%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET765+4 : TPTP v9.3.1. Released v2.2.0.
% 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 : n014.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 08:57:24 AM UTC 2026
% Result : Theorem 222.16s 222.45s
% Output : Proof 223.23s
% 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(disjoint,axiom,
! [A,B] :
( disjoint(A,B)
<=> ~ ? [X] :
( member(X,B)
& member(X,A) ) ),
file('SET006+2.ax',disjoint) ).
fof(partition,axiom,
! [A,E] :
( partition(A,E)
<=> ( ! [X,Y] :
( ( member(Y,A)
& member(X,A) )
=> ( ? [Z] :
( member(Z,Y)
& member(Z,X) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> ? [Y] :
( member(X,Y)
& member(Y,A) ) )
& ! [X] :
( member(X,A)
=> subset(X,E) ) ) ),
file('SET006+2.ax',partition) ).
fof(equivalence,axiom,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X,Y,Z] :
( ( member(Z,A)
& member(Y,A)
& member(X,A) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,A)
& member(X,A) )
=> ( apply(R,X,Y)
=> apply(R,Y,X) ) )
& ! [X] :
( member(X,A)
=> apply(R,X,X) ) ) ),
file('SET006+2.ax',equivalence) ).
fof(equivalence_class,axiom,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( apply(R,A,X)
& member(X,E) ) ),
file('SET006+2.ax',equivalence_class) ).
fof(pre_order,axiom,
! [R,E] :
( pre_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] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('SET006+2.ax',pre_order) ).
fof(thIII01,conjecture,
! [E,R,X] :
( ( subset(X,E)
& equivalence(R,E) )
=> equivalence(R,X) ),
file('theBenchmark.p',thIII01) ).
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]) ).
fof(f_1_5,plain,
( ! [U_5,U_7] :
( ~ member(sK1(U_7,U_5),U_5)
| ~ sP0(U_5,U_7) )
& ! [U_5,U_7] :
( member(sK1(U_7,U_5),U_7)
| ~ sP0(U_5,U_7) )
& ! [U_5,U_7] :
( subset(U_7,U_5)
| sP0(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(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_4]) ).
cnf(f_1_6,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subset(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( subset(U_7,U_5)
| sP0(U_5,U_7) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( member(sK1(U_7,U_5),U_7)
| ~ sP0(U_5,U_7) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,plain,
( ~ member(sK1(U_7,U_5),U_5)
| ~ sP0(U_5,U_7) ),
inference(clausify,[status(thm)],[f_1_5]) ).
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]) ).
fof(f_2_4,plain,
( ! [U_12,U_10] :
( subset(U_10,U_12)
| ~ sP1(U_12,U_10) )
& ! [U_12,U_10] :
( subset(U_12,U_10)
| ~ sP1(U_12,U_10) )
& ! [U_13,U_11] :
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( sP1(U_12,U_10)
| ~ equal_set(U_12,U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_2_3]) ).
cnf(f_2_5,plain,
( sP1(U_12,U_10)
| ~ equal_set(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_4]) ).
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_4]) ).
cnf(f_2_7,plain,
( subset(U_12,U_10)
| ~ sP1(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_8,plain,
( subset(U_10,U_12)
| ~ sP1(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_4]) ).
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]) ).
fof(f_3_4,plain,
( ! [U_19,U_17] :
( member(U_19,power_set(U_17))
| ~ subset(U_19,U_17) )
& ! [U_16,U_18] :
( subset(U_18,U_16)
| ~ member(U_18,power_set(U_16)) ) ),
inference(definitional_conversion,[status(esa)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(U_18,U_16)
| ~ member(U_18,power_set(U_16)) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( member(U_19,power_set(U_17))
| ~ subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_3_4]) ).
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]) ).
fof(f_4_4,plain,
( ! [U_25,U_23,U_27] :
( member(U_27,U_23)
| ~ sP2(U_25,U_23,U_27) )
& ! [U_25,U_23,U_27] :
( member(U_27,U_25)
| ~ sP2(U_25,U_23,U_27) )
& ! [U_24,U_26,U_28] :
( member(U_28,intersection(U_26,U_24))
| ~ member(U_28,U_24)
| ~ member(U_28,U_26) )
& ! [U_25,U_23,U_27] :
( sP2(U_25,U_23,U_27)
| ~ member(U_27,intersection(U_25,U_23)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_4_3]) ).
cnf(f_4_5,plain,
( sP2(U_25,U_23,U_27)
| ~ member(U_27,intersection(U_25,U_23)) ),
inference(clausify,[status(thm)],[f_4_4]) ).
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_4]) ).
cnf(f_4_7,plain,
( member(U_27,U_25)
| ~ sP2(U_25,U_23,U_27) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_8,plain,
( member(U_27,U_23)
| ~ sP2(U_25,U_23,U_27) ),
inference(clausify,[status(thm)],[f_4_4]) ).
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]) ).
fof(f_5_4,plain,
( ! [U_33,U_37,U_35] :
( ~ member(U_37,U_33)
| ~ sP3(U_33,U_37,U_35) )
& ! [U_33,U_37,U_35] :
( ~ member(U_37,U_35)
| ~ sP3(U_33,U_37,U_35) )
& ! [U_33,U_37,U_35] :
( member(U_37,union(U_35,U_33))
| sP3(U_33,U_37,U_35) )
& ! [U_34,U_32,U_36] :
( member(U_36,U_32)
| member(U_36,U_34)
| ~ member(U_36,union(U_34,U_32)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_5_3]) ).
cnf(f_5_5,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_4]) ).
cnf(f_5_6,plain,
( member(U_37,union(U_35,U_33))
| sP3(U_33,U_37,U_35) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ member(U_37,U_35)
| ~ sP3(U_33,U_37,U_35) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_8,plain,
( ~ member(U_37,U_33)
| ~ sP3(U_33,U_37,U_35) ),
inference(clausify,[status(thm)],[f_5_4]) ).
