%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET798+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 : n002.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 08:57:28 AM UTC 2026
% Result : Theorem 25.78s 26.05s
% Output : Proof 25.90s
% 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(order,axiom,
! [R,E] :
( 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) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('SET006+3.ax',order) ).
fof(total_order,axiom,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( apply(R,Y,X)
| apply(R,X,Y) ) )
& order(R,E) ) ),
file('SET006+3.ax',total_order) ).
fof(upper_bound,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
file('SET006+3.ax',upper_bound) ).
fof(lower_bound,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('SET006+3.ax',lower_bound) ).
fof(greatest,axiom,
! [R,E,M] :
( greatest(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,M) )
& member(M,E) ) ),
file('SET006+3.ax',greatest) ).
fof(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('SET006+3.ax',least) ).
fof(max,axiom,
! [R,E,M] :
( max(M,R,E)
<=> ( ! [X] :
( ( apply(R,M,X)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('SET006+3.ax',max) ).
fof(min,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( ( apply(R,X,M)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('SET006+3.ax',min) ).
fof(least_upper_bound,axiom,
! [A,X,R,E] :
( least_upper_bound(A,X,R,E)
<=> ( ! [M] :
( ( upper_bound(M,R,X)
& member(M,E) )
=> apply(R,A,M) )
& upper_bound(A,R,X)
& member(A,X) ) ),
file('SET006+3.ax',least_upper_bound) ).
fof(greatest_lower_bound,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( ! [M] :
( ( lower_bound(M,R,X)
& member(M,E) )
=> apply(R,M,A) )
& lower_bound(A,R,X)
& member(A,X) ) ),
file('SET006+3.ax',greatest_lower_bound) ).
fof(thIV10,conjecture,
! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
file('theBenchmark.p',thIV10) ).
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,
! [R,E] :
( ( 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] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] :
( ~ apply(R,X,X)
& 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] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) )
| ~ order(R,E) ) ),
inference(fof_nnf,[status(thm)],[order]) ).
fof(f_12_2,plain,
! [U_92,U_91] :
( ( order(U_92,U_91)
| ? [U_90,U_89,U_88] :
( ~ apply(U_92,U_90,U_88)
& apply(U_92,U_89,U_88)
& apply(U_92,U_90,U_89)
& member(U_88,U_91)
& member(U_89,U_91)
& member(U_90,U_91) )
| ? [U_87,U_86] :
( U_87 != U_86
& apply(U_92,U_86,U_87)
& apply(U_92,U_87,U_86)
& member(U_86,U_91)
& member(U_87,U_91) )
| ? [U_85] :
( ~ apply(U_92,U_85,U_85)
& member(U_85,U_91) ) )
& ( ( ! [U_84,U_83,U_82] :
( apply(U_92,U_84,U_82)
| ~ apply(U_92,U_83,U_82)
| ~ apply(U_92,U_84,U_83)
| ~ member(U_82,U_91)
| ~ member(U_83,U_91)
| ~ member(U_84,U_91) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_92,U_80,U_81)
| ~ apply(U_92,U_81,U_80)
| ~ member(U_80,U_91)
| ~ member(U_81,U_91) )
& ! [U_79] :
( apply(U_92,U_79,U_79)
| ~ member(U_79,U_91) ) )
| ~ order(U_92,U_91) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ? [U_90,U_89,U_88] :
( ~ apply(U_96,U_90,U_88)
& apply(U_96,U_89,U_88)
& apply(U_96,U_90,U_89)
& member(U_88,U_94)
& member(U_89,U_94)
& member(U_90,U_94) )
| ? [U_87,U_86] :
( U_87 != U_86
& apply(U_96,U_86,U_87)
& apply(U_96,U_87,U_86)
& member(U_86,U_94)
& member(U_87,U_94) )
| ? [U_85] :
( ~ apply(U_96,U_85,U_85)
& member(U_85,U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ? [U_90,U_89,U_88] :
( ~ apply(U_96,U_90,U_88)
& apply(U_96,U_89,U_88)
& apply(U_96,U_90,U_89)
& member(U_88,U_94)
& member(U_89,U_94)
& member(U_90,U_94) )
| ? [U_87,U_86] :
( U_87 != U_86
& apply(U_96,U_86,U_87)
& apply(U_96,U_87,U_86)
& member(U_86,U_94)
& member(U_87,U_94) )
| ( ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
& member(sK4(U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_85,sK4(U_96,U_94))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ? [U_90,U_89,U_88] :
( ~ apply(U_96,U_90,U_88)
& apply(U_96,U_89,U_88)
& apply(U_96,U_90,U_89)
& member(U_88,U_94)
& member(U_89,U_94)
& member(U_90,U_94) )
| ? [U_86] :
( sK5(U_96,U_94) != U_86
& apply(U_96,U_86,sK5(U_96,U_94))
& apply(U_96,sK5(U_96,U_94),U_86)
& member(U_86,U_94)
& member(sK5(U_96,U_94),U_94) )
| ( ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
& member(sK4(U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_87,sK5(U_96,U_94))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ? [U_90,U_89,U_88] :
( ~ apply(U_96,U_90,U_88)
& apply(U_96,U_89,U_88)
& apply(U_96,U_90,U_89)
& member(U_88,U_94)
& member(U_89,U_94)
& member(U_90,U_94) )
| ( sK5(U_96,U_94) != sK6(U_96,U_94)
& apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
& apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
& member(sK6(U_96,U_94),U_94)
& member(sK5(U_96,U_94),U_94) )
| ( ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
& member(sK4(U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_86,sK6(U_96,U_94))],[f_12_5]) ).
