%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET635+3 : 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 : n006.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 08:57:11 AM UTC 2026
% Result : Theorem 15.97s 16.26s
% Output : Proof 16.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('theBenchmark.p',difference_empty_set) ).
fof(union_empty_set,axiom,
! [B] : union(B,empty_set) = B,
file('theBenchmark.p',union_empty_set) ).
fof(difference_and_intersection_and_union,axiom,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
file('theBenchmark.p',difference_and_intersection_and_union) ).
fof(difference_and_intersection,axiom,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
file('theBenchmark.p',difference_and_intersection) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(prove_th117,conjecture,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
file('theBenchmark.p',prove_th117) ).
fof(f_1_1,plain,
! [B,C] : subset(intersection(B,C),B),
inference(fof_nnf,[status(thm)],[intersection_is_subset]) ).
fof(f_1_2,plain,
! [U_1,U_0] : subset(intersection(U_1,U_0),U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
subset(intersection(U_1,U_0),U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C] :
( ( difference(B,C) = empty_set
| ~ subset(B,C) )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(fof_nnf,[status(thm)],[difference_empty_set]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ( difference(U_3,U_2) = empty_set
| ~ subset(U_3,U_2) )
& ( subset(U_3,U_2)
| difference(U_3,U_2) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_7,U_5] :
( difference(U_7,U_5) = empty_set
| ~ subset(U_7,U_5) )
& ! [U_6,U_4] :
( subset(U_6,U_4)
| difference(U_6,U_4) != empty_set ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_6,U_4)
| difference(U_6,U_4) != empty_set ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( difference(U_7,U_5) = empty_set
| ~ subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B] : union(B,empty_set) = B,
inference(fof_nnf,[status(thm)],[union_empty_set]) ).
fof(f_3_2,plain,
! [U_8] : union(U_8,empty_set) = U_8,
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
union(U_8,empty_set) = U_8,
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(fof_nnf,[status(thm)],[difference_and_intersection_and_union]) ).
fof(f_4_2,plain,
! [U_11,U_10,U_9] : difference(U_11,intersection(U_10,U_9)) = union(difference(U_11,U_10),difference(U_11,U_9)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
difference(U_11,intersection(U_10,U_9)) = union(difference(U_11,U_10),difference(U_11,U_9)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
inference(fof_nnf,[status(thm)],[difference_and_intersection]) ).
fof(f_5_2,plain,
! [U_14,U_13,U_12] : intersection(U_14,difference(U_13,U_12)) = difference(intersection(U_14,U_13),U_12),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
intersection(U_14,difference(U_13,U_12)) = difference(intersection(U_14,U_13),U_12),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [B,C,D] :
( ( member(D,intersection(B,C))
| ~ member(D,C)
| ~ member(D,B) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(fof_nnf,[status(thm)],[intersection_defn]) ).
fof(f_6_2,plain,
! [U_17,U_16,U_15] :
( ( member(U_15,intersection(U_17,U_16))
| ~ member(U_15,U_16)
| ~ member(U_15,U_17) )
& ( ( member(U_15,U_16)
& member(U_15,U_17) )
| ~ member(U_15,intersection(U_17,U_16)) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_23,U_21,U_19] :
( member(U_19,intersection(U_23,U_21))
| ~ member(U_19,U_21)
| ~ member(U_19,U_23) )
& ! [U_22,U_20,U_18] :
( ( member(U_18,U_20)
& member(U_18,U_22) )
| ~ member(U_18,intersection(U_22,U_20)) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( member(U_18,U_22)
| ~ member(U_18,intersection(U_22,U_20)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( member(U_18,U_20)
| ~ member(U_18,intersection(U_22,U_20)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( member(U_19,intersection(U_23,U_21))
| ~ member(U_19,U_21)
| ~ member(U_19,U_23) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [B,C,D] :
( ( member(D,difference(B,C))
| member(D,C)
| ~ member(D,B) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(fof_nnf,[status(thm)],[difference_defn]) ).