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]) ).
fof(f_6_3,plain,
! [U_38] : ~ member(U_38,empty_set),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
~ member(U_38,empty_set),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
fof(f_7_4,plain,
( ! [U_44,U_42,U_46] :
( ~ member(U_46,U_44)
| ~ sP4(U_44,U_42,U_46) )
& ! [U_44,U_42,U_46] :
( member(U_46,U_42)
| ~ sP4(U_44,U_42,U_46) )
& ! [U_45,U_47,U_43] :
( member(U_47,difference(U_43,U_45))
| member(U_47,U_45)
| ~ member(U_47,U_43) )
& ! [U_44,U_42,U_46] :
( sP4(U_44,U_42,U_46)
| ~ member(U_46,difference(U_42,U_44)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_7_3]) ).
cnf(f_7_5,plain,
( sP4(U_44,U_42,U_46)
| ~ member(U_46,difference(U_42,U_44)) ),
inference(clausify,[status(thm)],[f_7_4]) ).
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_4]) ).
cnf(f_7_7,plain,
( member(U_46,U_42)
| ~ sP4(U_44,U_42,U_46) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_8,plain,
( ~ member(U_46,U_44)
| ~ sP4(U_44,U_42,U_46) ),
inference(clausify,[status(thm)],[f_7_4]) ).
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]) ).
fof(f_8_4,plain,
( ! [U_51,U_53] :
( member(U_53,singleton(U_51))
| U_53 != U_51 )
& ! [U_50,U_52] :
( U_52 = U_50
| ~ member(U_52,singleton(U_50)) ) ),
inference(definitional_conversion,[status(esa)],[f_8_3]) ).
cnf(f_8_5,plain,
( U_52 = U_50
| ~ member(U_52,singleton(U_50)) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( member(U_53,singleton(U_51))
| U_53 != U_51 ),
inference(clausify,[status(thm)],[f_8_4]) ).
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]) ).
fof(f_9_4,plain,
( ! [U_62,U_58,U_60] :
( U_62 != U_58
| ~ sP5(U_62,U_58,U_60) )
& ! [U_62,U_58,U_60] :
( U_62 != U_60
| ~ sP5(U_62,U_58,U_60) )
& ! [U_62,U_58,U_60] :
( member(U_62,unordered_pair(U_60,U_58))
| sP5(U_62,U_58,U_60) )
& ! [U_57,U_61,U_59] :
( U_61 = U_57
| U_61 = U_59
| ~ member(U_61,unordered_pair(U_59,U_57)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_9_3]) ).
cnf(f_9_5,plain,
( U_61 = U_57
| U_61 = U_59
| ~ member(U_61,unordered_pair(U_59,U_57)) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( member(U_62,unordered_pair(U_60,U_58))
| sP5(U_62,U_58,U_60) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_7,plain,
( U_62 != U_60
| ~ sP5(U_62,U_58,U_60) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_8,plain,
( U_62 != U_58
| ~ sP5(U_62,U_58,U_60) ),
inference(clausify,[status(thm)],[f_9_4]) ).
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]) ).
fof(f_10_5,plain,
( ! [U_69,U_67] :
( member(U_69,sK2(U_69,U_67))
| ~ sP6(U_69,U_67) )
& ! [U_69,U_67] :
( member(sK2(U_69,U_67),U_67)
| ~ sP6(U_69,U_67) )
& ! [U_68,U_64,U_70] :
( member(U_70,sum(U_68))
| ~ member(U_70,U_64)
| ~ member(U_64,U_68) )
& ! [U_69,U_67] :
( sP6(U_69,U_67)
| ~ member(U_69,sum(U_67)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_10_4]) ).
cnf(f_10_6,plain,
( sP6(U_69,U_67)
| ~ member(U_69,sum(U_67)) ),
inference(clausify,[status(thm)],[f_10_5]) ).
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_5]) ).
cnf(f_10_8,plain,
( member(sK2(U_69,U_67),U_67)
| ~ sP6(U_69,U_67) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( member(U_69,sK2(U_69,U_67))
| ~ sP6(U_69,U_67) ),
inference(clausify,[status(thm)],[f_10_5]) ).
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]) ).
fof(f_11_5,plain,
( ! [U_78,U_76] :
( ~ member(U_78,sK3(U_78,U_76))
| ~ sP7(U_78,U_76) )
& ! [U_78,U_76] :
( member(sK3(U_78,U_76),U_76)
| ~ sP7(U_78,U_76) )
& ! [U_78,U_76] :
( member(U_78,product(U_76))
| sP7(U_78,U_76) )
& ! [U_75,U_77,U_71] :
( member(U_77,U_71)
| ~ member(U_71,U_75)
| ~ member(U_77,product(U_75)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_11_4]) ).
cnf(f_11_6,plain,
( member(U_77,U_71)
| ~ member(U_71,U_75)
| ~ member(U_77,product(U_75)) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( member(U_78,product(U_76))
| sP7(U_78,U_76) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( member(sK3(U_78,U_76),U_76)
| ~ sP7(U_78,U_76) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,plain,
( ~ member(U_78,sK3(U_78,U_76))
| ~ sP7(U_78,U_76) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_1,plain,
! [A,B] :
( ( disjoint(A,B)
| ? [X] :
( member(X,B)
& member(X,A) ) )
& ( ! [X] :
( ~ member(X,B)
| ~ member(X,A) )
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[disjoint]) ).
fof(f_12_2,plain,
! [U_82,U_81] :
( ( disjoint(U_82,U_81)
| ? [U_80] :
( member(U_80,U_81)
& member(U_80,U_82) ) )
& ( ! [U_79] :
( ~ member(U_79,U_81)
| ~ member(U_79,U_82) )
| ~ disjoint(U_82,U_81) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_86,U_84] :
( disjoint(U_86,U_84)
| ? [U_80] :
( member(U_80,U_84)
& member(U_80,U_86) ) )
& ! [U_85,U_83] :
( ! [U_79] :
( ~ member(U_79,U_83)
| ~ member(U_79,U_85) )
| ~ disjoint(U_85,U_83) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_86,U_84] :
( disjoint(U_86,U_84)
| ( member(sK4(U_86,U_84),U_84)
& member(sK4(U_86,U_84),U_86) ) )
& ! [U_85,U_83] :
( ! [U_79] :
( ~ member(U_79,U_83)
| ~ member(U_79,U_85) )
| ~ disjoint(U_85,U_83) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4(U_86,U_84))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_84,U_86] :
( member(sK4(U_86,U_84),U_84)
| ~ sP8(U_84,U_86) )
& ! [U_84,U_86] :
( member(sK4(U_86,U_84),U_86)
| ~ sP8(U_84,U_86) )
& ! [U_84,U_86] :
( disjoint(U_86,U_84)
| sP8(U_84,U_86) )
& ! [U_83,U_85,U_79] :
( ~ member(U_79,U_83)
| ~ member(U_79,U_85)
| ~ disjoint(U_85,U_83) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_12_4]) ).
