%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET585+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 : n001.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 08:57:01 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_subset,axiom,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('theBenchmark.p',transitivity_of_subset) ).
fof(subset_of_union,axiom,
! [B,C] : subset(B,union(B,C)),
file('theBenchmark.p',subset_of_union) ).
fof(intersection_is_subset,axiom,
! [B,C] : subset(intersection(B,C),B),
file('theBenchmark.p',intersection_is_subset) ).
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(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_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(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_intersection_subset_of_union,conjecture,
! [B,C,D] : subset(intersection(B,C),union(B,D)),
file('theBenchmark.p',prove_intersection_subset_of_union) ).
fof(f_1_1,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[transitivity_of_subset]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( subset(U_2,U_0)
| ~ subset(U_1,U_0)
| ~ subset(U_2,U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C] : subset(B,union(B,C)),
inference(fof_nnf,[status(thm)],[subset_of_union]) ).
fof(f_2_2,plain,
! [U_4,U_3] : subset(U_4,union(U_4,U_3)),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
subset(U_4,union(U_4,U_3)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B,C] : subset(intersection(B,C),B),
inference(fof_nnf,[status(thm)],[intersection_is_subset]) ).
fof(f_3_2,plain,
! [U_6,U_5] : subset(intersection(U_6,U_5),U_6),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
subset(intersection(U_6,U_5),U_6),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_9,U_8,U_7] :
( ( member(U_7,union(U_9,U_8))
| ( ~ member(U_7,U_8)
& ~ member(U_7,U_9) ) )
& ( member(U_7,U_8)
| member(U_7,U_9)
| ~ member(U_7,union(U_9,U_8)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_15,U_13,U_11] :
( member(U_11,union(U_15,U_13))
| ( ~ member(U_11,U_13)
& ~ member(U_11,U_15) ) )
& ! [U_14,U_12,U_10] :
( member(U_10,U_12)
| member(U_10,U_14)
| ~ member(U_10,union(U_14,U_12)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_10,U_12)
| member(U_10,U_14)
| ~ member(U_10,union(U_14,U_12)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ member(U_11,U_15)
| member(U_11,union(U_15,U_13)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( ~ member(U_11,U_13)
| member(U_11,union(U_15,U_13)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_18,U_17,U_16] :
( ( member(U_16,intersection(U_18,U_17))
| ~ member(U_16,U_17)
| ~ member(U_16,U_18) )
& ( ( member(U_16,U_17)
& member(U_16,U_18) )
| ~ member(U_16,intersection(U_18,U_17)) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_24,U_22,U_20] :
( member(U_20,intersection(U_24,U_22))
| ~ member(U_20,U_22)
| ~ member(U_20,U_24) )
& ! [U_23,U_21,U_19] :
( ( member(U_19,U_21)
& member(U_19,U_23) )
| ~ member(U_19,intersection(U_23,U_21)) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( member(U_19,U_23)
| ~ member(U_19,intersection(U_23,U_21)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( member(U_19,U_21)
| ~ member(U_19,intersection(U_23,U_21)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( member(U_20,intersection(U_24,U_22))
| ~ member(U_20,U_22)
| ~ member(U_20,U_24) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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_28,U_27] :
( ( subset(U_28,U_27)
| ? [U_26] :
( ~ member(U_26,U_27)
& member(U_26,U_28) ) )
& ( ! [U_25] :
( member(U_25,U_27)
| ~ member(U_25,U_28) )
| ~ subset(U_28,U_27) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_32,U_30] :
( subset(U_32,U_30)
| ? [U_26] :
( ~ member(U_26,U_30)
& member(U_26,U_32) ) )
& ! [U_31,U_29] :
( ! [U_25] :
( member(U_25,U_29)
| ~ member(U_25,U_31) )
| ~ subset(U_31,U_29) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_32,U_30] :
( subset(U_32,U_30)
| ( ~ member(sK1(U_32,U_30),U_30)
& member(sK1(U_32,U_30),U_32) ) )
& ! [U_31,U_29] :
( ! [U_25] :
( member(U_25,U_29)
| ~ member(U_25,U_31) )
| ~ subset(U_31,U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_26,sK1(U_32,U_30))],[f_6_3]) ).