fof(f_12_7,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ? [U_89,U_88] :
( ~ apply(U_96,sK7(U_96,U_94),U_88)
& apply(U_96,U_89,U_88)
& apply(U_96,sK7(U_96,U_94),U_89)
& member(U_88,U_94)
& member(U_89,U_94)
& member(sK7(U_96,U_94),U_94) )
| ( sK5(U_96,U_94) != sK6(U_96,U_94)
& apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
& apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
& member(sK6(U_96,U_94),U_94)
& member(sK5(U_96,U_94),U_94) )
| ( ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
& member(sK4(U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_90,sK7(U_96,U_94))],[f_12_6]) ).
fof(f_12_8,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ? [U_88] :
( ~ apply(U_96,sK7(U_96,U_94),U_88)
& apply(U_96,sK8(U_96,U_94),U_88)
& apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
& member(U_88,U_94)
& member(sK8(U_96,U_94),U_94)
& member(sK7(U_96,U_94),U_94) )
| ( sK5(U_96,U_94) != sK6(U_96,U_94)
& apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
& apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
& member(sK6(U_96,U_94),U_94)
& member(sK5(U_96,U_94),U_94) )
| ( ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
& member(sK4(U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_89,sK8(U_96,U_94))],[f_12_7]) ).
fof(f_12_9,plain,
( ! [U_96,U_94] :
( order(U_96,U_94)
| ( ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
& apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
& apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
& member(sK9(U_96,U_94),U_94)
& member(sK8(U_96,U_94),U_94)
& member(sK7(U_96,U_94),U_94) )
| ( sK5(U_96,U_94) != sK6(U_96,U_94)
& apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
& apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
& member(sK6(U_96,U_94),U_94)
& member(sK5(U_96,U_94),U_94) )
| ( ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
& member(sK4(U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_84,U_83,U_82] :
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93) )
& ! [U_81,U_80] :
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93) )
& ! [U_79] :
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93) ) )
| ~ order(U_95,U_93) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_88,sK9(U_96,U_94))],[f_12_8]) ).
cnf(f_12_10,plain,
( apply(U_95,U_79,U_79)
| ~ member(U_79,U_93)
| ~ order(U_95,U_93) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_11,plain,
( U_81 = U_80
| ~ apply(U_95,U_80,U_81)
| ~ apply(U_95,U_81,U_80)
| ~ member(U_80,U_93)
| ~ member(U_81,U_93)
| ~ order(U_95,U_93) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_12,plain,
( apply(U_95,U_84,U_82)
| ~ apply(U_95,U_83,U_82)
| ~ apply(U_95,U_84,U_83)
| ~ member(U_82,U_93)
| ~ member(U_83,U_93)
| ~ member(U_84,U_93)
| ~ order(U_95,U_93) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_13,plain,
( member(sK5(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_14,plain,
( member(sK6(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_15,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_16,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_17,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_18,plain,
( member(sK5(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_19,plain,
( member(sK6(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_20,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_21,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_22,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_23,plain,
( member(sK5(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_24,plain,
( member(sK6(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_25,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_26,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_27,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| member(sK4(U_96,U_94),U_94)
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_28,plain,
( member(sK5(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_29,plain,
( member(sK6(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_30,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_31,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_32,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK7(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_33,plain,
( member(sK5(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_34,plain,
( member(sK6(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_35,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_36,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_37,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK8(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_38,plain,
( member(sK5(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_39,plain,
( member(sK6(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_40,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_41,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_42,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| member(sK9(U_96,U_94),U_94)
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_43,plain,
( member(sK5(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_44,plain,
( member(sK6(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_45,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_46,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_47,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_48,plain,
( member(sK5(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_49,plain,
( member(sK6(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_50,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_51,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_52,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| member(sK4(U_96,U_94),U_94)
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_53,plain,
( member(sK5(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_54,plain,
( member(sK6(U_96,U_94),U_94)
| member(sK4(U_96,U_94),U_94)
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_55,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_56,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| member(sK4(U_96,U_94),U_94)
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_57,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| member(sK4(U_96,U_94),U_94)
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_58,plain,
( member(sK5(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_59,plain,
( member(sK6(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_60,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_61,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_62,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK7(U_96,U_94),sK8(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_63,plain,
( member(sK5(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_64,plain,
( member(sK6(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_65,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_66,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_67,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| apply(U_96,sK8(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_68,plain,
( member(sK5(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_69,plain,
( member(sK6(U_96,U_94),U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_70,plain,
( apply(U_96,sK5(U_96,U_94),sK6(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_71,plain,
( apply(U_96,sK6(U_96,U_94),sK5(U_96,U_94))
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_72,plain,
( sK5(U_96,U_94) != sK6(U_96,U_94)
| ~ apply(U_96,sK4(U_96,U_94),sK4(U_96,U_94))
| ~ apply(U_96,sK7(U_96,U_94),sK9(U_96,U_94))
| order(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
fof(f_13_1,plain,
! [R,E] :
( ( total_order(R,E)
| ? [X,Y] :
( ~ apply(R,Y,X)
& ~ apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ~ order(R,E) )
& ( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(fof_nnf,[status(thm)],[total_order]) ).
