%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET637+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 : n017.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 258.54s 258.81s
% Output : Proof 260.86s
% 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(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('theBenchmark.p',not_equal_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(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(prove_th119,conjecture,
! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
file('theBenchmark.p',prove_th119) ).
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] :
( ( 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_2_2,plain,
! [U_12,U_11] :
( ( intersect(U_12,U_11)
| ! [U_10] :
( ~ member(U_10,U_11)
| ~ member(U_10,U_12) ) )
& ( ? [U_9] :
( member(U_9,U_11)
& member(U_9,U_12) )
| ~ intersect(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ? [U_9] :
( member(U_9,U_13)
& member(U_9,U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ( member(sK1(U_15,U_13),U_13)
& member(sK1(U_15,U_13),U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_15,U_13))],[f_2_3]) ).
cnf(f_2_5,plain,
( member(sK1(U_15,U_13),U_15)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( member(sK1(U_15,U_13),U_13)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( intersect(U_16,U_14)
| ~ member(U_10,U_14)
| ~ member(U_10,U_16) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_3_2,plain,
! [U_17] : ~ member(U_17,empty_set),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ member(U_17,empty_set),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_21,U_20] :
( ( U_21 = U_20
| ? [U_19] :
( ( ~ member(U_19,U_21)
& member(U_19,U_20) )
| ( ~ member(U_19,U_20)
& member(U_19,U_21) ) ) )
& ( ! [U_18] :
( ( member(U_18,U_21)
| ~ member(U_18,U_20) )
& ( member(U_18,U_20)
| ~ member(U_18,U_21) ) )
| U_21 != U_20 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_29,U_27] :
( U_29 = U_27
| ? [U_25] :
( ~ member(U_25,U_29)
& member(U_25,U_27) )
| ? [U_24] :
( ~ member(U_24,U_27)
& member(U_24,U_29) ) )
& ! [U_28,U_26] :
( ( ! [U_23] :
( member(U_23,U_28)
| ~ member(U_23,U_26) )
& ! [U_22] :
( member(U_22,U_26)
| ~ member(U_22,U_28) ) )
| U_28 != U_26 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_29,U_27] :
( U_29 = U_27
| ? [U_25] :
( ~ member(U_25,U_29)
& member(U_25,U_27) )
| ( ~ member(sK2(U_29,U_27),U_27)
& member(sK2(U_29,U_27),U_29) ) )
& ! [U_28,U_26] :
( ( ! [U_23] :
( member(U_23,U_28)
| ~ member(U_23,U_26) )
& ! [U_22] :
( member(U_22,U_26)
| ~ member(U_22,U_28) ) )
| U_28 != U_26 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_24,sK2(U_29,U_27))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_29,U_27] :
( U_29 = U_27
| ( ~ member(sK3(U_29,U_27),U_29)
& member(sK3(U_29,U_27),U_27) )
| ( ~ member(sK2(U_29,U_27),U_27)
& member(sK2(U_29,U_27),U_29) ) )
& ! [U_28,U_26] :
( ( ! [U_23] :
( member(U_23,U_28)
| ~ member(U_23,U_26) )
& ! [U_22] :
( member(U_22,U_26)
| ~ member(U_22,U_28) ) )
| U_28 != U_26 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3(U_29,U_27))],[f_4_4]) ).
cnf(f_4_6,plain,
( member(U_22,U_26)
| ~ member(U_22,U_28)
| U_28 != U_26 ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( member(U_23,U_28)
| ~ member(U_23,U_26)
| U_28 != U_26 ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( member(sK3(U_29,U_27),U_27)
| member(sK2(U_29,U_27),U_29)
| U_29 = U_27 ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( ~ member(sK3(U_29,U_27),U_29)
| member(sK2(U_29,U_27),U_29)
| U_29 = U_27 ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( member(sK3(U_29,U_27),U_27)
| ~ member(sK2(U_29,U_27),U_27)
| U_29 = U_27 ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( ~ member(sK3(U_29,U_27),U_29)
| ~ member(sK2(U_29,U_27),U_27)
| U_29 = U_27 ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
! [B,C] :
( ( not_equal(B,C)
| B = C )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(fof_nnf,[status(thm)],[not_equal_defn]) ).
