%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET010+3 : 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 08:55:52 AM UTC 2026
% Result : Theorem 38.94s 39.60s
% Output : Proof 39.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
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(union_subset,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('theBenchmark.p',union_subset) ).
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
fof(subset_difference,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('theBenchmark.p',subset_difference) ).
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(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(prove_difference_and_intersection_and_union,conjecture,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
file('theBenchmark.p',prove_difference_and_intersection_and_union) ).
fof(f_1_1,plain,
! [B,C,D] :
( ( member(D,union(B,C))
| ( ~ member(D,C)
& ~ member(D,B) ) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(fof_nnf,[status(thm)],[union_defn]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,union(U_2,U_1))
| ( ~ member(U_0,U_1)
& ~ member(U_0,U_2) ) )
& ( member(U_0,U_1)
| member(U_0,U_2)
| ~ member(U_0,union(U_2,U_1)) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_8,U_6,U_4] :
( member(U_4,union(U_8,U_6))
| ( ~ member(U_4,U_6)
& ~ member(U_4,U_8) ) )
& ! [U_7,U_5,U_3] :
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_4,U_8,U_6] :
( ~ member(U_4,U_6)
| ~ sP0(U_4,U_8,U_6) )
& ! [U_4,U_8,U_6] :
( ~ member(U_4,U_8)
| ~ sP0(U_4,U_8,U_6) )
& ! [U_4,U_8,U_6] :
( member(U_4,union(U_8,U_6))
| sP0(U_4,U_8,U_6) )
& ! [U_5,U_3,U_7] :
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(U_4,union(U_8,U_6))
| sP0(U_4,U_8,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ member(U_4,U_8)
| ~ sP0(U_4,U_8,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( ~ member(U_4,U_6)
| ~ sP0(U_4,U_8,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_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_2_2,plain,
! [U_11,U_10,U_9] :
( ( member(U_9,intersection(U_11,U_10))
| ~ member(U_9,U_10)
| ~ member(U_9,U_11) )
& ( ( member(U_9,U_10)
& member(U_9,U_11) )
| ~ member(U_9,intersection(U_11,U_10)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_17,U_15,U_13] :
( member(U_13,intersection(U_17,U_15))
| ~ member(U_13,U_15)
| ~ member(U_13,U_17) )
& ! [U_16,U_14,U_12] :
( ( member(U_12,U_14)
& member(U_12,U_16) )
| ~ member(U_12,intersection(U_16,U_14)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_12,U_14,U_16] :
( member(U_12,U_14)
| ~ sP1(U_12,U_14,U_16) )
& ! [U_12,U_14,U_16] :
( member(U_12,U_16)
| ~ sP1(U_12,U_14,U_16) )
& ! [U_15,U_13,U_17] :
( member(U_13,intersection(U_17,U_15))
| ~ member(U_13,U_15)
| ~ member(U_13,U_17) )
& ! [U_12,U_14,U_16] :
( sP1(U_12,U_14,U_16)
| ~ member(U_12,intersection(U_16,U_14)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_2_3]) ).
cnf(f_2_5,plain,
( sP1(U_12,U_14,U_16)
| ~ member(U_12,intersection(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(U_13,intersection(U_17,U_15))
| ~ member(U_13,U_15)
| ~ member(U_13,U_17) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( member(U_12,U_16)
| ~ sP1(U_12,U_14,U_16) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_8,plain,
( member(U_12,U_14)
| ~ sP1(U_12,U_14,U_16) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_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_3_2,plain,
! [U_20,U_19,U_18] :
( ( member(U_18,difference(U_20,U_19))
| member(U_18,U_19)
| ~ member(U_18,U_20) )
& ( ( ~ member(U_18,U_19)
& member(U_18,U_20) )
| ~ member(U_18,difference(U_20,U_19)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_26,U_24,U_22] :
( member(U_22,difference(U_26,U_24))
| member(U_22,U_24)
| ~ member(U_22,U_26) )
& ! [U_25,U_23,U_21] :
( ( ~ member(U_21,U_23)
& member(U_21,U_25) )
| ~ member(U_21,difference(U_25,U_23)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_23,U_21,U_25] :
( ~ member(U_21,U_23)
| ~ sP2(U_23,U_21,U_25) )
& ! [U_23,U_21,U_25] :
( member(U_21,U_25)
| ~ sP2(U_23,U_21,U_25) )
& ! [U_26,U_22,U_24] :
( member(U_22,difference(U_26,U_24))
| member(U_22,U_24)
| ~ member(U_22,U_26) )
& ! [U_23,U_21,U_25] :
( sP2(U_23,U_21,U_25)
| ~ member(U_21,difference(U_25,U_23)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_3_3]) ).
