%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET629+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 : n005.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 08:57:10 AM UTC 2026
% Result : Theorem 0.38s 0.65s
% Output : Proof 0.38s
% 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(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
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_and_difference_disjoint,conjecture,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('theBenchmark.p',prove_intersection_and_difference_disjoint) ).
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,C] :
( ( intersect(B,C)
| ! [D] :
( ~ member(D,C)
| ~ member(D,B) ) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(f_3_2,plain,
! [U_21,U_20] :
( ( intersect(U_21,U_20)
| ! [U_19] :
( ~ member(U_19,U_20)
| ~ member(U_19,U_21) ) )
& ( ? [U_18] :
( member(U_18,U_20)
& member(U_18,U_21) )
| ~ intersect(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_25,U_23] :
( intersect(U_25,U_23)
| ! [U_19] :
( ~ member(U_19,U_23)
| ~ member(U_19,U_25) ) )
& ! [U_24,U_22] :
( ? [U_18] :
( member(U_18,U_22)
& member(U_18,U_24) )
| ~ intersect(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_25,U_23] :
( intersect(U_25,U_23)
| ! [U_19] :
( ~ member(U_19,U_23)
| ~ member(U_19,U_25) ) )
& ! [U_24,U_22] :
( ( member(sK1(U_24,U_22),U_22)
& member(sK1(U_24,U_22),U_24) )
| ~ intersect(U_24,U_22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_18,sK1(U_24,U_22))],[f_3_3]) ).
cnf(f_3_5,plain,
( member(sK1(U_24,U_22),U_24)
| ~ intersect(U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( member(sK1(U_24,U_22),U_22)
| ~ intersect(U_24,U_22) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( intersect(U_25,U_23)
| ~ member(U_19,U_23)
| ~ member(U_19,U_25) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [B,C] :
( ( disjoint(B,C)
| intersect(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(fof_nnf,[status(thm)],[disjoint_defn]) ).
fof(f_4_2,plain,
! [U_27,U_26] :
( ( disjoint(U_27,U_26)
| intersect(U_27,U_26) )
& ( ~ intersect(U_27,U_26)
| ~ disjoint(U_27,U_26) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_31,U_29] :
( disjoint(U_31,U_29)
| intersect(U_31,U_29) )
& ! [U_30,U_28] :
( ~ intersect(U_30,U_28)
| ~ disjoint(U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ intersect(U_30,U_28)
| ~ disjoint(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( disjoint(U_31,U_29)
| intersect(U_31,U_29) ),
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_33,U_32] : intersection(U_33,U_32) = intersection(U_32,U_33),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
intersection(U_33,U_32) = intersection(U_32,U_33),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_6_2,plain,
! [U_35,U_34] :
( intersect(U_34,U_35)
| ~ intersect(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( intersect(U_34,U_35)
| ~ intersect(U_35,U_34) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_39,U_38] :
( ( U_39 = U_38
| ? [U_37] :
( ( ~ member(U_37,U_39)
& member(U_37,U_38) )
| ( ~ member(U_37,U_38)
& member(U_37,U_39) ) ) )
& ( ! [U_36] :
( ( member(U_36,U_39)
| ~ member(U_36,U_38) )
& ( member(U_36,U_38)
| ~ member(U_36,U_39) ) )
| U_39 != U_38 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ? [U_43] :
( ~ member(U_43,U_47)
& member(U_43,U_45) )
| ? [U_42] :
( ~ member(U_42,U_45)
& member(U_42,U_47) ) )
& ! [U_46,U_44] :
( ( ! [U_41] :
( member(U_41,U_46)
| ~ member(U_41,U_44) )
& ! [U_40] :
( member(U_40,U_44)
| ~ member(U_40,U_46) ) )
| U_46 != U_44 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ? [U_43] :
( ~ member(U_43,U_47)
& member(U_43,U_45) )
| ( ~ member(sK2(U_47,U_45),U_45)
& member(sK2(U_47,U_45),U_47) ) )
& ! [U_46,U_44] :
( ( ! [U_41] :
( member(U_41,U_46)
| ~ member(U_41,U_44) )
& ! [U_40] :
( member(U_40,U_44)
| ~ member(U_40,U_46) ) )
| U_46 != U_44 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_42,sK2(U_47,U_45))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ( ~ member(sK3(U_47,U_45),U_47)
& member(sK3(U_47,U_45),U_45) )
| ( ~ member(sK2(U_47,U_45),U_45)
& member(sK2(U_47,U_45),U_47) ) )
& ! [U_46,U_44] :
( ( ! [U_41] :
( member(U_41,U_46)
| ~ member(U_41,U_44) )
& ! [U_40] :
( member(U_40,U_44)
| ~ member(U_40,U_46) ) )
| U_46 != U_44 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_43,sK3(U_47,U_45))],[f_7_4]) ).
cnf(f_7_6,plain,
( member(U_40,U_44)
| ~ member(U_40,U_46)
| U_46 != U_44 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( member(U_41,U_46)
| ~ member(U_41,U_44)
| U_46 != U_44 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( member(sK3(U_47,U_45),U_45)
| member(sK2(U_47,U_45),U_47)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( ~ member(sK3(U_47,U_45),U_47)
| member(sK2(U_47,U_45),U_47)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( member(sK3(U_47,U_45),U_45)
| ~ member(sK2(U_47,U_45),U_45)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ member(sK3(U_47,U_45),U_47)
| ~ member(sK2(U_47,U_45),U_45)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),difference(B,C)),
inference(negate,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
fof(f_8_2,negated_conjecture,
? [B,C] : ~ disjoint(intersection(B,C),difference(B,C)),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_49,U_48] : ~ disjoint(intersection(U_49,U_48),difference(U_49,U_48)),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_48] : ~ disjoint(intersection(sK4,U_48),difference(sK4,U_48)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_49,sK4)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
~ disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_48,sK5)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
~ disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(definitional_conversion,[status(esa)],[f_8_5]) ).
cnf(f_8_7,negated_conjecture,
~ disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(clausify,[status(thm)],[f_8_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,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_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,
( 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_10,axiom,
( intersect(Eq_y_0,Eq_y_1)
| ~ intersect(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,
( 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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET629+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
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 22:44:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.38/0.65 % SZS status Theorem for theBenchmark
% 0.38/0.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------