cnf(f_12_6,plain,
( ~ member(U_79,U_83)
| ~ member(U_79,U_85)
| ~ disjoint(U_85,U_83) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( disjoint(U_86,U_84)
| sP8(U_84,U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( member(sK4(U_86,U_84),U_86)
| ~ sP8(U_84,U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( member(sK4(U_86,U_84),U_84)
| ~ sP8(U_84,U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
! [A,E] :
( ( partition(A,E)
| ? [X,Y] :
( X != Y
& ? [Z] :
( member(Z,Y)
& member(Z,X) )
& member(Y,A)
& member(X,A) )
| ? [X] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
& member(X,E) )
| ? [X] :
( ~ subset(X,E)
& member(X,A) ) )
& ( ( ! [X,Y] :
( X = Y
| ! [Z] :
( ~ member(Z,Y)
| ~ member(Z,X) )
| ~ member(Y,A)
| ~ member(X,A) )
& ! [X] :
( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,E) )
& ! [X] :
( subset(X,E)
| ~ member(X,A) ) )
| ~ partition(A,E) ) ),
inference(fof_nnf,[status(thm)],[partition]) ).
fof(f_13_2,plain,
! [U_100,U_99] :
( ( partition(U_100,U_99)
| ? [U_98,U_97] :
( U_98 != U_97
& ? [U_96] :
( member(U_96,U_97)
& member(U_96,U_98) )
& member(U_97,U_100)
& member(U_98,U_100) )
| ? [U_95] :
( ! [U_94] :
( ~ member(U_95,U_94)
| ~ member(U_94,U_100) )
& member(U_95,U_99) )
| ? [U_93] :
( ~ subset(U_93,U_99)
& member(U_93,U_100) ) )
& ( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_100)
| ~ member(U_92,U_100) )
& ! [U_89] :
( ? [U_88] :
( member(U_89,U_88)
& member(U_88,U_100) )
| ~ member(U_89,U_99) )
& ! [U_87] :
( subset(U_87,U_99)
| ~ member(U_87,U_100) ) )
| ~ partition(U_100,U_99) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ? [U_98,U_97] :
( U_98 != U_97
& ? [U_96] :
( member(U_96,U_97)
& member(U_96,U_98) )
& member(U_97,U_104)
& member(U_98,U_104) )
| ? [U_95] :
( ! [U_94] :
( ~ member(U_95,U_94)
| ~ member(U_94,U_104) )
& member(U_95,U_102) )
| ? [U_93] :
( ~ subset(U_93,U_102)
& member(U_93,U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ? [U_88] :
( member(U_89,U_88)
& member(U_88,U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ? [U_98,U_97] :
( U_98 != U_97
& ? [U_96] :
( member(U_96,U_97)
& member(U_96,U_98) )
& member(U_97,U_104)
& member(U_98,U_104) )
| ? [U_95] :
( ! [U_94] :
( ~ member(U_95,U_94)
| ~ member(U_94,U_104) )
& member(U_95,U_102) )
| ? [U_93] :
( ~ subset(U_93,U_102)
& member(U_93,U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ( member(U_89,sK5(U_103,U_101,U_89))
& member(sK5(U_103,U_101,U_89),U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_88,sK5(U_103,U_101,U_89))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ? [U_98,U_97] :
( U_98 != U_97
& ? [U_96] :
( member(U_96,U_97)
& member(U_96,U_98) )
& member(U_97,U_104)
& member(U_98,U_104) )
| ? [U_95] :
( ! [U_94] :
( ~ member(U_95,U_94)
| ~ member(U_94,U_104) )
& member(U_95,U_102) )
| ( ~ subset(sK6(U_104,U_102),U_102)
& member(sK6(U_104,U_102),U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ( member(U_89,sK5(U_103,U_101,U_89))
& member(sK5(U_103,U_101,U_89),U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_93,sK6(U_104,U_102))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ? [U_98,U_97] :
( U_98 != U_97
& ? [U_96] :
( member(U_96,U_97)
& member(U_96,U_98) )
& member(U_97,U_104)
& member(U_98,U_104) )
| ( ! [U_94] :
( ~ member(sK7(U_104,U_102),U_94)
| ~ member(U_94,U_104) )
& member(sK7(U_104,U_102),U_102) )
| ( ~ subset(sK6(U_104,U_102),U_102)
& member(sK6(U_104,U_102),U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ( member(U_89,sK5(U_103,U_101,U_89))
& member(sK5(U_103,U_101,U_89),U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_95,sK7(U_104,U_102))],[f_13_5]) ).
fof(f_13_7,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ? [U_97] :
( sK8(U_104,U_102) != U_97
& ? [U_96] :
( member(U_96,U_97)
& member(U_96,sK8(U_104,U_102)) )
& member(U_97,U_104)
& member(sK8(U_104,U_102),U_104) )
| ( ! [U_94] :
( ~ member(sK7(U_104,U_102),U_94)
| ~ member(U_94,U_104) )
& member(sK7(U_104,U_102),U_102) )
| ( ~ subset(sK6(U_104,U_102),U_102)
& member(sK6(U_104,U_102),U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ( member(U_89,sK5(U_103,U_101,U_89))
& member(sK5(U_103,U_101,U_89),U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_98,sK8(U_104,U_102))],[f_13_6]) ).
fof(f_13_8,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ( sK8(U_104,U_102) != sK9(U_104,U_102)
& ? [U_96] :
( member(U_96,sK9(U_104,U_102))
& member(U_96,sK8(U_104,U_102)) )
& member(sK9(U_104,U_102),U_104)
& member(sK8(U_104,U_102),U_104) )
| ( ! [U_94] :
( ~ member(sK7(U_104,U_102),U_94)
| ~ member(U_94,U_104) )
& member(sK7(U_104,U_102),U_102) )
| ( ~ subset(sK6(U_104,U_102),U_102)
& member(sK6(U_104,U_102),U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ( member(U_89,sK5(U_103,U_101,U_89))
& member(sK5(U_103,U_101,U_89),U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_97,sK9(U_104,U_102))],[f_13_7]) ).
