0.21/0.46 % --qbf_sk_in true
% 0.21/0.46 % --qbf_pred_elim true
% 0.21/0.46 % --qbf_split 32
% 0.21/0.46
% 0.21/0.46 % ------ BMC1 Options
% 0.21/0.46
% 0.21/0.46 % --bmc1_incremental false
% 0.21/0.46 % --bmc1_axioms reachable_all
% 0.21/0.46 % --bmc1_min_bound 0
% 0.21/0.46 % --bmc1_max_bound -1
% 0.21/0.46 % --bmc1_max_bound_default -1
% 0.21/0.46 % --bmc1_symbol_reachability true
% 0.21/0.46 % --bmc1_property_lemmas false
% 0.21/0.46 % --bmc1_k_induction false
% 0.21/0.46 % --bmc1_non_equiv_states false
% 0.21/0.46 % --bmc1_deadlock false
% 0.21/0.46 % --bmc1_ucm false
% 0.21/0.46 % --bmc1_add_unsat_core none
% 0.21/0.46 % --bmc1_unsat_core_children false
% 0.21/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.46 % --bmc1_out_stat full
% 0.21/0.46 % --bmc1_ground_init false
% 0.21/0.46 % --bmc1_pre_inst_next_state false
% 0.21/0.46 % --bmc1_pre_inst_state false
% 0.21/0.46 % --bmc1_pre_inst_reach_state false
% 0.21/0.46 % --bmc1_out_unsat_core false
% 0.21/0.46 % --bmc1_aig_witness_out false
% 0.21/0.46 % --bmc1_verbose false
% 0.21/0.46 % --bmc1_dump_clauses_tptp false
% 0.21/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.46 % --bmc1_dump_file -
% 0.21/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.46 % --bmc1_ucm_extend_mode 1
% 0.21/0.46 % --bmc1_ucm_init_mode 2
% 0.21/0.46 % --bmc1_ucm_cone_mode none
% 0.21/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.46 % --bmc1_ucm_relax_model 4
% 0.21/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.46 % --bmc1_ucm_layered_model none
% 0.21/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.46
% 0.21/0.46 % ------ AIG Options
% 0.21/0.46
% 0.21/0.46 % --aig_mode false
% 0.21/0.46
% 0.21/0.46 % ------ Instantiation Options
% 0.21/0.46
% 0.21/0.46 % --instantiation_flag true
% 0.21/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.46 % --inst_solver_per_active 750
% 0.21/0.46 % --inst_solver_calls_frac 0.5
% 0.21/0.46 % --inst_passive_queue_type priority_queues
% 0.21/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.46 % --inst_passive_queues_freq [25;2]
% 0.21/0.46 % --inst_dismatching true
% 0.21/0.46 % --inst_eager_unprocessed_to_passive true
% 0.21/0.46 % --inst_prop_sim_given true
% 4.53/4.72 % --inst_prop_sim_new false
% 4.53/4.72 % --inst_orphan_elimination true
% 4.53/4.72 % --inst_learning_loop_flag true
% 4.53/4.72 % --inst_learning_start 3000
% 4.53/4.72 % --inst_learning_factor 2
% 4.53/4.72 % --inst_start_prop_sim_after_learn 3
% 4.53/4.72 % --inst_sel_renew solver
% 4.53/4.72 % --inst_lit_activity_flag true
% 4.53/4.72 % --inst_out_proof true
% 4.53/4.72
% 4.53/4.72 % ------ Resolution Options
% 4.53/4.72
% 4.53/4.72 % --resolution_flag true
% 4.53/4.72 % --res_lit_sel kbo_max
% 4.53/4.72 % --res_to_prop_solver none
% 4.53/4.72 % --res_prop_simpl_new false
% 4.53/4.72 % --res_prop_simpl_given false
% 4.53/4.72 % --res_passive_queue_type priority_queues
% 4.53/4.72 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 4.53/4.72 % --res_passive_queues_freq [15;5]
% 4.53/4.72 % --res_forward_subs full
% 4.53/4.72 % --res_backward_subs full
% 4.53/4.72 % --res_forward_subs_resolution true
% 4.53/4.72 % --res_backward_subs_resolution true
% 4.53/4.72 % --res_orphan_elimination false
% 4.53/4.72 % --res_time_limit 1000.
% 4.53/4.72 % --res_out_proof true
% 4.53/4.72 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_647154.s
% 4.53/4.72 % --modulo true
% 4.53/4.72
% 4.53/4.72 % ------ Combination Options
% 4.53/4.72
% 4.53/4.72 % --comb_res_mult 1000
% 4.53/4.72 % --comb_inst_mult 300
% 4.53/4.72 % ------
% 4.53/4.72
% 4.53/4.72
% 4.53/4.72
% 4.53/4.72 % ------ Proving...
