%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:57:29 AM UTC 2026
% Result : Theorem 228.15s 233.42s
% Output : Proof 228.72s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('SET006+0.ax',equal_set) ).
fof(power_set,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('SET006+0.ax',power_set) ).
fof(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('SET006+0.ax',intersection) ).
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('SET006+0.ax',union) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('SET006+0.ax',empty_set) ).
fof(difference,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('SET006+0.ax',difference) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('SET006+0.ax',singleton) ).
fof(unordered_pair,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = B
| X = A ) ),
file('SET006+0.ax',unordered_pair) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('SET006+0.ax',sum) ).
fof(product,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
file('SET006+0.ax',product) ).
fof(ordinal_number,axiom,
! [A] :
( member(A,on)
<=> ( ! [X] :
( member(X,A)
=> subset(X,A) )
& strict_well_order(member_predicate,A)
& set(A) ) ),
file('SET006+4.ax',ordinal_number) ).
fof(strict_well_order,axiom,
! [R,E] :
( strict_well_order(R,E)
<=> ( ! [A] :
( ( ? [X] : member(X,A)
& subset(A,E) )
=> ? [Y] : least(Y,R,A) )
& strict_order(R,E) ) ),
file('SET006+4.ax',strict_well_order) ).
fof(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> ( apply(R,M,X)
| M = X ) )
& member(M,E) ) ),
file('SET006+4.ax',least) ).
fof(rel_member,axiom,
! [X,Y] :
( apply(member_predicate,X,Y)
<=> member(X,Y) ),
file('SET006+4.ax',rel_member) ).
fof(strict_order,axiom,
! [R,E] :
( strict_order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ~ ( apply(R,Y,X)
& apply(R,X,Y) ) ) ) ),
file('SET006+4.ax',strict_order) ).
fof(set_member,axiom,
! [X] :
( set(X)
=> ! [Y] :
( member(Y,X)
=> set(Y) ) ),
file('SET006+4.ax',set_member) ).
fof(initial_segment,axiom,
! [X,R,A,Y] :
( member(Y,initial_segment(X,R,A))
<=> ( apply(R,Y,X)
& member(Y,A) ) ),
file('SET006+4.ax',initial_segment) ).
fof(successor,axiom,
! [A,X] :
( member(X,suc(A))
<=> member(X,union(A,singleton(A))) ),
file('SET006+4.ax',successor) ).
fof(thV2,conjecture,
! [A] :
( member(A,on)
=> ~ member(A,A) ),
file('theBenchmark.p',thV2) ).
fof(f_1_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [X] :
( ~ member(X,B)
& member(X,A) ) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( subset(U_3,U_2)
| ? [U_1] :
( ~ member(U_1,U_2)
& member(U_1,U_3) ) )
& ( ! [U_0] :
( member(U_0,U_2)
| ~ member(U_0,U_3) )
| ~ subset(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ? [U_1] :
( ~ member(U_1,U_5)
& member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ( ~ member(sK1(U_7,U_5),U_5)
& member(sK1(U_7,U_5),U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subset(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK1(U_7,U_5),U_7)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ member(sK1(U_7,U_5),U_5)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [A,B] :
( ( equal_set(A,B)
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(fof_nnf,[status(thm)],[equal_set]) ).
fof(f_2_2,plain,
! [U_9,U_8] :
( ( equal_set(U_9,U_8)
| ~ subset(U_8,U_9)
| ~ subset(U_9,U_8) )
& ( ( subset(U_8,U_9)
& subset(U_9,U_8) )
| ~ equal_set(U_9,U_8) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( ( subset(U_10,U_12)
& subset(U_12,U_10) )
| ~ equal_set(U_12,U_10) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_12,U_10)
| ~ equal_set(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( subset(U_10,U_12)
| ~ equal_set(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X,A] :
( ( member(X,power_set(A))
| ~ subset(X,A) )
& ( subset(X,A)
| ~ member(X,power_set(A)) ) ),
inference(fof_nnf,[status(thm)],[power_set]) ).
fof(f_3_2,plain,
! [U_15,U_14] :
( ( member(U_15,power_set(U_14))
| ~ subset(U_15,U_14) )
& ( subset(U_15,U_14)
| ~ member(U_15,power_set(U_14)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_19,U_17] :
( member(U_19,power_set(U_17))
| ~ subset(U_19,U_17) )
& ! [U_18,U_16] :
( subset(U_18,U_16)
| ~ member(U_18,power_set(U_16)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(U_18,U_16)
| ~ member(U_18,power_set(U_16)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( member(U_19,power_set(U_17))
| ~ subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X,A,B] :
( ( member(X,intersection(A,B))
| ~ member(X,B)
| ~ member(X,A) )
& ( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(fof_nnf,[status(thm)],[intersection]) ).