fof(f_13_9,plain,
( ! [U_104,U_102] :
( partition(U_104,U_102)
| ( sK8(U_104,U_102) != sK9(U_104,U_102)
& member(sK10(U_104,U_102),sK9(U_104,U_102))
& member(sK10(U_104,U_102),sK8(U_104,U_102))
& member(sK9(U_104,U_102),U_104)
& member(sK8(U_104,U_102),U_104) )
| ( ! [U_94] :
( ~ member(sK7(U_104,U_102),U_94)
| ~ member(U_94,U_104) )
& member(sK7(U_104,U_102),U_102) )
| ( ~ subset(sK6(U_104,U_102),U_102)
& member(sK6(U_104,U_102),U_104) ) )
& ! [U_103,U_101] :
( ( ! [U_92,U_91] :
( U_92 = U_91
| ! [U_90] :
( ~ member(U_90,U_91)
| ~ member(U_90,U_92) )
| ~ member(U_91,U_103)
| ~ member(U_92,U_103) )
& ! [U_89] :
( ( member(U_89,sK5(U_103,U_101,U_89))
& member(sK5(U_103,U_101,U_89),U_103) )
| ~ member(U_89,U_101) )
& ! [U_87] :
( subset(U_87,U_101)
| ~ member(U_87,U_103) ) )
| ~ partition(U_103,U_101) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_96,sK10(U_104,U_102))],[f_13_8]) ).
fof(f_13_10,plain,
( ! [U_102,U_104] :
( sK8(U_104,U_102) != sK9(U_104,U_102)
| ~ sP13(U_102,U_104) )
& ! [U_102,U_104] :
( member(sK10(U_104,U_102),sK9(U_104,U_102))
| ~ sP13(U_102,U_104) )
& ! [U_102,U_104] :
( member(sK10(U_104,U_102),sK8(U_104,U_102))
| ~ sP13(U_102,U_104) )
& ! [U_102,U_104] :
( member(sK9(U_104,U_102),U_104)
| ~ sP13(U_102,U_104) )
& ! [U_102,U_104] :
( member(sK8(U_104,U_102),U_104)
| ~ sP13(U_102,U_104) )
& ! [U_94,U_102,U_104] :
( ~ member(sK7(U_104,U_102),U_94)
| ~ member(U_94,U_104)
| ~ sP12(U_94,U_102,U_104) )
& ! [U_94,U_102,U_104] :
( member(sK7(U_104,U_102),U_102)
| ~ sP12(U_94,U_102,U_104) )
& ! [U_102,U_104] :
( ~ subset(sK6(U_104,U_102),U_102)
| ~ sP11(U_102,U_104) )
& ! [U_102,U_104] :
( member(sK6(U_104,U_102),U_104)
| ~ sP11(U_102,U_104) )
& ! [U_89,U_101,U_103] :
( member(U_89,sK5(U_103,U_101,U_89))
| ~ sP9(U_89,U_101,U_103) )
& ! [U_89,U_101,U_103] :
( member(sK5(U_103,U_101,U_89),U_103)
| ~ sP9(U_89,U_101,U_103) )
& ! [U_89,U_90,U_92,U_87,U_91,U_101,U_103] :
( U_92 = U_91
| ~ member(U_90,U_91)
| ~ member(U_90,U_92)
| ~ member(U_91,U_103)
| ~ member(U_92,U_103)
| ~ sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103) )
& ! [U_89,U_90,U_92,U_87,U_91,U_101,U_103] :
( sP9(U_89,U_101,U_103)
| ~ member(U_89,U_101)
| ~ sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103) )
& ! [U_89,U_90,U_92,U_87,U_91,U_101,U_103] :
( subset(U_87,U_101)
| ~ member(U_87,U_103)
| ~ sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103) )
& ! [U_94,U_102,U_104] :
( partition(U_104,U_102)
| sP13(U_102,U_104)
| sP12(U_94,U_102,U_104)
| sP11(U_102,U_104) )
& ! [U_89,U_90,U_92,U_87,U_91,U_101,U_103] :
( sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103)
| ~ partition(U_103,U_101) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10,sP11,sP12,sP13])],[f_13_9]) ).
cnf(f_13_11,plain,
( sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103)
| ~ partition(U_103,U_101) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_12,plain,
( partition(U_104,U_102)
| sP13(U_102,U_104)
| sP12(U_94,U_102,U_104)
| sP11(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_13,plain,
( subset(U_87,U_101)
| ~ member(U_87,U_103)
| ~ sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_14,plain,
( sP9(U_89,U_101,U_103)
| ~ member(U_89,U_101)
| ~ sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_15,plain,
( U_92 = U_91
| ~ member(U_90,U_91)
| ~ member(U_90,U_92)
| ~ member(U_91,U_103)
| ~ member(U_92,U_103)
| ~ sP10(U_89,U_90,U_92,U_87,U_91,U_101,U_103) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_16,plain,
( member(sK5(U_103,U_101,U_89),U_103)
| ~ sP9(U_89,U_101,U_103) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_17,plain,
( member(U_89,sK5(U_103,U_101,U_89))
| ~ sP9(U_89,U_101,U_103) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_18,plain,
( member(sK6(U_104,U_102),U_104)
| ~ sP11(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_19,plain,
( ~ subset(sK6(U_104,U_102),U_102)
| ~ sP11(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_20,plain,
( member(sK7(U_104,U_102),U_102)
| ~ sP12(U_94,U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_21,plain,
( ~ member(sK7(U_104,U_102),U_94)
| ~ member(U_94,U_104)
| ~ sP12(U_94,U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_22,plain,
( member(sK8(U_104,U_102),U_104)
| ~ sP13(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_23,plain,
( member(sK9(U_104,U_102),U_104)
| ~ sP13(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_24,plain,
( member(sK10(U_104,U_102),sK8(U_104,U_102))
| ~ sP13(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_25,plain,
( member(sK10(U_104,U_102),sK9(U_104,U_102))
| ~ sP13(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
cnf(f_13_26,plain,
( sK8(U_104,U_102) != sK9(U_104,U_102)
| ~ sP13(U_102,U_104) ),
inference(clausify,[status(thm)],[f_13_10]) ).