fof(f_13_2,plain,
! [U_102,U_101] :
( ( total_order(U_102,U_101)
| ? [U_100,U_99] :
( ~ apply(U_102,U_99,U_100)
& ~ apply(U_102,U_100,U_99)
& member(U_99,U_101)
& member(U_100,U_101) )
| ~ order(U_102,U_101) )
& ( ( ! [U_98,U_97] :
( apply(U_102,U_97,U_98)
| apply(U_102,U_98,U_97)
| ~ member(U_97,U_101)
| ~ member(U_98,U_101) )
& order(U_102,U_101) )
| ~ total_order(U_102,U_101) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_106,U_104] :
( total_order(U_106,U_104)
| ? [U_100,U_99] :
( ~ apply(U_106,U_99,U_100)
& ~ apply(U_106,U_100,U_99)
& member(U_99,U_104)
& member(U_100,U_104) )
| ~ order(U_106,U_104) )
& ! [U_105,U_103] :
( ( ! [U_98,U_97] :
( apply(U_105,U_97,U_98)
| apply(U_105,U_98,U_97)
| ~ member(U_97,U_103)
| ~ member(U_98,U_103) )
& order(U_105,U_103) )
| ~ total_order(U_105,U_103) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_106,U_104] :
( total_order(U_106,U_104)
| ? [U_99] :
( ~ apply(U_106,U_99,sK10(U_106,U_104))
& ~ apply(U_106,sK10(U_106,U_104),U_99)
& member(U_99,U_104)
& member(sK10(U_106,U_104),U_104) )
| ~ order(U_106,U_104) )
& ! [U_105,U_103] :
( ( ! [U_98,U_97] :
( apply(U_105,U_97,U_98)
| apply(U_105,U_98,U_97)
| ~ member(U_97,U_103)
| ~ member(U_98,U_103) )
& order(U_105,U_103) )
| ~ total_order(U_105,U_103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_100,sK10(U_106,U_104))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_106,U_104] :
( total_order(U_106,U_104)
| ( ~ apply(U_106,sK11(U_106,U_104),sK10(U_106,U_104))
& ~ apply(U_106,sK10(U_106,U_104),sK11(U_106,U_104))
& member(sK11(U_106,U_104),U_104)
& member(sK10(U_106,U_104),U_104) )
| ~ order(U_106,U_104) )
& ! [U_105,U_103] :
( ( ! [U_98,U_97] :
( apply(U_105,U_97,U_98)
| apply(U_105,U_98,U_97)
| ~ member(U_97,U_103)
| ~ member(U_98,U_103) )
& order(U_105,U_103) )
| ~ total_order(U_105,U_103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_99,sK11(U_106,U_104))],[f_13_4]) ).
cnf(f_13_6,plain,
( order(U_105,U_103)
| ~ total_order(U_105,U_103) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( apply(U_105,U_97,U_98)
| apply(U_105,U_98,U_97)
| ~ member(U_97,U_103)
| ~ member(U_98,U_103)
| ~ total_order(U_105,U_103) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_8,plain,
( member(sK10(U_106,U_104),U_104)
| ~ order(U_106,U_104)
| total_order(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_9,plain,
( member(sK11(U_106,U_104),U_104)
| ~ order(U_106,U_104)
| total_order(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_10,plain,
( ~ apply(U_106,sK10(U_106,U_104),sK11(U_106,U_104))
| ~ order(U_106,U_104)
| total_order(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_11,plain,
( ~ apply(U_106,sK11(U_106,U_104),sK10(U_106,U_104))
| ~ order(U_106,U_104)
| total_order(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_5]) ).
fof(f_14_1,plain,
! [R,E,M] :
( ( upper_bound(M,R,E)
| ? [X] :
( ~ apply(R,X,M)
& member(X,E) ) )
& ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
| ~ upper_bound(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[upper_bound]) ).