cnf(f_3_5,plain,
( sP2(U_23,U_21,U_25)
| ~ member(U_21,difference(U_25,U_23)) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( member(U_22,difference(U_26,U_24))
| member(U_22,U_24)
| ~ member(U_22,U_26) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( member(U_21,U_25)
| ~ sP2(U_23,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_8,plain,
( ~ member(U_21,U_23)
| ~ sP2(U_23,U_21,U_25) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[union_subset]) ).
fof(f_4_2,plain,
! [U_29,U_28,U_27] :
( subset(union(U_29,U_27),U_28)
| ~ subset(U_27,U_28)
| ~ subset(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_28,U_29,U_27] :
( subset(union(U_29,U_27),U_28)
| ~ subset(U_27,U_28)
| ~ subset(U_29,U_28) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset(union(U_29,U_27),U_28)
| ~ subset(U_27,U_28)
| ~ subset(U_29,U_28) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B,C] : subset(intersection(B,C),B),
inference(fof_nnf,[status(thm)],[intersection_is_subset]) ).
fof(f_5_2,plain,
! [U_31,U_30] : subset(intersection(U_31,U_30),U_31),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_30,U_31] : subset(intersection(U_31,U_30),U_31),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
subset(intersection(U_31,U_30),U_31),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [B,C,D] :
( subset(difference(D,C),difference(D,B))
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[subset_difference]) ).
fof(f_6_2,plain,
! [U_34,U_33,U_32] :
( subset(difference(U_32,U_33),difference(U_32,U_34))
| ~ subset(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_34,U_33] :
( ! [U_32] : subset(difference(U_32,U_33),difference(U_32,U_34))
| ~ subset(U_34,U_33) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_33,U_34,U_32] :
( subset(difference(U_32,U_33),difference(U_32,U_34))
| ~ subset(U_34,U_33) ),
inference(definitional_conversion,[status(esa)],[f_6_3]) ).
cnf(f_6_5,plain,
( subset(difference(U_32,U_33),difference(U_32,U_34))
| ~ subset(U_34,U_33) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_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_7_2,plain,
! [U_36,U_35] :
( ( U_36 = U_35
| ~ subset(U_35,U_36)
| ~ subset(U_36,U_35) )
& ( ( subset(U_35,U_36)
& subset(U_36,U_35) )
| U_36 != U_35 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_40,U_38] :
( U_40 = U_38
| ~ subset(U_38,U_40)
| ~ subset(U_40,U_38) )
& ! [U_39,U_37] :
( ( subset(U_37,U_39)
& subset(U_39,U_37) )
| U_39 != U_37 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_39,U_37] :
( subset(U_37,U_39)
| ~ sP3(U_39,U_37) )
& ! [U_39,U_37] :
( subset(U_39,U_37)
| ~ sP3(U_39,U_37) )
& ! [U_38,U_40] :
( U_40 = U_38
| ~ subset(U_38,U_40)
| ~ subset(U_40,U_38) )
& ! [U_39,U_37] :
( sP3(U_39,U_37)
| U_39 != U_37 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_7_3]) ).