fof(f_14_1,plain,
! [A,R] :
( ( equivalence(R,A)
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,A)
& member(Y,A)
& member(X,A) )
| ? [X,Y] :
( ~ apply(R,Y,X)
& apply(R,X,Y)
& member(Y,A)
& member(X,A) )
| ? [X] :
( ~ apply(R,X,X)
& member(X,A) ) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,A)
| ~ member(Y,A)
| ~ member(X,A) )
& ! [X,Y] :
( apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,A)
| ~ member(X,A) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,A) ) )
| ~ equivalence(R,A) ) ),
inference(fof_nnf,[status(thm)],[equivalence]) ).
fof(f_14_2,plain,
! [U_118,U_117] :
( ( equivalence(U_117,U_118)
| ? [U_116,U_115,U_114] :
( ~ apply(U_117,U_116,U_114)
& apply(U_117,U_115,U_114)
& apply(U_117,U_116,U_115)
& member(U_114,U_118)
& member(U_115,U_118)
& member(U_116,U_118) )
| ? [U_113,U_112] :
( ~ apply(U_117,U_112,U_113)
& apply(U_117,U_113,U_112)
& member(U_112,U_118)
& member(U_113,U_118) )
| ? [U_111] :
( ~ apply(U_117,U_111,U_111)
& member(U_111,U_118) ) )
& ( ( ! [U_110,U_109,U_108] :
( apply(U_117,U_110,U_108)
| ~ apply(U_117,U_109,U_108)
| ~ apply(U_117,U_110,U_109)
| ~ member(U_108,U_118)
| ~ member(U_109,U_118)
| ~ member(U_110,U_118) )
& ! [U_107,U_106] :
( apply(U_117,U_106,U_107)
| ~ apply(U_117,U_107,U_106)
| ~ member(U_106,U_118)
| ~ member(U_107,U_118) )
& ! [U_105] :
( apply(U_117,U_105,U_105)
| ~ member(U_105,U_118) ) )
| ~ equivalence(U_117,U_118) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ? [U_116,U_115,U_114] :
( ~ apply(U_120,U_116,U_114)
& apply(U_120,U_115,U_114)
& apply(U_120,U_116,U_115)
& member(U_114,U_122)
& member(U_115,U_122)
& member(U_116,U_122) )
| ? [U_113,U_112] :
( ~ apply(U_120,U_112,U_113)
& apply(U_120,U_113,U_112)
& member(U_112,U_122)
& member(U_113,U_122) )
| ? [U_111] :
( ~ apply(U_120,U_111,U_111)
& member(U_111,U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ? [U_116,U_115,U_114] :
( ~ apply(U_120,U_116,U_114)
& apply(U_120,U_115,U_114)
& apply(U_120,U_116,U_115)
& member(U_114,U_122)
& member(U_115,U_122)
& member(U_116,U_122) )
| ? [U_113,U_112] :
( ~ apply(U_120,U_112,U_113)
& apply(U_120,U_113,U_112)
& member(U_112,U_122)
& member(U_113,U_122) )
| ( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
& member(sK11(U_122,U_120),U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_111,sK11(U_122,U_120))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ? [U_116,U_115,U_114] :
( ~ apply(U_120,U_116,U_114)
& apply(U_120,U_115,U_114)
& apply(U_120,U_116,U_115)
& member(U_114,U_122)
& member(U_115,U_122)
& member(U_116,U_122) )
| ? [U_112] :
( ~ apply(U_120,U_112,sK12(U_122,U_120))
& apply(U_120,sK12(U_122,U_120),U_112)
& member(U_112,U_122)
& member(sK12(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
& member(sK11(U_122,U_120),U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_113,sK12(U_122,U_120))],[f_14_4]) ).
fof(f_14_6,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ? [U_116,U_115,U_114] :
( ~ apply(U_120,U_116,U_114)
& apply(U_120,U_115,U_114)
& apply(U_120,U_116,U_115)
& member(U_114,U_122)
& member(U_115,U_122)
& member(U_116,U_122) )
| ( ~ apply(U_120,sK13(U_122,U_120),sK12(U_122,U_120))
& apply(U_120,sK12(U_122,U_120),sK13(U_122,U_120))
& member(sK13(U_122,U_120),U_122)
& member(sK12(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
& member(sK11(U_122,U_120),U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_112,sK13(U_122,U_120))],[f_14_5]) ).
fof(f_14_7,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ? [U_115,U_114] :
( ~ apply(U_120,sK14(U_122,U_120),U_114)
& apply(U_120,U_115,U_114)
& apply(U_120,sK14(U_122,U_120),U_115)
& member(U_114,U_122)
& member(U_115,U_122)
& member(sK14(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK13(U_122,U_120),sK12(U_122,U_120))
& apply(U_120,sK12(U_122,U_120),sK13(U_122,U_120))
& member(sK13(U_122,U_120),U_122)
& member(sK12(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
& member(sK11(U_122,U_120),U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_116,sK14(U_122,U_120))],[f_14_6]) ).
fof(f_14_8,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ? [U_114] :
( ~ apply(U_120,sK14(U_122,U_120),U_114)
& apply(U_120,sK15(U_122,U_120),U_114)
& apply(U_120,sK14(U_122,U_120),sK15(U_122,U_120))
& member(U_114,U_122)
& member(sK15(U_122,U_120),U_122)
& member(sK14(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK13(U_122,U_120),sK12(U_122,U_120))
& apply(U_120,sK12(U_122,U_120),sK13(U_122,U_120))
& member(sK13(U_122,U_120),U_122)
& member(sK12(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
& member(sK11(U_122,U_120),U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_115,sK15(U_122,U_120))],[f_14_7]) ).
fof(f_14_9,plain,
( ! [U_122,U_120] :
( equivalence(U_120,U_122)
| ( ~ apply(U_120,sK14(U_122,U_120),sK16(U_122,U_120))
& apply(U_120,sK15(U_122,U_120),sK16(U_122,U_120))
& apply(U_120,sK14(U_122,U_120),sK15(U_122,U_120))
& member(sK16(U_122,U_120),U_122)
& member(sK15(U_122,U_120),U_122)
& member(sK14(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK13(U_122,U_120),sK12(U_122,U_120))
& apply(U_120,sK12(U_122,U_120),sK13(U_122,U_120))
& member(sK13(U_122,U_120),U_122)
& member(sK12(U_122,U_120),U_122) )
| ( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
& member(sK11(U_122,U_120),U_122) ) )
& ! [U_121,U_119] :
( ( ! [U_110,U_109,U_108] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121) )
& ! [U_107,U_106] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121) )
& ! [U_105] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121) ) )
| ~ equivalence(U_119,U_121) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_114,sK16(U_122,U_120))],[f_14_8]) ).