fof(f_4_2,plain,
! [U_22,U_21,U_20] :
( ( member(U_22,intersection(U_21,U_20))
| ~ member(U_22,U_20)
| ~ member(U_22,U_21) )
& ( ( member(U_22,U_20)
& member(U_22,U_21) )
| ~ member(U_22,intersection(U_21,U_20)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_28,U_26,U_24] :
( member(U_28,intersection(U_26,U_24))
| ~ member(U_28,U_24)
| ~ member(U_28,U_26) )
& ! [U_27,U_25,U_23] :
( ( member(U_27,U_23)
& member(U_27,U_25) )
| ~ member(U_27,intersection(U_25,U_23)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_27,U_25)
| ~ member(U_27,intersection(U_25,U_23)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( member(U_27,U_23)
| ~ member(U_27,intersection(U_25,U_23)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( member(U_28,intersection(U_26,U_24))
| ~ member(U_28,U_24)
| ~ member(U_28,U_26) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X,A,B] :
( ( member(X,union(A,B))
| ( ~ member(X,B)
& ~ member(X,A) ) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(fof_nnf,[status(thm)],[union]) ).
fof(f_5_2,plain,
! [U_31,U_30,U_29] :
( ( member(U_31,union(U_30,U_29))
| ( ~ member(U_31,U_29)
& ~ member(U_31,U_30) ) )
& ( member(U_31,U_29)
| member(U_31,U_30)
| ~ member(U_31,union(U_30,U_29)) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_37,U_35,U_33] :
( member(U_37,union(U_35,U_33))
| ( ~ member(U_37,U_33)
& ~ member(U_37,U_35) ) )
& ! [U_36,U_34,U_32] :
( member(U_36,U_32)
| member(U_36,U_34)
| ~ member(U_36,union(U_34,U_32)) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( member(U_36,U_32)
| member(U_36,U_34)
| ~ member(U_36,union(U_34,U_32)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( ~ member(U_37,U_35)
| member(U_37,union(U_35,U_33)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( ~ member(U_37,U_33)
| member(U_37,union(U_35,U_33)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [X] : ~ member(X,empty_set),
inference(fof_nnf,[status(thm)],[empty_set]) ).
fof(f_6_2,plain,
! [U_38] : ~ member(U_38,empty_set),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
~ member(U_38,empty_set),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B,A,E] :
( ( member(B,difference(E,A))
| member(B,A)
| ~ member(B,E) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(fof_nnf,[status(thm)],[difference]) ).
fof(f_7_2,plain,
! [U_41,U_40,U_39] :
( ( member(U_41,difference(U_39,U_40))
| member(U_41,U_40)
| ~ member(U_41,U_39) )
& ( ( ~ member(U_41,U_40)
& member(U_41,U_39) )
| ~ member(U_41,difference(U_39,U_40)) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_47,U_45,U_43] :
( member(U_47,difference(U_43,U_45))
| member(U_47,U_45)
| ~ member(U_47,U_43) )
& ! [U_46,U_44,U_42] :
( ( ~ member(U_46,U_44)
& member(U_46,U_42) )
| ~ member(U_46,difference(U_42,U_44)) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( member(U_46,U_42)
| ~ member(U_46,difference(U_42,U_44)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ member(U_46,U_44)
| ~ member(U_46,difference(U_42,U_44)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( member(U_47,difference(U_43,U_45))
| member(U_47,U_45)
| ~ member(U_47,U_43) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [X,A] :
( ( member(X,singleton(A))
| X != A )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(fof_nnf,[status(thm)],[singleton]) ).
fof(f_8_2,plain,
! [U_49,U_48] :
( ( member(U_49,singleton(U_48))
| U_49 != U_48 )
& ( U_49 = U_48
| ~ member(U_49,singleton(U_48)) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_53,U_51] :
( member(U_53,singleton(U_51))
| U_53 != U_51 )
& ! [U_52,U_50] :
( U_52 = U_50
| ~ member(U_52,singleton(U_50)) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_52 = U_50
| ~ member(U_52,singleton(U_50)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( member(U_53,singleton(U_51))
| U_53 != U_51 ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [X,A,B] :
( ( member(X,unordered_pair(A,B))
| ( X != B
& X != A ) )
& ( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(fof_nnf,[status(thm)],[unordered_pair]) ).
