%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET366+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 08:56:46 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : Proof 0.08s
% 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(thI47,conjecture,
! [A] : member(empty_set,power_set(A)),
file('theBenchmark.p',thI47) ).
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,negated_conjecture,
~ ! [A] : member(empty_set,power_set(A)),
inference(negate,[status(cth)],[thI47]) ).
fof(f_12_2,negated_conjecture,
? [A] : ~ member(empty_set,power_set(A)),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_79] : ~ member(empty_set,power_set(U_79)),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
~ member(empty_set,power_set(sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_79,sK4)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
~ member(empty_set,power_set(sK4)),
inference(definitional_conversion,[status(esa)],[f_12_4]) ).
cnf(f_12_6,negated_conjecture,
~ member(empty_set,power_set(sK4)),
inference(clausify,[status(thm)],[f_12_5]) ).
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,
( 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_16,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_17,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET366+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 22:15:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------