fof(f_14_10,plain,
( ! [U_122,U_120] :
( ~ apply(U_120,sK14(U_122,U_120),sK16(U_122,U_120))
| ~ sP17(U_122,U_120) )
& ! [U_122,U_120] :
( apply(U_120,sK15(U_122,U_120),sK16(U_122,U_120))
| ~ sP17(U_122,U_120) )
& ! [U_122,U_120] :
( apply(U_120,sK14(U_122,U_120),sK15(U_122,U_120))
| ~ sP17(U_122,U_120) )
& ! [U_122,U_120] :
( member(sK16(U_122,U_120),U_122)
| ~ sP17(U_122,U_120) )
& ! [U_122,U_120] :
( member(sK15(U_122,U_120),U_122)
| ~ sP17(U_122,U_120) )
& ! [U_122,U_120] :
( member(sK14(U_122,U_120),U_122)
| ~ sP17(U_122,U_120) )
& ! [U_122,U_120] :
( ~ apply(U_120,sK13(U_122,U_120),sK12(U_122,U_120))
| ~ sP16(U_122,U_120) )
& ! [U_122,U_120] :
( apply(U_120,sK12(U_122,U_120),sK13(U_122,U_120))
| ~ sP16(U_122,U_120) )
& ! [U_122,U_120] :
( member(sK13(U_122,U_120),U_122)
| ~ sP16(U_122,U_120) )
& ! [U_122,U_120] :
( member(sK12(U_122,U_120),U_122)
| ~ sP16(U_122,U_120) )
& ! [U_122,U_120] :
( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
| ~ sP15(U_122,U_120) )
& ! [U_122,U_120] :
( member(sK11(U_122,U_120),U_122)
| ~ sP15(U_122,U_120) )
& ! [U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121] :
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121)
| ~ sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121) )
& ! [U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121] :
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121)
| ~ sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121) )
& ! [U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121] :
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121)
| ~ sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121) )
& ! [U_122,U_120] :
( equivalence(U_120,U_122)
| sP17(U_122,U_120)
| sP16(U_122,U_120)
| sP15(U_122,U_120) )
& ! [U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121] :
( sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121)
| ~ equivalence(U_119,U_121) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15,sP16,sP17])],[f_14_9]) ).
cnf(f_14_11,plain,
( sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121)
| ~ equivalence(U_119,U_121) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_12,plain,
( equivalence(U_120,U_122)
| sP17(U_122,U_120)
| sP16(U_122,U_120)
| sP15(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_13,plain,
( apply(U_119,U_105,U_105)
| ~ member(U_105,U_121)
| ~ sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_14,plain,
( apply(U_119,U_106,U_107)
| ~ apply(U_119,U_107,U_106)
| ~ member(U_106,U_121)
| ~ member(U_107,U_121)
| ~ sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_15,plain,
( apply(U_119,U_110,U_108)
| ~ apply(U_119,U_109,U_108)
| ~ apply(U_119,U_110,U_109)
| ~ member(U_108,U_121)
| ~ member(U_109,U_121)
| ~ member(U_110,U_121)
| ~ sP14(U_107,U_119,U_108,U_109,U_110,U_105,U_106,U_121) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_16,plain,
( member(sK11(U_122,U_120),U_122)
| ~ sP15(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_17,plain,
( ~ apply(U_120,sK11(U_122,U_120),sK11(U_122,U_120))
| ~ sP15(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_18,plain,
( member(sK12(U_122,U_120),U_122)
| ~ sP16(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_19,plain,
( member(sK13(U_122,U_120),U_122)
| ~ sP16(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_20,plain,
( apply(U_120,sK12(U_122,U_120),sK13(U_122,U_120))
| ~ sP16(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_21,plain,
( ~ apply(U_120,sK13(U_122,U_120),sK12(U_122,U_120))
| ~ sP16(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_22,plain,
( member(sK14(U_122,U_120),U_122)
| ~ sP17(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_23,plain,
( member(sK15(U_122,U_120),U_122)
| ~ sP17(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_24,plain,
( member(sK16(U_122,U_120),U_122)
| ~ sP17(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_25,plain,
( apply(U_120,sK14(U_122,U_120),sK15(U_122,U_120))
| ~ sP17(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_26,plain,
( apply(U_120,sK15(U_122,U_120),sK16(U_122,U_120))
| ~ sP17(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
cnf(f_14_27,plain,
( ~ apply(U_120,sK14(U_122,U_120),sK16(U_122,U_120))
| ~ sP17(U_122,U_120) ),
inference(clausify,[status(thm)],[f_14_10]) ).
fof(f_15_1,plain,
! [R,E,A,X] :
( ( member(X,equivalence_class(A,E,R))
| ~ apply(R,A,X)
| ~ member(X,E) )
& ( ( apply(R,A,X)
& member(X,E) )
| ~ member(X,equivalence_class(A,E,R)) ) ),
inference(fof_nnf,[status(thm)],[equivalence_class]) ).
fof(f_15_2,plain,
! [U_126,U_125,U_124,U_123] :
( ( member(U_123,equivalence_class(U_124,U_125,U_126))
| ~ apply(U_126,U_124,U_123)
| ~ member(U_123,U_125) )
& ( ( apply(U_126,U_124,U_123)
& member(U_123,U_125) )
| ~ member(U_123,equivalence_class(U_124,U_125,U_126)) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_134,U_132,U_130,U_128] :
( member(U_128,equivalence_class(U_130,U_132,U_134))
| ~ apply(U_134,U_130,U_128)
| ~ member(U_128,U_132) )
& ! [U_133,U_131,U_129,U_127] :
( ( apply(U_133,U_129,U_127)
& member(U_127,U_131) )
| ~ member(U_127,equivalence_class(U_129,U_131,U_133)) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_131,U_133,U_127,U_129] :
( apply(U_133,U_129,U_127)
| ~ sP18(U_131,U_133,U_127,U_129) )
& ! [U_131,U_133,U_127,U_129] :
( member(U_127,U_131)
| ~ sP18(U_131,U_133,U_127,U_129) )
& ! [U_130,U_128,U_134,U_132] :
( member(U_128,equivalence_class(U_130,U_132,U_134))
| ~ apply(U_134,U_130,U_128)
| ~ member(U_128,U_132) )
& ! [U_131,U_133,U_127,U_129] :
( sP18(U_131,U_133,U_127,U_129)
| ~ member(U_127,equivalence_class(U_129,U_131,U_133)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP18(U_131,U_133,U_127,U_129)
| ~ member(U_127,equivalence_class(U_129,U_131,U_133)) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( member(U_128,equivalence_class(U_130,U_132,U_134))
| ~ apply(U_134,U_130,U_128)
| ~ member(U_128,U_132) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( member(U_127,U_131)
| ~ sP18(U_131,U_133,U_127,U_129) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_8,plain,
( apply(U_133,U_129,U_127)
| ~ sP18(U_131,U_133,U_127,U_129) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [R,E] :
( ( pre_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] :
( ~ 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] :
( apply(R,X,X)
| ~ member(X,E) ) )
| ~ pre_order(R,E) ) ),
inference(fof_nnf,[status(thm)],[pre_order]) ).