fof(f_9_2,plain,
! [U_56,U_55,U_54] :
( ( member(U_56,unordered_pair(U_55,U_54))
| ( U_56 != U_54
& U_56 != U_55 ) )
& ( U_56 = U_54
| U_56 = U_55
| ~ member(U_56,unordered_pair(U_55,U_54)) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_62,U_60,U_58] :
( member(U_62,unordered_pair(U_60,U_58))
| ( U_62 != U_58
& U_62 != U_60 ) )
& ! [U_61,U_59,U_57] :
( U_61 = U_57
| U_61 = U_59
| ~ member(U_61,unordered_pair(U_59,U_57)) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_61 = U_57
| U_61 = U_59
| ~ member(U_61,unordered_pair(U_59,U_57)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( U_62 != U_60
| member(U_62,unordered_pair(U_60,U_58)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( U_62 != U_58
| member(U_62,unordered_pair(U_60,U_58)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [X,A] :
( ( member(X,sum(A))
| ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) ) )
& ( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(fof_nnf,[status(thm)],[sum]) ).
fof(f_10_2,plain,
! [U_66,U_65] :
( ( member(U_66,sum(U_65))
| ! [U_64] :
( ~ member(U_66,U_64)
| ~ member(U_64,U_65) ) )
& ( ? [U_63] :
( member(U_66,U_63)
& member(U_63,U_65) )
| ~ member(U_66,sum(U_65)) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_70,U_68] :
( member(U_70,sum(U_68))
| ! [U_64] :
( ~ member(U_70,U_64)
| ~ member(U_64,U_68) ) )
& ! [U_69,U_67] :
( ? [U_63] :
( member(U_69,U_63)
& member(U_63,U_67) )
| ~ member(U_69,sum(U_67)) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_70,U_68] :
( member(U_70,sum(U_68))
| ! [U_64] :
( ~ member(U_70,U_64)
| ~ member(U_64,U_68) ) )
& ! [U_69,U_67] :
( ( member(U_69,sK2(U_69,U_67))
& member(sK2(U_69,U_67),U_67) )
| ~ member(U_69,sum(U_67)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_63,sK2(U_69,U_67))],[f_10_3]) ).
cnf(f_10_5,plain,
( member(sK2(U_69,U_67),U_67)
| ~ member(U_69,sum(U_67)) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( member(U_69,sK2(U_69,U_67))
| ~ member(U_69,sum(U_67)) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_7,plain,
( member(U_70,sum(U_68))
| ~ member(U_70,U_64)
| ~ member(U_64,U_68) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [X,A] :
( ( member(X,product(A))
| ? [Y] :
( ~ member(X,Y)
& member(Y,A) ) )
& ( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(fof_nnf,[status(thm)],[product]) ).
fof(f_11_2,plain,
! [U_74,U_73] :
( ( member(U_74,product(U_73))
| ? [U_72] :
( ~ member(U_74,U_72)
& member(U_72,U_73) ) )
& ( ! [U_71] :
( member(U_74,U_71)
| ~ member(U_71,U_73) )
| ~ member(U_74,product(U_73)) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_78,U_76] :
( member(U_78,product(U_76))
| ? [U_72] :
( ~ member(U_78,U_72)
& member(U_72,U_76) ) )
& ! [U_77,U_75] :
( ! [U_71] :
( member(U_77,U_71)
| ~ member(U_71,U_75) )
| ~ member(U_77,product(U_75)) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_78,U_76] :
( member(U_78,product(U_76))
| ( ~ member(U_78,sK3(U_78,U_76))
& member(sK3(U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ! [U_71] :
( member(U_77,U_71)
| ~ member(U_71,U_75) )
| ~ member(U_77,product(U_75)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_72,sK3(U_78,U_76))],[f_11_3]) ).
cnf(f_11_5,plain,
( member(U_77,U_71)
| ~ member(U_71,U_75)
| ~ member(U_77,product(U_75)) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( member(sK3(U_78,U_76),U_76)
| member(U_78,product(U_76)) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_7,plain,
( ~ member(U_78,sK3(U_78,U_76))
| member(U_78,product(U_76)) ),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
! [A] :
( ( member(A,on)
| ? [X] :
( ~ subset(X,A)
& member(X,A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A) )
& ( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(fof_nnf,[status(thm)],[ordinal_number]) ).
fof(f_12_2,plain,
! [U_81] :
( ( member(U_81,on)
| ? [U_80] :
( ~ subset(U_80,U_81)
& member(U_80,U_81) )
| ~ strict_well_order(member_predicate,U_81)
| ~ set(U_81) )
& ( ( ! [U_79] :
( subset(U_79,U_81)
| ~ member(U_79,U_81) )
& strict_well_order(member_predicate,U_81)
& set(U_81) )
| ~ member(U_81,on) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_83] :
( member(U_83,on)
| ? [U_80] :
( ~ subset(U_80,U_83)
& member(U_80,U_83) )
| ~ strict_well_order(member_predicate,U_83)
| ~ set(U_83) )
& ! [U_82] :
( ( ! [U_79] :
( subset(U_79,U_82)
| ~ member(U_79,U_82) )
& strict_well_order(member_predicate,U_82)
& set(U_82) )
| ~ member(U_82,on) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_83] :
( member(U_83,on)
| ( ~ subset(sK4(U_83),U_83)
& member(sK4(U_83),U_83) )
| ~ strict_well_order(member_predicate,U_83)
| ~ set(U_83) )
& ! [U_82] :
( ( ! [U_79] :
( subset(U_79,U_82)
| ~ member(U_79,U_82) )
& strict_well_order(member_predicate,U_82)
& set(U_82) )
| ~ member(U_82,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4(U_83))],[f_12_3]) ).