fof(f_14_2,plain,
! [U_111,U_110,U_109] :
( ( upper_bound(U_109,U_111,U_110)
| ? [U_108] :
( ~ apply(U_111,U_108,U_109)
& member(U_108,U_110) ) )
& ( ! [U_107] :
( apply(U_111,U_107,U_109)
| ~ member(U_107,U_110) )
| ~ upper_bound(U_109,U_111,U_110) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_117,U_115,U_113] :
( upper_bound(U_113,U_117,U_115)
| ? [U_108] :
( ~ apply(U_117,U_108,U_113)
& member(U_108,U_115) ) )
& ! [U_116,U_114,U_112] :
( ! [U_107] :
( apply(U_116,U_107,U_112)
| ~ member(U_107,U_114) )
| ~ upper_bound(U_112,U_116,U_114) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_117,U_115,U_113] :
( upper_bound(U_113,U_117,U_115)
| ( ~ apply(U_117,sK12(U_117,U_115,U_113),U_113)
& member(sK12(U_117,U_115,U_113),U_115) ) )
& ! [U_116,U_114,U_112] :
( ! [U_107] :
( apply(U_116,U_107,U_112)
| ~ member(U_107,U_114) )
| ~ upper_bound(U_112,U_116,U_114) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_108,sK12(U_117,U_115,U_113))],[f_14_3]) ).
cnf(f_14_5,plain,
( apply(U_116,U_107,U_112)
| ~ member(U_107,U_114)
| ~ upper_bound(U_112,U_116,U_114) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( member(sK12(U_117,U_115,U_113),U_115)
| upper_bound(U_113,U_117,U_115) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_7,plain,
( ~ apply(U_117,sK12(U_117,U_115,U_113),U_113)
| upper_bound(U_113,U_117,U_115) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
! [R,E,M] :
( ( lower_bound(M,R,E)
| ? [X] :
( ~ apply(R,M,X)
& member(X,E) ) )
& ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[lower_bound]) ).
fof(f_15_2,plain,
! [U_122,U_121,U_120] :
( ( lower_bound(U_120,U_122,U_121)
| ? [U_119] :
( ~ apply(U_122,U_120,U_119)
& member(U_119,U_121) ) )
& ( ! [U_118] :
( apply(U_122,U_120,U_118)
| ~ member(U_118,U_121) )
| ~ lower_bound(U_120,U_122,U_121) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_128,U_126,U_124] :
( lower_bound(U_124,U_128,U_126)
| ? [U_119] :
( ~ apply(U_128,U_124,U_119)
& member(U_119,U_126) ) )
& ! [U_127,U_125,U_123] :
( ! [U_118] :
( apply(U_127,U_123,U_118)
| ~ member(U_118,U_125) )
| ~ lower_bound(U_123,U_127,U_125) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_128,U_126,U_124] :
( lower_bound(U_124,U_128,U_126)
| ( ~ apply(U_128,U_124,sK13(U_128,U_126,U_124))
& member(sK13(U_128,U_126,U_124),U_126) ) )
& ! [U_127,U_125,U_123] :
( ! [U_118] :
( apply(U_127,U_123,U_118)
| ~ member(U_118,U_125) )
| ~ lower_bound(U_123,U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_119,sK13(U_128,U_126,U_124))],[f_15_3]) ).
cnf(f_15_5,plain,
( apply(U_127,U_123,U_118)
| ~ member(U_118,U_125)
| ~ lower_bound(U_123,U_127,U_125) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( member(sK13(U_128,U_126,U_124),U_126)
| lower_bound(U_124,U_128,U_126) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( ~ apply(U_128,U_124,sK13(U_128,U_126,U_124))
| lower_bound(U_124,U_128,U_126) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [R,E,M] :
( ( greatest(M,R,E)
| ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| ~ member(M,E) )
& ( ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[greatest]) ).
fof(f_16_2,plain,
! [U_133,U_132,U_131] :
( ( greatest(U_131,U_133,U_132)
| ? [U_130] :
( ~ apply(U_133,U_130,U_131)
& member(U_130,U_132) )
| ~ member(U_131,U_132) )
& ( ( ! [U_129] :
( apply(U_133,U_129,U_131)
| ~ member(U_129,U_132) )
& member(U_131,U_132) )
| ~ greatest(U_131,U_133,U_132) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_139,U_137,U_135] :
( greatest(U_135,U_139,U_137)
| ? [U_130] :
( ~ apply(U_139,U_130,U_135)
& member(U_130,U_137) )
| ~ member(U_135,U_137) )
& ! [U_138,U_136,U_134] :
( ( ! [U_129] :
( apply(U_138,U_129,U_134)
| ~ member(U_129,U_136) )
& member(U_134,U_136) )
| ~ greatest(U_134,U_138,U_136) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_139,U_137,U_135] :
( greatest(U_135,U_139,U_137)
| ( ~ apply(U_139,sK14(U_139,U_137,U_135),U_135)
& member(sK14(U_139,U_137,U_135),U_137) )
| ~ member(U_135,U_137) )
& ! [U_138,U_136,U_134] :
( ( ! [U_129] :
( apply(U_138,U_129,U_134)
| ~ member(U_129,U_136) )
& member(U_134,U_136) )
| ~ greatest(U_134,U_138,U_136) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_130,sK14(U_139,U_137,U_135))],[f_16_3]) ).