cnf(f_6_5,plain,
( member(U_25,U_29)
| ~ member(U_25,U_31)
| ~ subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( member(sK1(U_32,U_30),U_32)
| subset(U_32,U_30) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ member(sK1(U_32,U_30),U_30)
| subset(U_32,U_30) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_7_2,plain,
! [U_34,U_33] : union(U_34,U_33) = union(U_33,U_34),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
union(U_34,U_33) = union(U_33,U_34),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_8_2,plain,
! [U_36,U_35] : intersection(U_36,U_35) = intersection(U_35,U_36),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
intersection(U_36,U_35) = intersection(U_35,U_36),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_9_2,plain,
! [U_37] : subset(U_37,U_37),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
subset(U_37,U_37),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_41,U_40] :
( ( U_41 = U_40
| ? [U_39] :
( ( ~ member(U_39,U_41)
& member(U_39,U_40) )
| ( ~ member(U_39,U_40)
& member(U_39,U_41) ) ) )
& ( ! [U_38] :
( ( member(U_38,U_41)
| ~ member(U_38,U_40) )
& ( member(U_38,U_40)
| ~ member(U_38,U_41) ) )
| U_41 != U_40 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_49,U_47] :
( U_49 = U_47
| ? [U_45] :
( ~ member(U_45,U_49)
& member(U_45,U_47) )
| ? [U_44] :
( ~ member(U_44,U_47)
& member(U_44,U_49) ) )
& ! [U_48,U_46] :
( ( ! [U_43] :
( member(U_43,U_48)
| ~ member(U_43,U_46) )
& ! [U_42] :
( member(U_42,U_46)
| ~ member(U_42,U_48) ) )
| U_48 != U_46 ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_49,U_47] :
( U_49 = U_47
| ? [U_45] :
( ~ member(U_45,U_49)
& member(U_45,U_47) )
| ( ~ member(sK2(U_49,U_47),U_47)
& member(sK2(U_49,U_47),U_49) ) )
& ! [U_48,U_46] :
( ( ! [U_43] :
( member(U_43,U_48)
| ~ member(U_43,U_46) )
& ! [U_42] :
( member(U_42,U_46)
| ~ member(U_42,U_48) ) )
| U_48 != U_46 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_44,sK2(U_49,U_47))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_49,U_47] :
( U_49 = U_47
| ( ~ member(sK3(U_49,U_47),U_49)
& member(sK3(U_49,U_47),U_47) )
| ( ~ member(sK2(U_49,U_47),U_47)
& member(sK2(U_49,U_47),U_49) ) )
& ! [U_48,U_46] :
( ( ! [U_43] :
( member(U_43,U_48)
| ~ member(U_43,U_46) )
& ! [U_42] :
( member(U_42,U_46)
| ~ member(U_42,U_48) ) )
| U_48 != U_46 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_45,sK3(U_49,U_47))],[f_10_4]) ).
cnf(f_10_6,plain,
( member(U_42,U_46)
| ~ member(U_42,U_48)
| U_48 != U_46 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( member(U_43,U_48)
| ~ member(U_43,U_46)
| U_48 != U_46 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( member(sK3(U_49,U_47),U_47)
| member(sK2(U_49,U_47),U_49)
| U_49 = U_47 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( ~ member(sK3(U_49,U_47),U_49)
| member(sK2(U_49,U_47),U_49)
| U_49 = U_47 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( member(sK3(U_49,U_47),U_47)
| ~ member(sK2(U_49,U_47),U_47)
| U_49 = U_47 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( ~ member(sK3(U_49,U_47),U_49)
| ~ member(sK2(U_49,U_47),U_47)
| U_49 = U_47 ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,negated_conjecture,
~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
inference(negate,[status(cth)],[prove_intersection_subset_of_union]) ).
fof(f_11_2,negated_conjecture,
? [B,C,D] : ~ subset(intersection(B,C),union(B,D)),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_52,U_51,U_50] : ~ subset(intersection(U_52,U_51),union(U_52,U_50)),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_51,U_50] : ~ subset(intersection(sK4,U_51),union(sK4,U_50)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_52,sK4)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
? [U_50] : ~ subset(intersection(sK4,sK5),union(sK4,U_50)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_51,sK5)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
~ subset(intersection(sK4,sK5),union(sK4,sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_50,sK6)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
~ subset(intersection(sK4,sK5),union(sK4,sK6)),
inference(definitional_conversion,[status(esa)],[f_11_6]) ).
cnf(f_11_8,negated_conjecture,
~ subset(intersection(sK4,sK5),union(sK4,sK6)),
inference(clausify,[status(thm)],[f_11_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,
( 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,
( 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_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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET585+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 22:46:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------