fof(f_16_2,plain,
! [U_144,U_143] :
( ( pre_order(U_144,U_143)
| ? [U_142,U_141,U_140] :
( ~ apply(U_144,U_142,U_140)
& apply(U_144,U_141,U_140)
& apply(U_144,U_142,U_141)
& member(U_140,U_143)
& member(U_141,U_143)
& member(U_142,U_143) )
| ? [U_139] :
( ~ apply(U_144,U_139,U_139)
& member(U_139,U_143) ) )
& ( ( ! [U_138,U_137,U_136] :
( apply(U_144,U_138,U_136)
| ~ apply(U_144,U_137,U_136)
| ~ apply(U_144,U_138,U_137)
| ~ member(U_136,U_143)
| ~ member(U_137,U_143)
| ~ member(U_138,U_143) )
& ! [U_135] :
( apply(U_144,U_135,U_135)
| ~ member(U_135,U_143) ) )
| ~ pre_order(U_144,U_143) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_148,U_146] :
( pre_order(U_148,U_146)
| ? [U_142,U_141,U_140] :
( ~ apply(U_148,U_142,U_140)
& apply(U_148,U_141,U_140)
& apply(U_148,U_142,U_141)
& member(U_140,U_146)
& member(U_141,U_146)
& member(U_142,U_146) )
| ? [U_139] :
( ~ apply(U_148,U_139,U_139)
& member(U_139,U_146) ) )
& ! [U_147,U_145] :
( ( ! [U_138,U_137,U_136] :
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145) )
& ! [U_135] :
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145) ) )
| ~ pre_order(U_147,U_145) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_148,U_146] :
( pre_order(U_148,U_146)
| ? [U_142,U_141,U_140] :
( ~ apply(U_148,U_142,U_140)
& apply(U_148,U_141,U_140)
& apply(U_148,U_142,U_141)
& member(U_140,U_146)
& member(U_141,U_146)
& member(U_142,U_146) )
| ( ~ apply(U_148,sK17(U_148,U_146),sK17(U_148,U_146))
& member(sK17(U_148,U_146),U_146) ) )
& ! [U_147,U_145] :
( ( ! [U_138,U_137,U_136] :
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145) )
& ! [U_135] :
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145) ) )
| ~ pre_order(U_147,U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_139,sK17(U_148,U_146))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_148,U_146] :
( pre_order(U_148,U_146)
| ? [U_141,U_140] :
( ~ apply(U_148,sK18(U_148,U_146),U_140)
& apply(U_148,U_141,U_140)
& apply(U_148,sK18(U_148,U_146),U_141)
& member(U_140,U_146)
& member(U_141,U_146)
& member(sK18(U_148,U_146),U_146) )
| ( ~ apply(U_148,sK17(U_148,U_146),sK17(U_148,U_146))
& member(sK17(U_148,U_146),U_146) ) )
& ! [U_147,U_145] :
( ( ! [U_138,U_137,U_136] :
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145) )
& ! [U_135] :
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145) ) )
| ~ pre_order(U_147,U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_142,sK18(U_148,U_146))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_148,U_146] :
( pre_order(U_148,U_146)
| ? [U_140] :
( ~ apply(U_148,sK18(U_148,U_146),U_140)
& apply(U_148,sK19(U_148,U_146),U_140)
& apply(U_148,sK18(U_148,U_146),sK19(U_148,U_146))
& member(U_140,U_146)
& member(sK19(U_148,U_146),U_146)
& member(sK18(U_148,U_146),U_146) )
| ( ~ apply(U_148,sK17(U_148,U_146),sK17(U_148,U_146))
& member(sK17(U_148,U_146),U_146) ) )
& ! [U_147,U_145] :
( ( ! [U_138,U_137,U_136] :
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145) )
& ! [U_135] :
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145) ) )
| ~ pre_order(U_147,U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_141,sK19(U_148,U_146))],[f_16_5]) ).
fof(f_16_7,plain,
( ! [U_148,U_146] :
( pre_order(U_148,U_146)
| ( ~ apply(U_148,sK18(U_148,U_146),sK20(U_148,U_146))
& apply(U_148,sK19(U_148,U_146),sK20(U_148,U_146))
& apply(U_148,sK18(U_148,U_146),sK19(U_148,U_146))
& member(sK20(U_148,U_146),U_146)
& member(sK19(U_148,U_146),U_146)
& member(sK18(U_148,U_146),U_146) )
| ( ~ apply(U_148,sK17(U_148,U_146),sK17(U_148,U_146))
& member(sK17(U_148,U_146),U_146) ) )
& ! [U_147,U_145] :
( ( ! [U_138,U_137,U_136] :
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145) )
& ! [U_135] :
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145) ) )
| ~ pre_order(U_147,U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_140,sK20(U_148,U_146))],[f_16_6]) ).