cnf(f_7_5,plain,
( sP3(U_39,U_37)
| U_39 != U_37 ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( U_40 = U_38
| ~ subset(U_38,U_40)
| ~ subset(U_40,U_38) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
( subset(U_39,U_37)
| ~ sP3(U_39,U_37) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_8,plain,
( subset(U_37,U_39)
| ~ sP3(U_39,U_37) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_8_2,plain,
! [U_42,U_41] : union(U_42,U_41) = union(U_41,U_42),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_41,U_42] : union(U_42,U_41) = union(U_41,U_42),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
union(U_42,U_41) = union(U_41,U_42),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_9_2,plain,
! [U_44,U_43] : intersection(U_44,U_43) = intersection(U_43,U_44),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_44,U_43] : intersection(U_44,U_43) = intersection(U_43,U_44),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
intersection(U_44,U_43) = intersection(U_43,U_44),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_48,U_47] :
( ( subset(U_48,U_47)
| ? [U_46] :
( ~ member(U_46,U_47)
& member(U_46,U_48) ) )
& ( ! [U_45] :
( member(U_45,U_47)
| ~ member(U_45,U_48) )
| ~ subset(U_48,U_47) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_52,U_50] :
( subset(U_52,U_50)
| ? [U_46] :
( ~ member(U_46,U_50)
& member(U_46,U_52) ) )
& ! [U_51,U_49] :
( ! [U_45] :
( member(U_45,U_49)
| ~ member(U_45,U_51) )
| ~ subset(U_51,U_49) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_52,U_50] :
( subset(U_52,U_50)
| ( ~ member(sK1(U_52,U_50),U_50)
& member(sK1(U_52,U_50),U_52) ) )
& ! [U_51,U_49] :
( ! [U_45] :
( member(U_45,U_49)
| ~ member(U_45,U_51) )
| ~ subset(U_51,U_49) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_46,sK1(U_52,U_50))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_50,U_52] :
( ~ member(sK1(U_52,U_50),U_50)
| ~ sP4(U_50,U_52) )
& ! [U_50,U_52] :
( member(sK1(U_52,U_50),U_52)
| ~ sP4(U_50,U_52) )
& ! [U_50,U_52] :
( subset(U_52,U_50)
| sP4(U_50,U_52) )
& ! [U_45,U_49,U_51] :
( member(U_45,U_49)
| ~ member(U_45,U_51)
| ~ subset(U_51,U_49) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_10_4]) ).
cnf(f_10_6,plain,
( member(U_45,U_49)
| ~ member(U_45,U_51)
| ~ subset(U_51,U_49) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( subset(U_52,U_50)
| sP4(U_50,U_52) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( member(sK1(U_52,U_50),U_52)
| ~ sP4(U_50,U_52) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( ~ member(sK1(U_52,U_50),U_50)
| ~ sP4(U_50,U_52) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_11_2,plain,
! [U_53] : subset(U_53,U_53),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_53] : subset(U_53,U_53),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
subset(U_53,U_53),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_57,U_56] :
( ( U_57 = U_56
| ? [U_55] :
( ( ~ member(U_55,U_57)
& member(U_55,U_56) )
| ( ~ member(U_55,U_56)
& member(U_55,U_57) ) ) )
& ( ! [U_54] :
( ( member(U_54,U_57)
| ~ member(U_54,U_56) )
& ( member(U_54,U_56)
| ~ member(U_54,U_57) ) )
| U_57 != U_56 ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_65,U_63] :
( U_65 = U_63
| ? [U_61] :
( ~ member(U_61,U_65)
& member(U_61,U_63) )
| ? [U_60] :
( ~ member(U_60,U_63)
& member(U_60,U_65) ) )
& ! [U_64,U_62] :
( ( ! [U_59] :
( member(U_59,U_64)
| ~ member(U_59,U_62) )
& ! [U_58] :
( member(U_58,U_62)
| ~ member(U_58,U_64) ) )
| U_64 != U_62 ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_65,U_63] :
( U_65 = U_63
| ? [U_61] :
( ~ member(U_61,U_65)
& member(U_61,U_63) )
| ( ~ member(sK2(U_65,U_63),U_63)
& member(sK2(U_65,U_63),U_65) ) )
& ! [U_64,U_62] :
( ( ! [U_59] :
( member(U_59,U_64)
| ~ member(U_59,U_62) )
& ! [U_58] :
( member(U_58,U_62)
| ~ member(U_58,U_64) ) )
| U_64 != U_62 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_60,sK2(U_65,U_63))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_65,U_63] :
( U_65 = U_63
| ( ~ member(sK3(U_65,U_63),U_65)
& member(sK3(U_65,U_63),U_63) )
| ( ~ member(sK2(U_65,U_63),U_63)
& member(sK2(U_65,U_63),U_65) ) )
& ! [U_64,U_62] :
( ( ! [U_59] :
( member(U_59,U_64)
| ~ member(U_59,U_62) )
& ! [U_58] :
( member(U_58,U_62)
| ~ member(U_58,U_64) ) )
| U_64 != U_62 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_61,sK3(U_65,U_63))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_65,U_63] :
( ~ member(sK3(U_65,U_63),U_65)
| ~ sP7(U_65,U_63) )
& ! [U_65,U_63] :
( member(sK3(U_65,U_63),U_63)
| ~ sP7(U_65,U_63) )
& ! [U_65,U_63] :
( ~ member(sK2(U_65,U_63),U_63)
| ~ sP6(U_65,U_63) )
& ! [U_65,U_63] :
( member(sK2(U_65,U_63),U_65)
| ~ sP6(U_65,U_63) )
& ! [U_62,U_59,U_58,U_64] :
( member(U_59,U_64)
| ~ member(U_59,U_62)
| ~ sP5(U_62,U_59,U_58,U_64) )
& ! [U_62,U_59,U_58,U_64] :
( member(U_58,U_62)
| ~ member(U_58,U_64)
| ~ sP5(U_62,U_59,U_58,U_64) )
& ! [U_65,U_63] :
( U_65 = U_63
| sP7(U_65,U_63)
| sP6(U_65,U_63) )
& ! [U_62,U_59,U_58,U_64] :
( sP5(U_62,U_59,U_58,U_64)
| U_64 != U_62 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6,sP7])],[f_12_5]) ).