cnf(f_16_5,plain,
( member(U_134,U_136)
| ~ greatest(U_134,U_138,U_136) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_6,plain,
( apply(U_138,U_129,U_134)
| ~ member(U_129,U_136)
| ~ greatest(U_134,U_138,U_136) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_7,plain,
( member(sK14(U_139,U_137,U_135),U_137)
| ~ member(U_135,U_137)
| greatest(U_135,U_139,U_137) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_8,plain,
( ~ apply(U_139,sK14(U_139,U_137,U_135),U_135)
| ~ member(U_135,U_137)
| greatest(U_135,U_139,U_137) ),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [R,E,M] :
( ( least(M,R,E)
| ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E) )
& ( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[least]) ).
fof(f_17_2,plain,
! [U_144,U_143,U_142] :
( ( least(U_142,U_144,U_143)
| ? [U_141] :
( ~ apply(U_144,U_142,U_141)
& member(U_141,U_143) )
| ~ member(U_142,U_143) )
& ( ( ! [U_140] :
( apply(U_144,U_142,U_140)
| ~ member(U_140,U_143) )
& member(U_142,U_143) )
| ~ least(U_142,U_144,U_143) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_150,U_148,U_146] :
( least(U_146,U_150,U_148)
| ? [U_141] :
( ~ apply(U_150,U_146,U_141)
& member(U_141,U_148) )
| ~ member(U_146,U_148) )
& ! [U_149,U_147,U_145] :
( ( ! [U_140] :
( apply(U_149,U_145,U_140)
| ~ member(U_140,U_147) )
& member(U_145,U_147) )
| ~ least(U_145,U_149,U_147) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_150,U_148,U_146] :
( least(U_146,U_150,U_148)
| ( ~ apply(U_150,U_146,sK15(U_150,U_148,U_146))
& member(sK15(U_150,U_148,U_146),U_148) )
| ~ member(U_146,U_148) )
& ! [U_149,U_147,U_145] :
( ( ! [U_140] :
( apply(U_149,U_145,U_140)
| ~ member(U_140,U_147) )
& member(U_145,U_147) )
| ~ least(U_145,U_149,U_147) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_141,sK15(U_150,U_148,U_146))],[f_17_3]) ).
cnf(f_17_5,plain,
( member(U_145,U_147)
| ~ least(U_145,U_149,U_147) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( apply(U_149,U_145,U_140)
| ~ member(U_140,U_147)
| ~ least(U_145,U_149,U_147) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_7,plain,
( member(sK15(U_150,U_148,U_146),U_148)
| ~ member(U_146,U_148)
| least(U_146,U_150,U_148) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_8,plain,
( ~ apply(U_150,U_146,sK15(U_150,U_148,U_146))
| ~ member(U_146,U_148)
| least(U_146,U_150,U_148) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
! [R,E,M] :
( ( max(M,R,E)
| ? [X] :
( M != X
& apply(R,M,X)
& member(X,E) )
| ~ member(M,E) )
& ( ( ! [X] :
( M = X
| ~ apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[max]) ).
fof(f_18_2,plain,
! [U_155,U_154,U_153] :
( ( max(U_153,U_155,U_154)
| ? [U_152] :
( U_153 != U_152
& apply(U_155,U_153,U_152)
& member(U_152,U_154) )
| ~ member(U_153,U_154) )
& ( ( ! [U_151] :
( U_153 = U_151
| ~ apply(U_155,U_153,U_151)
| ~ member(U_151,U_154) )
& member(U_153,U_154) )
| ~ max(U_153,U_155,U_154) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_161,U_159,U_157] :
( max(U_157,U_161,U_159)
| ? [U_152] :
( U_157 != U_152
& apply(U_161,U_157,U_152)
& member(U_152,U_159) )
| ~ member(U_157,U_159) )
& ! [U_160,U_158,U_156] :
( ( ! [U_151] :
( U_156 = U_151
| ~ apply(U_160,U_156,U_151)
| ~ member(U_151,U_158) )
& member(U_156,U_158) )
| ~ max(U_156,U_160,U_158) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_161,U_159,U_157] :
( max(U_157,U_161,U_159)
| ( U_157 != sK16(U_161,U_159,U_157)
& apply(U_161,U_157,sK16(U_161,U_159,U_157))
& member(sK16(U_161,U_159,U_157),U_159) )
| ~ member(U_157,U_159) )
& ! [U_160,U_158,U_156] :
( ( ! [U_151] :
( U_156 = U_151
| ~ apply(U_160,U_156,U_151)
| ~ member(U_151,U_158) )
& member(U_156,U_158) )
| ~ max(U_156,U_160,U_158) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_152,sK16(U_161,U_159,U_157))],[f_18_3]) ).
cnf(f_18_5,plain,
( member(U_156,U_158)
| ~ max(U_156,U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( U_156 = U_151
| ~ apply(U_160,U_156,U_151)
| ~ member(U_151,U_158)
| ~ max(U_156,U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_7,plain,
( member(sK16(U_161,U_159,U_157),U_159)
| ~ member(U_157,U_159)
| max(U_157,U_161,U_159) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_8,plain,
( apply(U_161,U_157,sK16(U_161,U_159,U_157))
| ~ member(U_157,U_159)
| max(U_157,U_161,U_159) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_9,plain,
( U_157 != sK16(U_161,U_159,U_157)
| ~ member(U_157,U_159)
| max(U_157,U_161,U_159) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [R,E,M] :
( ( min(M,R,E)
| ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) )
| ~ member(M,E) )
& ( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[min]) ).