cnf(f_12_5,plain,
( set(U_82)
| ~ member(U_82,on) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( strict_well_order(member_predicate,U_82)
| ~ member(U_82,on) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
( subset(U_79,U_82)
| ~ member(U_79,U_82)
| ~ member(U_82,on) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_8,plain,
( member(sK4(U_83),U_83)
| ~ strict_well_order(member_predicate,U_83)
| ~ set(U_83)
| member(U_83,on) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_9,plain,
( ~ subset(sK4(U_83),U_83)
| ~ strict_well_order(member_predicate,U_83)
| ~ set(U_83)
| member(U_83,on) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [R,E] :
( ( strict_well_order(R,E)
| ? [A] :
( ! [Y] : ~ least(Y,R,A)
& ? [X] : member(X,A)
& subset(A,E) )
| ~ strict_order(R,E) )
& ( ( ! [A] :
( ? [Y] : least(Y,R,A)
| ! [X] : ~ member(X,A)
| ~ subset(A,E) )
& strict_order(R,E) )
| ~ strict_well_order(R,E) ) ),
inference(fof_nnf,[status(thm)],[strict_well_order]) ).
fof(f_13_2,plain,
! [U_91,U_90] :
( ( strict_well_order(U_91,U_90)
| ? [U_89] :
( ! [U_88] : ~ least(U_88,U_91,U_89)
& ? [U_87] : member(U_87,U_89)
& subset(U_89,U_90) )
| ~ strict_order(U_91,U_90) )
& ( ( ! [U_86] :
( ? [U_85] : least(U_85,U_91,U_86)
| ! [U_84] : ~ member(U_84,U_86)
| ~ subset(U_86,U_90) )
& strict_order(U_91,U_90) )
| ~ strict_well_order(U_91,U_90) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_95,U_93] :
( strict_well_order(U_95,U_93)
| ? [U_89] :
( ! [U_88] : ~ least(U_88,U_95,U_89)
& ? [U_87] : member(U_87,U_89)
& subset(U_89,U_93) )
| ~ strict_order(U_95,U_93) )
& ! [U_94,U_92] :
( ( ! [U_86] :
( ? [U_85] : least(U_85,U_94,U_86)
| ! [U_84] : ~ member(U_84,U_86)
| ~ subset(U_86,U_92) )
& strict_order(U_94,U_92) )
| ~ strict_well_order(U_94,U_92) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_95,U_93] :
( strict_well_order(U_95,U_93)
| ? [U_89] :
( ! [U_88] : ~ least(U_88,U_95,U_89)
& ? [U_87] : member(U_87,U_89)
& subset(U_89,U_93) )
| ~ strict_order(U_95,U_93) )
& ! [U_94,U_92] :
( ( ! [U_86] :
( least(sK5(U_94,U_92,U_86),U_94,U_86)
| ! [U_84] : ~ member(U_84,U_86)
| ~ subset(U_86,U_92) )
& strict_order(U_94,U_92) )
| ~ strict_well_order(U_94,U_92) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_85,sK5(U_94,U_92,U_86))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_95,U_93] :
( strict_well_order(U_95,U_93)
| ( ! [U_88] : ~ least(U_88,U_95,sK6(U_95,U_93))
& ? [U_87] : member(U_87,sK6(U_95,U_93))
& subset(sK6(U_95,U_93),U_93) )
| ~ strict_order(U_95,U_93) )
& ! [U_94,U_92] :
( ( ! [U_86] :
( least(sK5(U_94,U_92,U_86),U_94,U_86)
| ! [U_84] : ~ member(U_84,U_86)
| ~ subset(U_86,U_92) )
& strict_order(U_94,U_92) )
| ~ strict_well_order(U_94,U_92) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_89,sK6(U_95,U_93))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_95,U_93] :
( strict_well_order(U_95,U_93)
| ( ! [U_88] : ~ least(U_88,U_95,sK6(U_95,U_93))
& member(sK7(U_95,U_93),sK6(U_95,U_93))
& subset(sK6(U_95,U_93),U_93) )
| ~ strict_order(U_95,U_93) )
& ! [U_94,U_92] :
( ( ! [U_86] :
( least(sK5(U_94,U_92,U_86),U_94,U_86)
| ! [U_84] : ~ member(U_84,U_86)
| ~ subset(U_86,U_92) )
& strict_order(U_94,U_92) )
| ~ strict_well_order(U_94,U_92) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_87,sK7(U_95,U_93))],[f_13_5]) ).