cnf(f_12_7,plain,
( sP5(U_62,U_59,U_58,U_64)
| U_64 != U_62 ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,plain,
( U_65 = U_63
| sP7(U_65,U_63)
| sP6(U_65,U_63) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,plain,
( member(U_58,U_62)
| ~ member(U_58,U_64)
| ~ sP5(U_62,U_59,U_58,U_64) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_10,plain,
( member(U_59,U_64)
| ~ member(U_59,U_62)
| ~ sP5(U_62,U_59,U_58,U_64) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_11,plain,
( member(sK2(U_65,U_63),U_65)
| ~ sP6(U_65,U_63) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_12,plain,
( ~ member(sK2(U_65,U_63),U_63)
| ~ sP6(U_65,U_63) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_13,plain,
( member(sK3(U_65,U_63),U_63)
| ~ sP7(U_65,U_63) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_14,plain,
( ~ member(sK3(U_65,U_63),U_65)
| ~ sP7(U_65,U_63) ),
inference(clausify,[status(thm)],[f_12_6]) ).
fof(f_13_1,negated_conjecture,
~ ! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(negate,[status(cth)],[prove_difference_and_intersection_and_union]) ).
fof(f_13_2,negated_conjecture,
? [B,C,D] : difference(B,intersection(C,D)) != union(difference(B,C),difference(B,D)),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_68,U_67,U_66] : difference(U_68,intersection(U_67,U_66)) != union(difference(U_68,U_67),difference(U_68,U_66)),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_67,U_66] : difference(sK4,intersection(U_67,U_66)) != union(difference(sK4,U_67),difference(sK4,U_66)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_68,sK4)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
? [U_66] : difference(sK4,intersection(sK5,U_66)) != union(difference(sK4,sK5),difference(sK4,U_66)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_67,sK5)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
difference(sK4,intersection(sK5,sK6)) != union(difference(sK4,sK5),difference(sK4,sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_66,sK6)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
difference(sK4,intersection(sK5,sK6)) != union(difference(sK4,sK5),difference(sK4,sK6)),
inference(definitional_conversion,[status(esa)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
difference(sK4,intersection(sK5,sK6)) != union(difference(sK4,sK5),difference(sK4,sK6)),
inference(clausify,[status(thm)],[f_13_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,
( 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_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,
( 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_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,
( 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_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,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(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_13,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(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_14,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_15,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(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,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(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,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(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_18,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_19,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET010+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.76 % Computer : n011.cluster.edu
% 0.08/0.76 % Model : x86_64 x86_64
% 0.08/0.76 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.76 % Memory : 8046.5625MB
% 0.08/0.76 % OS : Linux 6.8.0-71-generic
% 0.08/0.76 % CPULimit : 300
% 0.08/0.76 % WCLimit : 300
% 0.08/0.76 % DateTime : Sat Sep 19 21:26:10 UTC 2026
% 0.08/0.77 % CPUTime :
% 38.94/39.60 % SZS status Theorem for theBenchmark
% 38.94/39.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------