% 4.53/4.72 %
% 4.53/4.72
% 4.53/4.72
% 4.53/4.72 % ------ Statistics
% 4.53/4.72
% 4.53/4.72 % ------ General
% 4.53/4.72
% 4.53/4.72 % num_of_input_clauses: 81
% 4.53/4.72 % num_of_input_neg_conjectures: 2
% 4.53/4.72 % num_of_splits: 0
% 4.53/4.72 % num_of_split_atoms: 0
% 4.53/4.72 % num_of_sem_filtered_clauses: 0
% 4.53/4.72 % num_of_subtypes: 0
% 4.53/4.72 % monotx_restored_types: 0
% 4.53/4.72 % sat_num_of_epr_types: 0
% 4.53/4.72 % sat_num_of_non_cyclic_types: 0
% 4.53/4.72 % sat_guarded_non_collapsed_types: 0
% 4.53/4.72 % is_epr: 0
% 4.53/4.72 % is_horn: 0
% 4.53/4.72 % has_eq: 1
% 4.53/4.72 % num_pure_diseq_elim: 0
% 4.53/4.72 % simp_replaced_by: 0
% 4.53/4.72 % res_preprocessed: 4
% 4.53/4.72 % prep_upred: 0
% 4.53/4.72 % prep_unflattend: 0
% 4.53/4.72 % pred_elim_cands: 0
% 4.53/4.72 % pred_elim: 0
% 4.53/4.72 % pred_elim_cl: 0
% 4.53/4.72 % pred_elim_cycles: 0
% 4.53/4.72 % forced_gc_time: 0
% 4.53/4.72 % gc_basic_clause_elim: 0
% 4.53/4.72 % parsing_time: 0.004
% 4.53/4.72 % sem_filter_time: 0.
% 4.53/4.72 % pred_elim_time: 0.
% 4.53/4.72 % out_proof_time: 0.
% 4.53/4.72 % monotx_time: 0.
% 4.53/4.72 % subtype_inf_time: 0.
% 4.53/4.72 % unif_index_cands_time: 0.037
% 4.53/4.72 % unif_index_add_time: 0.007
% 4.53/4.72 % total_time: 4.297
% 4.53/4.72 % num_of_symbols: 60
% 4.53/4.72 % num_of_terms: 255216
% 4.53/4.72
% 4.53/4.72 % ------ Propositional Solver
% 4.53/4.72
% 4.53/4.72 % prop_solver_calls: 7
% 4.53/4.72 % prop_fast_solver_calls: 6
% 4.53/4.72 % prop_num_of_clauses: 1628
% 4.53/4.72 % prop_preprocess_simplified: 1854
% 4.53/4.72 % prop_fo_subsumed: 0
% 4.53/4.72 % prop_solver_time: 0.
% 4.53/4.72 % prop_fast_solver_time: 0.
% 4.53/4.72 % prop_unsat_core_time: 0.
% 4.53/4.72
% 4.53/4.72 % ------ QBF
% 4.53/4.72
% 4.53/4.72 % qbf_q_res: 0
% 4.53/4.72 % qbf_num_tautologies: 0
% 4.53/4.72 % qbf_prep_cycles: 0
% 4.53/4.72
% 4.53/4.72 % ------ BMC1
% 4.53/4.72
% 4.53/4.72 % bmc1_current_bound: -1
% 4.53/4.72 % bmc1_last_solved_bound: -1
% 4.53/4.72 % bmc1_unsat_core_size: -1
% 4.53/4.72 % bmc1_unsat_core_parents_size: -1
% 4.53/4.72 % bmc1_merge_next_fun: 0
% 4.53/4.72 % bmc1_unsat_core_clauses_time: 0.
% 4.53/4.72
% 4.53/4.72 % ------ Instantiation
% 4.53/4.72
% 4.53/4.72 % inst_num_of_clauses: 1045
% 4.53/4.72 % inst_num_in_passive: 463
% 4.53/4.72 % inst_num_in_active: 316
% 4.53/4.72 % inst_num_in_unprocessed: 260
% 4.53/4.72 % inst_num_of_loops: 372
% 4.53/4.73 % inst_num_of_learning_restarts: 0
% 4.53/4.73 % inst_num_moves_active_passive: 51
% 4.53/4.73 % inst_lit_activity: 211
% 4.53/4.73 % inst_lit_activity_moves: 0
% 4.53/4.73 % inst_num_tautologies: 3
% 4.53/4.73 % inst_num_prop_implied: 0
% 4.53/4.73 % inst_num_existing_simplified: 0
% 4.53/4.73 % inst_num_eq_res_simplified: 0
% 4.53/4.73 % inst_num_child_elim: 0
% 4.53/4.73 % inst_num_of_dismatching_blockings: 740
% 4.53/4.73 % inst_num_of_non_proper_insts: 867
% 4.53/4.73 % inst_num_of_duplicates: 341
% 4.53/4.73 % inst_inst_num_from_inst_to_res: 0
% 4.53/4.73 % inst_dismatching_checking_time: 0.002
% 4.53/4.73
% 4.53/4.73 % ------ Resolution
% 4.53/4.73
% 4.53/4.73 % res_num_of_clauses: 47774
% 4.53/4.73 % res_num_in_passive: 45998
% 4.53/4.73 % res_num_in_active: 1712
% 4.53/4.73 % res_num_of_loops: 2000
% 4.53/4.73 % res_forward_subset_subsumed: 1049
% 4.53/4.73 % res_backward_subset_subsumed: 4
% 4.53/4.73 % res_forward_subsumed: 344
% 4.53/4.73 % res_backward_subsumed: 16
% 4.53/4.73 % res_forward_subsumption_resolution: 15
% 4.53/4.73 % res_backward_subsumption_resolution: 2
% 4.53/4.73 % res_clause_to_clause_subsumption: 37872
% 4.53/4.73 % res_orphan_elimination: 0
% 4.53/4.73 % res_tautology_del: 16
% 4.53/4.73 % res_num_eq_res_simplified: 0
% 4.53/4.73 % res_num_sel_changes: 0
% 4.53/4.73 % res_moves_from_active_to_pass: 0
% 4.53/4.73
% 4.53/4.73 % Status Unsatisfiable
% 4.53/4.73 % SZS status Theorem
% 4.53/4.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------