cnf(f_13_7,plain,
( strict_order(U_94,U_92)
| ~ strict_well_order(U_94,U_92) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,plain,
( least(sK5(U_94,U_92,U_86),U_94,U_86)
| ~ member(U_84,U_86)
| ~ subset(U_86,U_92)
| ~ strict_well_order(U_94,U_92) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,plain,
( subset(sK6(U_95,U_93),U_93)
| ~ strict_order(U_95,U_93)
| strict_well_order(U_95,U_93) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,plain,
( member(sK7(U_95,U_93),sK6(U_95,U_93))
| ~ strict_order(U_95,U_93)
| strict_well_order(U_95,U_93) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,plain,
( ~ least(U_88,U_95,sK6(U_95,U_93))
| ~ strict_order(U_95,U_93)
| strict_well_order(U_95,U_93) ),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_1,plain,
! [R,E,M] :
( ( least(M,R,E)
| ? [X] :
( ~ apply(R,M,X)
& M != X
& member(X,E) )
| ~ member(M,E) )
& ( ( ! [X] :
( apply(R,M,X)
| M = X
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[least]) ).
fof(f_14_2,plain,
! [U_100,U_99,U_98] :
( ( least(U_98,U_100,U_99)
| ? [U_97] :
( ~ apply(U_100,U_98,U_97)
& U_98 != U_97
& member(U_97,U_99) )
| ~ member(U_98,U_99) )
& ( ( ! [U_96] :
( apply(U_100,U_98,U_96)
| U_98 = U_96
| ~ member(U_96,U_99) )
& member(U_98,U_99) )
| ~ least(U_98,U_100,U_99) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_106,U_104,U_102] :
( least(U_102,U_106,U_104)
| ? [U_97] :
( ~ apply(U_106,U_102,U_97)
& U_102 != U_97
& member(U_97,U_104) )
| ~ member(U_102,U_104) )
& ! [U_105,U_103,U_101] :
( ( ! [U_96] :
( apply(U_105,U_101,U_96)
| U_101 = U_96
| ~ member(U_96,U_103) )
& member(U_101,U_103) )
| ~ least(U_101,U_105,U_103) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_106,U_104,U_102] :
( least(U_102,U_106,U_104)
| ( ~ apply(U_106,U_102,sK8(U_106,U_104,U_102))
& U_102 != sK8(U_106,U_104,U_102)
& member(sK8(U_106,U_104,U_102),U_104) )
| ~ member(U_102,U_104) )
& ! [U_105,U_103,U_101] :
( ( ! [U_96] :
( apply(U_105,U_101,U_96)
| U_101 = U_96
| ~ member(U_96,U_103) )
& member(U_101,U_103) )
| ~ least(U_101,U_105,U_103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_97,sK8(U_106,U_104,U_102))],[f_14_3]) ).
cnf(f_14_5,plain,
( member(U_101,U_103)
| ~ least(U_101,U_105,U_103) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( apply(U_105,U_101,U_96)
| U_101 = U_96
| ~ member(U_96,U_103)
| ~ least(U_101,U_105,U_103) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_7,plain,
( member(sK8(U_106,U_104,U_102),U_104)
| ~ member(U_102,U_104)
| least(U_102,U_106,U_104) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_8,plain,
( U_102 != sK8(U_106,U_104,U_102)
| ~ member(U_102,U_104)
| least(U_102,U_106,U_104) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_9,plain,
( ~ apply(U_106,U_102,sK8(U_106,U_104,U_102))
| ~ member(U_102,U_104)
| least(U_102,U_106,U_104) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [X,Y] :
( ( apply(member_predicate,X,Y)
| ~ member(X,Y) )
& ( member(X,Y)
| ~ apply(member_predicate,X,Y) ) ),
inference(fof_nnf,[status(thm)],[rel_member]) ).
fof(f_15_2,plain,
! [U_108,U_107] :
( ( apply(member_predicate,U_108,U_107)
| ~ member(U_108,U_107) )
& ( member(U_108,U_107)
| ~ apply(member_predicate,U_108,U_107) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_112,U_110] :
( apply(member_predicate,U_112,U_110)
| ~ member(U_112,U_110) )
& ! [U_111,U_109] :
( member(U_111,U_109)
| ~ apply(member_predicate,U_111,U_109) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( member(U_111,U_109)
| ~ apply(member_predicate,U_111,U_109) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( apply(member_predicate,U_112,U_110)
| ~ member(U_112,U_110) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [R,E] :
( ( strict_order(R,E)
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X,Y] :
( apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) ) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X,Y] :
( ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) ) )
| ~ strict_order(R,E) ) ),
inference(fof_nnf,[status(thm)],[strict_order]) ).