fof(f_7_2,plain,
! [U_26,U_25,U_24] :
( ( member(U_24,difference(U_26,U_25))
| member(U_24,U_25)
| ~ member(U_24,U_26) )
& ( ( ~ member(U_24,U_25)
& member(U_24,U_26) )
| ~ member(U_24,difference(U_26,U_25)) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_32,U_30,U_28] :
( member(U_28,difference(U_32,U_30))
| member(U_28,U_30)
| ~ member(U_28,U_32) )
& ! [U_31,U_29,U_27] :
( ( ~ member(U_27,U_29)
& member(U_27,U_31) )
| ~ member(U_27,difference(U_31,U_29)) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( member(U_27,U_31)
| ~ member(U_27,difference(U_31,U_29)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ member(U_27,U_29)
| ~ member(U_27,difference(U_31,U_29)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( member(U_28,difference(U_32,U_30))
| member(U_28,U_30)
| ~ member(U_28,U_32) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [B,C] :
( ( B = C
| ~ subset(C,B)
| ~ subset(B,C) )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(fof_nnf,[status(thm)],[equal_defn]) ).
fof(f_8_2,plain,
! [U_34,U_33] :
( ( U_34 = U_33
| ~ subset(U_33,U_34)
| ~ subset(U_34,U_33) )
& ( ( subset(U_33,U_34)
& subset(U_34,U_33) )
| U_34 != U_33 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_38,U_36] :
( U_38 = U_36
| ~ subset(U_36,U_38)
| ~ subset(U_38,U_36) )
& ! [U_37,U_35] :
( ( subset(U_35,U_37)
& subset(U_37,U_35) )
| U_37 != U_35 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( subset(U_37,U_35)
| U_37 != U_35 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(U_35,U_37)
| U_37 != U_35 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( U_38 = U_36
| ~ subset(U_36,U_38)
| ~ subset(U_38,U_36) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_9_2,plain,
! [U_40,U_39] : union(U_40,U_39) = union(U_39,U_40),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
union(U_40,U_39) = union(U_39,U_40),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_10_2,plain,
! [U_41] : ~ member(U_41,empty_set),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ member(U_41,empty_set),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_11_2,plain,
! [U_43,U_42] : intersection(U_43,U_42) = intersection(U_42,U_43),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
intersection(U_43,U_42) = intersection(U_42,U_43),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [B,C] :
( ( subset(B,C)
| ? [D] :
( ~ member(D,C)
& member(D,B) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(f_12_2,plain,
! [U_47,U_46] :
( ( subset(U_47,U_46)
| ? [U_45] :
( ~ member(U_45,U_46)
& member(U_45,U_47) ) )
& ( ! [U_44] :
( member(U_44,U_46)
| ~ member(U_44,U_47) )
| ~ subset(U_47,U_46) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_51,U_49] :
( subset(U_51,U_49)
| ? [U_45] :
( ~ member(U_45,U_49)
& member(U_45,U_51) ) )
& ! [U_50,U_48] :
( ! [U_44] :
( member(U_44,U_48)
| ~ member(U_44,U_50) )
| ~ subset(U_50,U_48) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_51,U_49] :
( subset(U_51,U_49)
| ( ~ member(sK1(U_51,U_49),U_49)
& member(sK1(U_51,U_49),U_51) ) )
& ! [U_50,U_48] :
( ! [U_44] :
( member(U_44,U_48)
| ~ member(U_44,U_50) )
| ~ subset(U_50,U_48) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_45,sK1(U_51,U_49))],[f_12_3]) ).
cnf(f_12_5,plain,
( member(U_44,U_48)
| ~ member(U_44,U_50)
| ~ subset(U_50,U_48) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( member(sK1(U_51,U_49),U_51)
| subset(U_51,U_49) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
( ~ member(sK1(U_51,U_49),U_49)
| subset(U_51,U_49) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_13_2,plain,
! [U_52] : subset(U_52,U_52),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
subset(U_52,U_52),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [B,C] :
( ( B = C
| ? [D] :
( ( ~ member(D,B)
& member(D,C) )
| ( ~ member(D,C)
& member(D,B) ) ) )
& ( ! [D] :
( ( member(D,B)
| ~ member(D,C) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(f_14_2,plain,
! [U_56,U_55] :
( ( U_56 = U_55
| ? [U_54] :
( ( ~ member(U_54,U_56)
& member(U_54,U_55) )
| ( ~ member(U_54,U_55)
& member(U_54,U_56) ) ) )
& ( ! [U_53] :
( ( member(U_53,U_56)
| ~ member(U_53,U_55) )
& ( member(U_53,U_55)
| ~ member(U_53,U_56) ) )
| U_56 != U_55 ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_64,U_62] :
( U_64 = U_62
| ? [U_60] :
( ~ member(U_60,U_64)
& member(U_60,U_62) )
| ? [U_59] :
( ~ member(U_59,U_62)
& member(U_59,U_64) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( member(U_58,U_63)
| ~ member(U_58,U_61) )
& ! [U_57] :
( member(U_57,U_61)
| ~ member(U_57,U_63) ) )
| U_63 != U_61 ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_64,U_62] :
( U_64 = U_62
| ? [U_60] :
( ~ member(U_60,U_64)
& member(U_60,U_62) )
| ( ~ member(sK2(U_64,U_62),U_62)
& member(sK2(U_64,U_62),U_64) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( member(U_58,U_63)
| ~ member(U_58,U_61) )
& ! [U_57] :
( member(U_57,U_61)
| ~ member(U_57,U_63) ) )
| U_63 != U_61 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_59,sK2(U_64,U_62))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_64,U_62] :
( U_64 = U_62
| ( ~ member(sK3(U_64,U_62),U_64)
& member(sK3(U_64,U_62),U_62) )
| ( ~ member(sK2(U_64,U_62),U_62)
& member(sK2(U_64,U_62),U_64) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( member(U_58,U_63)
| ~ member(U_58,U_61) )
& ! [U_57] :
( member(U_57,U_61)
| ~ member(U_57,U_63) ) )
| U_63 != U_61 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_60,sK3(U_64,U_62))],[f_14_4]) ).