fof(f_19_2,plain,
! [U_166,U_165,U_164] :
( ( min(U_164,U_166,U_165)
| ? [U_163] :
( U_164 != U_163
& apply(U_166,U_163,U_164)
& member(U_163,U_165) )
| ~ member(U_164,U_165) )
& ( ( ! [U_162] :
( U_164 = U_162
| ~ apply(U_166,U_162,U_164)
| ~ member(U_162,U_165) )
& member(U_164,U_165) )
| ~ min(U_164,U_166,U_165) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_172,U_170,U_168] :
( min(U_168,U_172,U_170)
| ? [U_163] :
( U_168 != U_163
& apply(U_172,U_163,U_168)
& member(U_163,U_170) )
| ~ member(U_168,U_170) )
& ! [U_171,U_169,U_167] :
( ( ! [U_162] :
( U_167 = U_162
| ~ apply(U_171,U_162,U_167)
| ~ member(U_162,U_169) )
& member(U_167,U_169) )
| ~ min(U_167,U_171,U_169) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_172,U_170,U_168] :
( min(U_168,U_172,U_170)
| ( U_168 != sK17(U_172,U_170,U_168)
& apply(U_172,sK17(U_172,U_170,U_168),U_168)
& member(sK17(U_172,U_170,U_168),U_170) )
| ~ member(U_168,U_170) )
& ! [U_171,U_169,U_167] :
( ( ! [U_162] :
( U_167 = U_162
| ~ apply(U_171,U_162,U_167)
| ~ member(U_162,U_169) )
& member(U_167,U_169) )
| ~ min(U_167,U_171,U_169) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_163,sK17(U_172,U_170,U_168))],[f_19_3]) ).
cnf(f_19_5,plain,
( member(U_167,U_169)
| ~ min(U_167,U_171,U_169) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
( U_167 = U_162
| ~ apply(U_171,U_162,U_167)
| ~ member(U_162,U_169)
| ~ min(U_167,U_171,U_169) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_7,plain,
( member(sK17(U_172,U_170,U_168),U_170)
| ~ member(U_168,U_170)
| min(U_168,U_172,U_170) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_8,plain,
( apply(U_172,sK17(U_172,U_170,U_168),U_168)
| ~ member(U_168,U_170)
| min(U_168,U_172,U_170) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_9,plain,
( U_168 != sK17(U_172,U_170,U_168)
| ~ member(U_168,U_170)
| min(U_168,U_172,U_170) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,X,R,E] :
( ( least_upper_bound(A,X,R,E)
| ? [M] :
( ~ apply(R,A,M)
& upper_bound(M,R,X)
& member(M,E) )
| ~ upper_bound(A,R,X)
| ~ member(A,X) )
& ( ( ! [M] :
( apply(R,A,M)
| ~ upper_bound(M,R,X)
| ~ member(M,E) )
& upper_bound(A,R,X)
& member(A,X) )
| ~ least_upper_bound(A,X,R,E) ) ),
inference(fof_nnf,[status(thm)],[least_upper_bound]) ).
fof(f_20_2,plain,
! [U_178,U_177,U_176,U_175] :
( ( least_upper_bound(U_178,U_177,U_176,U_175)
| ? [U_174] :
( ~ apply(U_176,U_178,U_174)
& upper_bound(U_174,U_176,U_177)
& member(U_174,U_175) )
| ~ upper_bound(U_178,U_176,U_177)
| ~ member(U_178,U_177) )
& ( ( ! [U_173] :
( apply(U_176,U_178,U_173)
| ~ upper_bound(U_173,U_176,U_177)
| ~ member(U_173,U_175) )
& upper_bound(U_178,U_176,U_177)
& member(U_178,U_177) )
| ~ least_upper_bound(U_178,U_177,U_176,U_175) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_186,U_184,U_182,U_180] :
( least_upper_bound(U_186,U_184,U_182,U_180)
| ? [U_174] :
( ~ apply(U_182,U_186,U_174)
& upper_bound(U_174,U_182,U_184)
& member(U_174,U_180) )
| ~ upper_bound(U_186,U_182,U_184)
| ~ member(U_186,U_184) )
& ! [U_185,U_183,U_181,U_179] :
( ( ! [U_173] :
( apply(U_181,U_185,U_173)
| ~ upper_bound(U_173,U_181,U_183)
| ~ member(U_173,U_179) )
& upper_bound(U_185,U_181,U_183)
& member(U_185,U_183) )
| ~ least_upper_bound(U_185,U_183,U_181,U_179) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_186,U_184,U_182,U_180] :
( least_upper_bound(U_186,U_184,U_182,U_180)
| ( ~ apply(U_182,U_186,sK18(U_186,U_184,U_182,U_180))
& upper_bound(sK18(U_186,U_184,U_182,U_180),U_182,U_184)
& member(sK18(U_186,U_184,U_182,U_180),U_180) )
| ~ upper_bound(U_186,U_182,U_184)
| ~ member(U_186,U_184) )
& ! [U_185,U_183,U_181,U_179] :
( ( ! [U_173] :
( apply(U_181,U_185,U_173)
| ~ upper_bound(U_173,U_181,U_183)
| ~ member(U_173,U_179) )
& upper_bound(U_185,U_181,U_183)
& member(U_185,U_183) )
| ~ least_upper_bound(U_185,U_183,U_181,U_179) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_174,sK18(U_186,U_184,U_182,U_180))],[f_20_3]) ).