fof(f_16_2,plain,
! [U_124,U_123] :
( ( strict_order(U_124,U_123)
| ? [U_122,U_121,U_120] :
( ~ apply(U_124,U_122,U_120)
& apply(U_124,U_121,U_120)
& apply(U_124,U_122,U_121)
& member(U_120,U_123)
& member(U_121,U_123)
& member(U_122,U_123) )
| ? [U_119,U_118] :
( apply(U_124,U_118,U_119)
& apply(U_124,U_119,U_118)
& member(U_118,U_123)
& member(U_119,U_123) ) )
& ( ( ! [U_117,U_116,U_115] :
( apply(U_124,U_117,U_115)
| ~ apply(U_124,U_116,U_115)
| ~ apply(U_124,U_117,U_116)
| ~ member(U_115,U_123)
| ~ member(U_116,U_123)
| ~ member(U_117,U_123) )
& ! [U_114,U_113] :
( ~ apply(U_124,U_113,U_114)
| ~ apply(U_124,U_114,U_113)
| ~ member(U_113,U_123)
| ~ member(U_114,U_123) ) )
| ~ strict_order(U_124,U_123) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_128,U_126] :
( strict_order(U_128,U_126)
| ? [U_122,U_121,U_120] :
( ~ apply(U_128,U_122,U_120)
& apply(U_128,U_121,U_120)
& apply(U_128,U_122,U_121)
& member(U_120,U_126)
& member(U_121,U_126)
& member(U_122,U_126) )
| ? [U_119,U_118] :
( apply(U_128,U_118,U_119)
& apply(U_128,U_119,U_118)
& member(U_118,U_126)
& member(U_119,U_126) ) )
& ! [U_127,U_125] :
( ( ! [U_117,U_116,U_115] :
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125) )
& ! [U_114,U_113] :
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125) ) )
| ~ strict_order(U_127,U_125) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_128,U_126] :
( strict_order(U_128,U_126)
| ? [U_122,U_121,U_120] :
( ~ apply(U_128,U_122,U_120)
& apply(U_128,U_121,U_120)
& apply(U_128,U_122,U_121)
& member(U_120,U_126)
& member(U_121,U_126)
& member(U_122,U_126) )
| ? [U_118] :
( apply(U_128,U_118,sK9(U_128,U_126))
& apply(U_128,sK9(U_128,U_126),U_118)
& member(U_118,U_126)
& member(sK9(U_128,U_126),U_126) ) )
& ! [U_127,U_125] :
( ( ! [U_117,U_116,U_115] :
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125) )
& ! [U_114,U_113] :
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125) ) )
| ~ strict_order(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_119,sK9(U_128,U_126))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_128,U_126] :
( strict_order(U_128,U_126)
| ? [U_122,U_121,U_120] :
( ~ apply(U_128,U_122,U_120)
& apply(U_128,U_121,U_120)
& apply(U_128,U_122,U_121)
& member(U_120,U_126)
& member(U_121,U_126)
& member(U_122,U_126) )
| ( apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
& apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
& member(sK10(U_128,U_126),U_126)
& member(sK9(U_128,U_126),U_126) ) )
& ! [U_127,U_125] :
( ( ! [U_117,U_116,U_115] :
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125) )
& ! [U_114,U_113] :
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125) ) )
| ~ strict_order(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_118,sK10(U_128,U_126))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_128,U_126] :
( strict_order(U_128,U_126)
| ? [U_121,U_120] :
( ~ apply(U_128,sK11(U_128,U_126),U_120)
& apply(U_128,U_121,U_120)
& apply(U_128,sK11(U_128,U_126),U_121)
& member(U_120,U_126)
& member(U_121,U_126)
& member(sK11(U_128,U_126),U_126) )
| ( apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
& apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
& member(sK10(U_128,U_126),U_126)
& member(sK9(U_128,U_126),U_126) ) )
& ! [U_127,U_125] :
( ( ! [U_117,U_116,U_115] :
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125) )
& ! [U_114,U_113] :
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125) ) )
| ~ strict_order(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_122,sK11(U_128,U_126))],[f_16_5]) ).