cnf(f_14_6,plain,
( member(U_57,U_61)
| ~ member(U_57,U_63)
| U_63 != U_61 ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( member(U_58,U_63)
| ~ member(U_58,U_61)
| U_63 != U_61 ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( member(sK3(U_64,U_62),U_62)
| member(sK2(U_64,U_62),U_64)
| U_64 = U_62 ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( ~ member(sK3(U_64,U_62),U_64)
| member(sK2(U_64,U_62),U_64)
| U_64 = U_62 ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( member(sK3(U_64,U_62),U_62)
| ~ member(sK2(U_64,U_62),U_62)
| U_64 = U_62 ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ member(sK3(U_64,U_62),U_64)
| ~ member(sK2(U_64,U_62),U_62)
| U_64 = U_62 ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_15_2,plain,
! [U_67] :
( ( empty(U_67)
| ? [U_66] : member(U_66,U_67) )
& ( ! [U_65] : ~ member(U_65,U_67)
| ~ empty(U_67) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_69] :
( empty(U_69)
| ? [U_66] : member(U_66,U_69) )
& ! [U_68] :
( ! [U_65] : ~ member(U_65,U_68)
| ~ empty(U_68) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_69] :
( empty(U_69)
| member(sK4(U_69),U_69) )
& ! [U_68] :
( ! [U_65] : ~ member(U_65,U_68)
| ~ empty(U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_66,sK4(U_69))],[f_15_3]) ).
cnf(f_15_5,plain,
( ~ member(U_65,U_68)
| ~ empty(U_68) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( empty(U_69)
| member(sK4(U_69),U_69) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,negated_conjecture,
~ ! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
inference(negate,[status(cth)],[prove_th117]) ).
fof(f_16_2,negated_conjecture,
? [B,C,D] : intersection(B,difference(C,D)) != difference(intersection(B,C),intersection(B,D)),
inference(fof_nnf,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
? [U_72,U_71,U_70] : intersection(U_72,difference(U_71,U_70)) != difference(intersection(U_72,U_71),intersection(U_72,U_70)),
inference(variable_rename,[status(thm)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
? [U_71,U_70] : intersection(sK5,difference(U_71,U_70)) != difference(intersection(sK5,U_71),intersection(sK5,U_70)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_72,sK5)],[f_16_3]) ).
fof(f_16_5,negated_conjecture,
? [U_70] : intersection(sK5,difference(sK6,U_70)) != difference(intersection(sK5,sK6),intersection(sK5,U_70)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_71,sK6)],[f_16_4]) ).
fof(f_16_6,negated_conjecture,
intersection(sK5,difference(sK6,sK7)) != difference(intersection(sK5,sK6),intersection(sK5,sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_70,sK7)],[f_16_5]) ).
fof(f_16_7,negated_conjecture,
intersection(sK5,difference(sK6,sK7)) != difference(intersection(sK5,sK6),intersection(sK5,sK7)),
inference(definitional_conversion,[status(esa)],[f_16_6]) ).
cnf(f_16_8,negated_conjecture,
intersection(sK5,difference(sK6,sK7)) != difference(intersection(sK5,sK6),intersection(sK5,sK7)),
inference(clausify,[status(thm)],[f_16_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,
( 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_5,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_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,
( 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_8,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_9,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_10,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,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_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| 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 : SET635+3 : 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
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 22:44:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 15.97/16.26 % SZS status Theorem for theBenchmark
% 15.97/16.26 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------