%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET008+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 : n026.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 08:55:51 AM UTC 2026
% Result : Theorem 0.67s 1.38s
% Output : Proof 0.76s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_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(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_intersection_difference_empty_set,conjecture,
! [B,C] : intersection(difference(B,C),C) = empty_set,
file('theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(f_1_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_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,intersection(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,intersection(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,intersection(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,intersection(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( member(U_3,U_7)
| ~ member(U_3,intersection(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_3,U_5)
| ~ member(U_3,intersection(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( member(U_4,intersection(U_8,U_6))
| ~ member(U_4,U_6)
| ~ member(U_4,U_8) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_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_2_2,plain,
! [U_11,U_10,U_9] :
( ( member(U_9,difference(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,difference(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,difference(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,difference(U_16,U_14)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( member(U_12,U_16)
| ~ member(U_12,difference(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ member(U_12,U_14)
| ~ member(U_12,difference(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( member(U_13,difference(U_17,U_15))
| member(U_13,U_15)
| ~ member(U_13,U_17) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_3_2,plain,
! [U_18] : ~ member(U_18,empty_set),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ member(U_18,empty_set),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_20,U_19] :
( ( U_20 = U_19
| ~ subset(U_19,U_20)
| ~ subset(U_20,U_19) )
& ( ( subset(U_19,U_20)
& subset(U_20,U_19) )
| U_20 != U_19 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_24,U_22] :
( U_24 = U_22
| ~ subset(U_22,U_24)
| ~ subset(U_24,U_22) )
& ! [U_23,U_21] :
( ( subset(U_21,U_23)
& subset(U_23,U_21) )
| U_23 != U_21 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset(U_23,U_21)
| U_23 != U_21 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( subset(U_21,U_23)
| U_23 != U_21 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( U_24 = U_22
| ~ subset(U_22,U_24)
| ~ subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_5_2,plain,
! [U_26,U_25] : intersection(U_26,U_25) = intersection(U_25,U_26),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
intersection(U_26,U_25) = intersection(U_25,U_26),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_30,U_29] :
( ( subset(U_30,U_29)
| ? [U_28] :
( ~ member(U_28,U_29)
& member(U_28,U_30) ) )
& ( ! [U_27] :
( member(U_27,U_29)
| ~ member(U_27,U_30) )
| ~ subset(U_30,U_29) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_34,U_32] :
( subset(U_34,U_32)
| ? [U_28] :
( ~ member(U_28,U_32)
& member(U_28,U_34) ) )
& ! [U_33,U_31] :
( ! [U_27] :
( member(U_27,U_31)
| ~ member(U_27,U_33) )
| ~ subset(U_33,U_31) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_34,U_32] :
( subset(U_34,U_32)
| ( ~ member(sK1(U_34,U_32),U_32)
& member(sK1(U_34,U_32),U_34) ) )
& ! [U_33,U_31] :
( ! [U_27] :
( member(U_27,U_31)
| ~ member(U_27,U_33) )
| ~ subset(U_33,U_31) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_28,sK1(U_34,U_32))],[f_6_3]) ).
cnf(f_6_5,plain,
( member(U_27,U_31)
| ~ member(U_27,U_33)
| ~ subset(U_33,U_31) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( member(sK1(U_34,U_32),U_34)
| subset(U_34,U_32) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ member(sK1(U_34,U_32),U_32)
| subset(U_34,U_32) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_7_2,plain,
! [U_35] : subset(U_35,U_35),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
subset(U_35,U_35),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_8_2,plain,
! [U_38] :
( ( empty(U_38)
| ? [U_37] : member(U_37,U_38) )
& ( ! [U_36] : ~ member(U_36,U_38)
| ~ empty(U_38) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_40] :
( empty(U_40)
| ? [U_37] : member(U_37,U_40) )
& ! [U_39] :
( ! [U_36] : ~ member(U_36,U_39)