fof(f_16_8,plain,
( ! [U_146,U_148] :
( ~ apply(U_148,sK18(U_148,U_146),sK20(U_148,U_146))
| ~ sP21(U_146,U_148) )
& ! [U_146,U_148] :
( apply(U_148,sK19(U_148,U_146),sK20(U_148,U_146))
| ~ sP21(U_146,U_148) )
& ! [U_146,U_148] :
( apply(U_148,sK18(U_148,U_146),sK19(U_148,U_146))
| ~ sP21(U_146,U_148) )
& ! [U_146,U_148] :
( member(sK20(U_148,U_146),U_146)
| ~ sP21(U_146,U_148) )
& ! [U_146,U_148] :
( member(sK19(U_148,U_146),U_146)
| ~ sP21(U_146,U_148) )
& ! [U_146,U_148] :
( member(sK18(U_148,U_146),U_146)
| ~ sP21(U_146,U_148) )
& ! [U_146,U_148] :
( ~ apply(U_148,sK17(U_148,U_146),sK17(U_148,U_146))
| ~ sP20(U_146,U_148) )
& ! [U_146,U_148] :
( member(sK17(U_148,U_146),U_146)
| ~ sP20(U_146,U_148) )
& ! [U_147,U_138,U_145,U_135,U_136,U_137] :
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145)
| ~ sP19(U_147,U_138,U_145,U_135,U_136,U_137) )
& ! [U_147,U_138,U_145,U_135,U_136,U_137] :
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145)
| ~ sP19(U_147,U_138,U_145,U_135,U_136,U_137) )
& ! [U_146,U_148] :
( pre_order(U_148,U_146)
| sP21(U_146,U_148)
| sP20(U_146,U_148) )
& ! [U_147,U_138,U_145,U_135,U_136,U_137] :
( sP19(U_147,U_138,U_145,U_135,U_136,U_137)
| ~ pre_order(U_147,U_145) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20,sP21])],[f_16_7]) ).
cnf(f_16_9,plain,
( sP19(U_147,U_138,U_145,U_135,U_136,U_137)
| ~ pre_order(U_147,U_145) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,plain,
( pre_order(U_148,U_146)
| sP21(U_146,U_148)
| sP20(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_11,plain,
( apply(U_147,U_135,U_135)
| ~ member(U_135,U_145)
| ~ sP19(U_147,U_138,U_145,U_135,U_136,U_137) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,plain,
( apply(U_147,U_138,U_136)
| ~ apply(U_147,U_137,U_136)
| ~ apply(U_147,U_138,U_137)
| ~ member(U_136,U_145)
| ~ member(U_137,U_145)
| ~ member(U_138,U_145)
| ~ sP19(U_147,U_138,U_145,U_135,U_136,U_137) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_13,plain,
( member(sK17(U_148,U_146),U_146)
| ~ sP20(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,plain,
( ~ apply(U_148,sK17(U_148,U_146),sK17(U_148,U_146))
| ~ sP20(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_15,plain,
( member(sK18(U_148,U_146),U_146)
| ~ sP21(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_16,plain,
( member(sK19(U_148,U_146),U_146)
| ~ sP21(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_17,plain,
( member(sK20(U_148,U_146),U_146)
| ~ sP21(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_18,plain,
( apply(U_148,sK18(U_148,U_146),sK19(U_148,U_146))
| ~ sP21(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_19,plain,
( apply(U_148,sK19(U_148,U_146),sK20(U_148,U_146))
| ~ sP21(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_20,plain,
( ~ apply(U_148,sK18(U_148,U_146),sK20(U_148,U_146))
| ~ sP21(U_146,U_148) ),
inference(clausify,[status(thm)],[f_16_8]) ).
fof(f_17_1,negated_conjecture,
~ ! [E,R,X] :
( ( subset(X,E)
& equivalence(R,E) )
=> equivalence(R,X) ),
inference(negate,[status(cth)],[thIII01]) ).
fof(f_17_2,negated_conjecture,
? [E,R,X] :
( ~ equivalence(R,X)
& subset(X,E)
& equivalence(R,E) ),
inference(fof_nnf,[status(thm)],[f_17_1]) ).
fof(f_17_3,negated_conjecture,
? [U_151,U_150,U_149] :
( ~ equivalence(U_150,U_149)
& subset(U_149,U_151)
& equivalence(U_150,U_151) ),
inference(variable_rename,[status(thm)],[f_17_2]) ).
fof(f_17_4,negated_conjecture,
? [U_150,U_149] :
( ~ equivalence(U_150,U_149)
& subset(U_149,sK21)
& equivalence(U_150,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_151,sK21)],[f_17_3]) ).
fof(f_17_5,negated_conjecture,
? [U_149] :
( ~ equivalence(sK22,U_149)
& subset(U_149,sK21)
& equivalence(sK22,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_150,sK22)],[f_17_4]) ).
fof(f_17_6,negated_conjecture,
( ~ equivalence(sK22,sK23)
& subset(sK23,sK21)
& equivalence(sK22,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_149,sK23)],[f_17_5]) ).
fof(f_17_7,negated_conjecture,
( ~ equivalence(sK22,sK23)
& subset(sK23,sK21)
& equivalence(sK22,sK21) ),
inference(definitional_conversion,[status(esa)],[f_17_6]) ).
cnf(f_17_8,negated_conjecture,
equivalence(sK22,sK21),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_9,negated_conjecture,
subset(sK23,sK21),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_10,negated_conjecture,
~ equivalence(sK22,sK23),
inference(clausify,[status(thm)],[f_17_7]) ).
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,
( equivalence_class(Eq_x_0,Eq_x_1,Eq_x_2) = equivalence_class(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,
( 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_14,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_15,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_16,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_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(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,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,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_34,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_35,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_36,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(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,
( partition(Eq_y_0,Eq_y_1)
| ~ partition(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( equivalence(Eq_y_0,Eq_y_1)
| ~ equivalence(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,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_40,axiom,
( pre_order(Eq_y_0,Eq_y_1)
| ~ pre_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_41,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(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_44,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(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_45,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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_46,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(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_47,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(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_51,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_52,axiom,
( sP11(Eq_y_0,Eq_y_1)
| ~ sP11(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(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_54,axiom,
( sP13(Eq_y_0,Eq_y_1)
| ~ sP13(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_56,axiom,
( sP15(Eq_y_0,Eq_y_1)
| ~ sP15(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP16(Eq_y_0,Eq_y_1)
| ~ sP16(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP17(Eq_y_0,Eq_y_1)
| ~ sP17(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(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_60,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_61,axiom,
( sP20(Eq_y_0,Eq_y_1)
| ~ sP20(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP21(Eq_y_0,Eq_y_1)
| ~ sP21(Eq_x_0,Eq_x_1)
| 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 : SET765+4 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 22:55:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 222.16/222.45 % SZS status Theorem for theBenchmark
% 222.16/222.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------