fof(f_16_7,plain,
( ! [U_128,U_126] :
( strict_order(U_128,U_126)
| ? [U_120] :
( ~ apply(U_128,sK11(U_128,U_126),U_120)
& apply(U_128,sK12(U_128,U_126),U_120)
& apply(U_128,sK11(U_128,U_126),sK12(U_128,U_126))
& member(U_120,U_126)
& member(sK12(U_128,U_126),U_126)
& member(sK11(U_128,U_126),U_126) )
| ( apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
& apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
& member(sK10(U_128,U_126),U_126)
& member(sK9(U_128,U_126),U_126) ) )
& ! [U_127,U_125] :
( ( ! [U_117,U_116,U_115] :
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125) )
& ! [U_114,U_113] :
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125) ) )
| ~ strict_order(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_121,sK12(U_128,U_126))],[f_16_6]) ).
fof(f_16_8,plain,
( ! [U_128,U_126] :
( strict_order(U_128,U_126)
| ( ~ apply(U_128,sK11(U_128,U_126),sK13(U_128,U_126))
& apply(U_128,sK12(U_128,U_126),sK13(U_128,U_126))
& apply(U_128,sK11(U_128,U_126),sK12(U_128,U_126))
& member(sK13(U_128,U_126),U_126)
& member(sK12(U_128,U_126),U_126)
& member(sK11(U_128,U_126),U_126) )
| ( apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
& apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
& member(sK10(U_128,U_126),U_126)
& member(sK9(U_128,U_126),U_126) ) )
& ! [U_127,U_125] :
( ( ! [U_117,U_116,U_115] :
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125) )
& ! [U_114,U_113] :
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125) ) )
| ~ strict_order(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_120,sK13(U_128,U_126))],[f_16_7]) ).
cnf(f_16_9,plain,
( ~ apply(U_127,U_113,U_114)
| ~ apply(U_127,U_114,U_113)
| ~ member(U_113,U_125)
| ~ member(U_114,U_125)
| ~ strict_order(U_127,U_125) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,plain,
( apply(U_127,U_117,U_115)
| ~ apply(U_127,U_116,U_115)
| ~ apply(U_127,U_117,U_116)
| ~ member(U_115,U_125)
| ~ member(U_116,U_125)
| ~ member(U_117,U_125)
| ~ strict_order(U_127,U_125) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_11,plain,
( member(sK11(U_128,U_126),U_126)
| member(sK9(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,plain,
( member(sK12(U_128,U_126),U_126)
| member(sK9(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_13,plain,
( member(sK13(U_128,U_126),U_126)
| member(sK9(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,plain,
( member(sK11(U_128,U_126),U_126)
| member(sK10(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_15,plain,
( member(sK12(U_128,U_126),U_126)
| member(sK10(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_16,plain,
( member(sK13(U_128,U_126),U_126)
| member(sK10(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_17,plain,
( apply(U_128,sK11(U_128,U_126),sK12(U_128,U_126))
| member(sK9(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_18,plain,
( apply(U_128,sK12(U_128,U_126),sK13(U_128,U_126))
| member(sK9(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_19,plain,
( ~ apply(U_128,sK11(U_128,U_126),sK13(U_128,U_126))
| member(sK9(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_20,plain,
( apply(U_128,sK11(U_128,U_126),sK12(U_128,U_126))
| member(sK10(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_21,plain,
( apply(U_128,sK12(U_128,U_126),sK13(U_128,U_126))
| member(sK10(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_22,plain,
( ~ apply(U_128,sK11(U_128,U_126),sK13(U_128,U_126))
| member(sK10(U_128,U_126),U_126)
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_23,plain,
( member(sK11(U_128,U_126),U_126)
| apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_24,plain,
( member(sK12(U_128,U_126),U_126)
| apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_25,plain,
( member(sK13(U_128,U_126),U_126)
| apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_26,plain,
( member(sK11(U_128,U_126),U_126)
| apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_27,plain,
( member(sK12(U_128,U_126),U_126)
| apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_28,plain,
( member(sK13(U_128,U_126),U_126)
| apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_29,plain,
( apply(U_128,sK11(U_128,U_126),sK12(U_128,U_126))
| apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_30,plain,
( apply(U_128,sK12(U_128,U_126),sK13(U_128,U_126))
| apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_31,plain,
( ~ apply(U_128,sK11(U_128,U_126),sK13(U_128,U_126))
| apply(U_128,sK9(U_128,U_126),sK10(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_32,plain,
( apply(U_128,sK11(U_128,U_126),sK12(U_128,U_126))
| apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_33,plain,
( apply(U_128,sK12(U_128,U_126),sK13(U_128,U_126))
| apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_34,plain,
( ~ apply(U_128,sK11(U_128,U_126),sK13(U_128,U_126))
| apply(U_128,sK10(U_128,U_126),sK9(U_128,U_126))
| strict_order(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
fof(f_17_1,plain,
! [X] :
( ! [Y] :
( set(Y)
| ~ member(Y,X) )
| ~ set(X) ),
inference(fof_nnf,[status(thm)],[set_member]) ).