cnf(f_20_5,plain,
( member(U_185,U_183)
| ~ least_upper_bound(U_185,U_183,U_181,U_179) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( upper_bound(U_185,U_181,U_183)
| ~ least_upper_bound(U_185,U_183,U_181,U_179) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
( apply(U_181,U_185,U_173)
| ~ upper_bound(U_173,U_181,U_183)
| ~ member(U_173,U_179)
| ~ least_upper_bound(U_185,U_183,U_181,U_179) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_8,plain,
( member(sK18(U_186,U_184,U_182,U_180),U_180)
| ~ upper_bound(U_186,U_182,U_184)
| ~ member(U_186,U_184)
| least_upper_bound(U_186,U_184,U_182,U_180) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_9,plain,
( upper_bound(sK18(U_186,U_184,U_182,U_180),U_182,U_184)
| ~ upper_bound(U_186,U_182,U_184)
| ~ member(U_186,U_184)
| least_upper_bound(U_186,U_184,U_182,U_180) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_10,plain,
( ~ apply(U_182,U_186,sK18(U_186,U_184,U_182,U_180))
| ~ upper_bound(U_186,U_182,U_184)
| ~ member(U_186,U_184)
| least_upper_bound(U_186,U_184,U_182,U_180) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [A,X,R,E] :
( ( greatest_lower_bound(A,X,R,E)
| ? [M] :
( ~ apply(R,M,A)
& lower_bound(M,R,X)
& member(M,E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X) )
& ( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(fof_nnf,[status(thm)],[greatest_lower_bound]) ).
fof(f_21_2,plain,
! [U_192,U_191,U_190,U_189] :
( ( greatest_lower_bound(U_192,U_191,U_190,U_189)
| ? [U_188] :
( ~ apply(U_190,U_188,U_192)
& lower_bound(U_188,U_190,U_191)
& member(U_188,U_189) )
| ~ lower_bound(U_192,U_190,U_191)
| ~ member(U_192,U_191) )
& ( ( ! [U_187] :
( apply(U_190,U_187,U_192)
| ~ lower_bound(U_187,U_190,U_191)
| ~ member(U_187,U_189) )
& lower_bound(U_192,U_190,U_191)
& member(U_192,U_191) )
| ~ greatest_lower_bound(U_192,U_191,U_190,U_189) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_200,U_198,U_196,U_194] :
( greatest_lower_bound(U_200,U_198,U_196,U_194)
| ? [U_188] :
( ~ apply(U_196,U_188,U_200)
& lower_bound(U_188,U_196,U_198)
& member(U_188,U_194) )
| ~ lower_bound(U_200,U_196,U_198)
| ~ member(U_200,U_198) )
& ! [U_199,U_197,U_195,U_193] :
( ( ! [U_187] :
( apply(U_195,U_187,U_199)
| ~ lower_bound(U_187,U_195,U_197)
| ~ member(U_187,U_193) )
& lower_bound(U_199,U_195,U_197)
& member(U_199,U_197) )
| ~ greatest_lower_bound(U_199,U_197,U_195,U_193) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_200,U_198,U_196,U_194] :
( greatest_lower_bound(U_200,U_198,U_196,U_194)
| ( ~ apply(U_196,sK19(U_200,U_198,U_196,U_194),U_200)
& lower_bound(sK19(U_200,U_198,U_196,U_194),U_196,U_198)
& member(sK19(U_200,U_198,U_196,U_194),U_194) )
| ~ lower_bound(U_200,U_196,U_198)
| ~ member(U_200,U_198) )
& ! [U_199,U_197,U_195,U_193] :
( ( ! [U_187] :
( apply(U_195,U_187,U_199)
| ~ lower_bound(U_187,U_195,U_197)
| ~ member(U_187,U_193) )
& lower_bound(U_199,U_195,U_197)
& member(U_199,U_197) )
| ~ greatest_lower_bound(U_199,U_197,U_195,U_193) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_188,sK19(U_200,U_198,U_196,U_194))],[f_21_3]) ).