| ~ empty(U_39) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_40] :
( empty(U_40)
| member(sK2(U_40),U_40) )
& ! [U_39] :
( ! [U_36] : ~ member(U_36,U_39)
| ~ empty(U_39) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_37,sK2(U_40))],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ member(U_36,U_39)
| ~ empty(U_39) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( empty(U_40)
| member(sK2(U_40),U_40) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_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_9_2,plain,
! [U_44,U_43] :
( ( U_44 = U_43
| ? [U_42] :
( ( ~ member(U_42,U_44)
& member(U_42,U_43) )
| ( ~ member(U_42,U_43)
& member(U_42,U_44) ) ) )
& ( ! [U_41] :
( ( member(U_41,U_44)
| ~ member(U_41,U_43) )
& ( member(U_41,U_43)
| ~ member(U_41,U_44) ) )
| U_44 != U_43 ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_52,U_50] :
( U_52 = U_50
| ? [U_48] :
( ~ member(U_48,U_52)
& member(U_48,U_50) )
| ? [U_47] :
( ~ member(U_47,U_50)
& member(U_47,U_52) ) )
& ! [U_51,U_49] :
( ( ! [U_46] :
( member(U_46,U_51)
| ~ member(U_46,U_49) )
& ! [U_45] :
( member(U_45,U_49)
| ~ member(U_45,U_51) ) )
| U_51 != U_49 ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_52,U_50] :
( U_52 = U_50
| ? [U_48] :
( ~ member(U_48,U_52)
& member(U_48,U_50) )
| ( ~ member(sK3(U_52,U_50),U_50)
& member(sK3(U_52,U_50),U_52) ) )
& ! [U_51,U_49] :
( ( ! [U_46] :
( member(U_46,U_51)
| ~ member(U_46,U_49) )
& ! [U_45] :
( member(U_45,U_49)
| ~ member(U_45,U_51) ) )
| U_51 != U_49 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_47,sK3(U_52,U_50))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_52,U_50] :
( U_52 = U_50
| ( ~ member(sK4(U_52,U_50),U_52)
& member(sK4(U_52,U_50),U_50) )
| ( ~ member(sK3(U_52,U_50),U_50)
& member(sK3(U_52,U_50),U_52) ) )
& ! [U_51,U_49] :
( ( ! [U_46] :
( member(U_46,U_51)
| ~ member(U_46,U_49) )
& ! [U_45] :
( member(U_45,U_49)
| ~ member(U_45,U_51) ) )
| U_51 != U_49 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_48,sK4(U_52,U_50))],[f_9_4]) ).
cnf(f_9_6,plain,
( member(U_45,U_49)
| ~ member(U_45,U_51)
| U_51 != U_49 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( member(U_46,U_51)
| ~ member(U_46,U_49)
| U_51 != U_49 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( member(sK4(U_52,U_50),U_50)
| member(sK3(U_52,U_50),U_52)
| U_52 = U_50 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ member(sK4(U_52,U_50),U_52)
| member(sK3(U_52,U_50),U_52)
| U_52 = U_50 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( member(sK4(U_52,U_50),U_50)
| ~ member(sK3(U_52,U_50),U_50)
| U_52 = U_50 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ member(sK4(U_52,U_50),U_52)
| ~ member(sK3(U_52,U_50),U_50)
| U_52 = U_50 ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,negated_conjecture,
~ ! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(negate,[status(cth)],[prove_intersection_difference_empty_set]) ).
fof(f_10_2,negated_conjecture,
? [B,C] : intersection(difference(B,C),C) != empty_set,
inference(fof_nnf,[status(thm)],[f_10_1]) ).
fof(f_10_3,negated_conjecture,
? [U_54,U_53] : intersection(difference(U_54,U_53),U_53) != empty_set,
inference(variable_rename,[status(thm)],[f_10_2]) ).
fof(f_10_4,negated_conjecture,
? [U_53] : intersection(difference(sK5,U_53),U_53) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_54,sK5)],[f_10_3]) ).
fof(f_10_5,negated_conjecture,
intersection(difference(sK5,sK6),sK6) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_53,sK6)],[f_10_4]) ).
fof(f_10_6,negated_conjecture,
intersection(difference(sK5,sK6),sK6) != empty_set,
inference(definitional_conversion,[status(esa)],[f_10_5]) ).
cnf(f_10_7,negated_conjecture,
intersection(difference(sK5,sK6),sK6) != empty_set,
inference(clausify,[status(thm)],[f_10_6]) ).
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,
( 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_7,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,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_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,
( 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 : SET008+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
% 0.11/0.78 % Computer : n026.cluster.edu
% 0.11/0.78 % Model : x86_64 x86_64
% 0.11/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.78 % Memory : 8046.5625MB
% 0.11/0.78 % OS : Linux 6.8.0-71-generic
% 0.11/0.78 % CPULimit : 300
% 0.11/0.78 % WCLimit : 300
% 0.11/0.78 % DateTime : Sat Sep 19 21:28:51 UTC 2026
% 0.11/0.78 % CPUTime :
% 0.67/1.38 % SZS status Theorem for theBenchmark
% 0.67/1.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------