fof(f_17_2,plain,
! [U_130] :
( ! [U_129] :
( set(U_129)
| ~ member(U_129,U_130) )
| ~ set(U_130) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( set(U_129)
| ~ member(U_129,U_130)
| ~ set(U_130) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [X,R,A,Y] :
( ( member(Y,initial_segment(X,R,A))
| ~ apply(R,Y,X)
| ~ member(Y,A) )
& ( ( apply(R,Y,X)
& member(Y,A) )
| ~ member(Y,initial_segment(X,R,A)) ) ),
inference(fof_nnf,[status(thm)],[initial_segment]) ).
fof(f_18_2,plain,
! [U_134,U_133,U_132,U_131] :
( ( member(U_131,initial_segment(U_134,U_133,U_132))
| ~ apply(U_133,U_131,U_134)
| ~ member(U_131,U_132) )
& ( ( apply(U_133,U_131,U_134)
& member(U_131,U_132) )
| ~ member(U_131,initial_segment(U_134,U_133,U_132)) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_142,U_140,U_138,U_136] :
( member(U_136,initial_segment(U_142,U_140,U_138))
| ~ apply(U_140,U_136,U_142)
| ~ member(U_136,U_138) )
& ! [U_141,U_139,U_137,U_135] :
( ( apply(U_139,U_135,U_141)
& member(U_135,U_137) )
| ~ member(U_135,initial_segment(U_141,U_139,U_137)) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( member(U_135,U_137)
| ~ member(U_135,initial_segment(U_141,U_139,U_137)) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( apply(U_139,U_135,U_141)
| ~ member(U_135,initial_segment(U_141,U_139,U_137)) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( member(U_136,initial_segment(U_142,U_140,U_138))
| ~ apply(U_140,U_136,U_142)
| ~ member(U_136,U_138) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,X] :
( ( member(X,suc(A))
| ~ member(X,union(A,singleton(A))) )
& ( member(X,union(A,singleton(A)))
| ~ member(X,suc(A)) ) ),
inference(fof_nnf,[status(thm)],[successor]) ).
fof(f_19_2,plain,
! [U_144,U_143] :
( ( member(U_143,suc(U_144))
| ~ member(U_143,union(U_144,singleton(U_144))) )
& ( member(U_143,union(U_144,singleton(U_144)))
| ~ member(U_143,suc(U_144)) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_148,U_146] :
( member(U_146,suc(U_148))
| ~ member(U_146,union(U_148,singleton(U_148))) )
& ! [U_147,U_145] :
( member(U_145,union(U_147,singleton(U_147)))
| ~ member(U_145,suc(U_147)) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( member(U_145,union(U_147,singleton(U_147)))
| ~ member(U_145,suc(U_147)) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( member(U_146,suc(U_148))
| ~ member(U_146,union(U_148,singleton(U_148))) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,negated_conjecture,
~ ! [A] :
( member(A,on)
=> ~ member(A,A) ),
inference(negate,[status(cth)],[thV2]) ).
fof(f_20_2,negated_conjecture,
? [A] :
( member(A,A)
& member(A,on) ),
inference(fof_nnf,[status(thm)],[f_20_1]) ).
fof(f_20_3,negated_conjecture,
? [U_149] :
( member(U_149,U_149)
& member(U_149,on) ),
inference(variable_rename,[status(thm)],[f_20_2]) ).
fof(f_20_4,negated_conjecture,
( member(sK14,sK14)
& member(sK14,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_149,sK14)],[f_20_3]) ).
cnf(f_20_5,negated_conjecture,
member(sK14,on),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,negated_conjecture,
member(sK14,sK14),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( power_set(Eq_x_0) = power_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( intersection(Eq_x_0,Eq_x_1) = intersection(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( union(Eq_x_0,Eq_x_1) = union(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( difference(Eq_x_0,Eq_x_1) = difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sum(Eq_x_0) = sum(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( product(Eq_x_0) = product(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( initial_segment(Eq_x_0,Eq_x_1,Eq_x_2) = initial_segment(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( suc(Eq_x_0) = suc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( equal_set(Eq_y_0,Eq_y_1)
| ~ equal_set(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( set(Eq_y_0)
| ~ set(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( strict_well_order(Eq_y_0,Eq_y_1)
| ~ strict_well_order(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( strict_order(Eq_y_0,Eq_y_1)
| ~ strict_order(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( least(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ least(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( apply(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ apply(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n016.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 19 23:05:26 UTC 2026
% 0.10/5.38 % CPUTime :
% 228.15/233.42 % SZS status Theorem for theBenchmark
% 228.15/233.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------