cnf(f_21_5,plain,
( member(U_199,U_197)
| ~ greatest_lower_bound(U_199,U_197,U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( lower_bound(U_199,U_195,U_197)
| ~ greatest_lower_bound(U_199,U_197,U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( apply(U_195,U_187,U_199)
| ~ lower_bound(U_187,U_195,U_197)
| ~ member(U_187,U_193)
| ~ greatest_lower_bound(U_199,U_197,U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_8,plain,
( member(sK19(U_200,U_198,U_196,U_194),U_194)
| ~ lower_bound(U_200,U_196,U_198)
| ~ member(U_200,U_198)
| greatest_lower_bound(U_200,U_198,U_196,U_194) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_9,plain,
( lower_bound(sK19(U_200,U_198,U_196,U_194),U_196,U_198)
| ~ lower_bound(U_200,U_196,U_198)
| ~ member(U_200,U_198)
| greatest_lower_bound(U_200,U_198,U_196,U_194) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_10,plain,
( ~ apply(U_196,sK19(U_200,U_198,U_196,U_194),U_200)
| ~ lower_bound(U_200,U_196,U_198)
| ~ member(U_200,U_198)
| greatest_lower_bound(U_200,U_198,U_196,U_194) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
inference(negate,[status(cth)],[thIV10]) ).
fof(f_22_2,negated_conjecture,
? [R,E] :
( ? [X,Y] :
( ? [M] :
( ~ lower_bound(M,R,X)
& lower_bound(M,R,Y) )
& subset(X,Y)
& subset(Y,E)
& subset(X,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[f_22_1]) ).
fof(f_22_3,negated_conjecture,
? [U_205,U_204] :
( ? [U_203,U_202] :
( ? [U_201] :
( ~ lower_bound(U_201,U_205,U_203)
& lower_bound(U_201,U_205,U_202) )
& subset(U_203,U_202)
& subset(U_202,U_204)
& subset(U_203,U_204) )
& order(U_205,U_204) ),
inference(variable_rename,[status(thm)],[f_22_2]) ).
fof(f_22_4,negated_conjecture,
? [U_204] :
( ? [U_203,U_202] :
( ? [U_201] :
( ~ lower_bound(U_201,sK20,U_203)
& lower_bound(U_201,sK20,U_202) )
& subset(U_203,U_202)
& subset(U_202,U_204)
& subset(U_203,U_204) )
& order(sK20,U_204) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_205,sK20)],[f_22_3]) ).
fof(f_22_5,negated_conjecture,
( ? [U_203,U_202] :
( ? [U_201] :
( ~ lower_bound(U_201,sK20,U_203)
& lower_bound(U_201,sK20,U_202) )
& subset(U_203,U_202)
& subset(U_202,sK21)
& subset(U_203,sK21) )
& order(sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_204,sK21)],[f_22_4]) ).
fof(f_22_6,negated_conjecture,
( ? [U_202] :
( ? [U_201] :
( ~ lower_bound(U_201,sK20,sK22)
& lower_bound(U_201,sK20,U_202) )
& subset(sK22,U_202)
& subset(U_202,sK21)
& subset(sK22,sK21) )
& order(sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_203,sK22)],[f_22_5]) ).
fof(f_22_7,negated_conjecture,
( ? [U_201] :
( ~ lower_bound(U_201,sK20,sK22)
& lower_bound(U_201,sK20,sK23) )
& subset(sK22,sK23)
& subset(sK23,sK21)
& subset(sK22,sK21)
& order(sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_202,sK23)],[f_22_6]) ).
fof(f_22_8,negated_conjecture,
( ~ lower_bound(sK24,sK20,sK22)
& lower_bound(sK24,sK20,sK23)
& subset(sK22,sK23)
& subset(sK23,sK21)
& subset(sK22,sK21)
& order(sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_201,sK24)],[f_22_7]) ).
fof(f_22_9,negated_conjecture,
( ~ lower_bound(sK24,sK20,sK22)
& lower_bound(sK24,sK20,sK23)
& subset(sK22,sK23)
& subset(sK23,sK21)
& subset(sK22,sK21)
& order(sK20,sK21) ),
inference(definitional_conversion,[status(esa)],[f_22_8]) ).
cnf(f_22_10,negated_conjecture,
order(sK20,sK21),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_11,negated_conjecture,
subset(sK22,sK21),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_12,negated_conjecture,
subset(sK23,sK21),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_13,negated_conjecture,
subset(sK22,sK23),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_14,negated_conjecture,
lower_bound(sK24,sK20,sK23),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_15,negated_conjecture,
~ lower_bound(sK24,sK20,sK22),
inference(clausify,[status(thm)],[f_22_9]) ).
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,
( 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_13,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_14,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_15,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( sK5(Eq_x_0,Eq_x_1) = sK5(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,
( 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_18,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_19,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(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,
( 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_21,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_22,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_23,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(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_24,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(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_25,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(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_26,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(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_27,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(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_28,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(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_29,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,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_32,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_33,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_34,axiom,
( order(Eq_y_0,Eq_y_1)
| ~ 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_35,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(equality_36,axiom,
( total_order(Eq_y_0,Eq_y_1)
| ~ total_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_37,axiom,
( upper_bound(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ upper_bound(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_38,axiom,
( lower_bound(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ lower_bound(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_39,axiom,
( greatest(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ greatest(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_40,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_41,axiom,
( max(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ max(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_42,axiom,
( min(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ min(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_43,axiom,
( least_upper_bound(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ least_upper_bound(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( greatest_lower_bound(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ greatest_lower_bound(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| 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
% 0.00/0.02 % Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:02:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 25.78/26.05 % SZS status Theorem for theBenchmark
% 25.78/26.05 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------