fof(f_5_2,plain,
! [U_31,U_30] :
( ( not_equal(U_31,U_30)
| U_31 = U_30 )
& ( U_31 != U_30
| ~ not_equal(U_31,U_30) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_35,U_33] :
( not_equal(U_35,U_33)
| U_35 = U_33 )
& ! [U_34,U_32] :
( U_34 != U_32
| ~ not_equal(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( U_34 != U_32
| ~ not_equal(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( not_equal(U_35,U_33)
| U_35 = U_33 ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_6_2,plain,
! [U_37,U_36] : intersection(U_37,U_36) = intersection(U_36,U_37),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
intersection(U_37,U_36) = intersection(U_36,U_37),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_7_2,plain,
! [U_39,U_38] :
( intersect(U_38,U_39)
| ~ intersect(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( intersect(U_38,U_39)
| ~ intersect(U_39,U_38) ),
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_42] :
( ( empty(U_42)
| ? [U_41] : member(U_41,U_42) )
& ( ! [U_40] : ~ member(U_40,U_42)
| ~ empty(U_42) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_44] :
( empty(U_44)
| ? [U_41] : member(U_41,U_44) )
& ! [U_43] :
( ! [U_40] : ~ member(U_40,U_43)
| ~ empty(U_43) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_44] :
( empty(U_44)
| member(sK4(U_44),U_44) )
& ! [U_43] :
( ! [U_40] : ~ member(U_40,U_43)
| ~ empty(U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_41,sK4(U_44))],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ member(U_40,U_43)
| ~ empty(U_43) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( empty(U_44)
| member(sK4(U_44),U_44) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
inference(negate,[status(cth)],[prove_th119]) ).
fof(f_9_2,negated_conjecture,
? [B,C] :
( ( ~ intersect(B,C)
& not_equal(intersection(B,C),empty_set) )
| ( ~ not_equal(intersection(B,C),empty_set)
& intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_46,U_45] :
( ( ~ intersect(U_46,U_45)
& not_equal(intersection(U_46,U_45),empty_set) )
| ( ~ not_equal(intersection(U_46,U_45),empty_set)
& intersect(U_46,U_45) ) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ? [U_50,U_48] :
( ~ intersect(U_50,U_48)
& not_equal(intersection(U_50,U_48),empty_set) )
| ? [U_49,U_47] :
( ~ not_equal(intersection(U_49,U_47),empty_set)
& intersect(U_49,U_47) ) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ? [U_50,U_48] :
( ~ intersect(U_50,U_48)
& not_equal(intersection(U_50,U_48),empty_set) )
| ? [U_47] :
( ~ not_equal(intersection(sK5,U_47),empty_set)
& intersect(sK5,U_47) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_49,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_50,U_48] :
( ~ intersect(U_50,U_48)
& not_equal(intersection(U_50,U_48),empty_set) )
| ( ~ not_equal(intersection(sK5,sK6),empty_set)
& intersect(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_47,sK6)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ? [U_48] :
( ~ intersect(sK7,U_48)
& not_equal(intersection(sK7,U_48),empty_set) )
| ( ~ not_equal(intersection(sK5,sK6),empty_set)
& intersect(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_50,sK7)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ( ~ intersect(sK7,sK8)
& not_equal(intersection(sK7,sK8),empty_set) )
| ( ~ not_equal(intersection(sK5,sK6),empty_set)
& intersect(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_48,sK8)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
( not_equal(intersection(sK7,sK8),empty_set)
| intersect(sK5,sK6) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,negated_conjecture,
( ~ intersect(sK7,sK8)
| intersect(sK5,sK6) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_11,negated_conjecture,
( not_equal(intersection(sK7,sK8),empty_set)
| ~ not_equal(intersection(sK5,sK6),empty_set) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_12,negated_conjecture,
( ~ intersect(sK7,sK8)
| ~ not_equal(intersection(sK5,sK6),empty_set) ),
inference(clausify,[status(thm)],[f_9_8]) ).
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,
( 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_6,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_7,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_8,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| 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,
( not_equal(Eq_y_0,Eq_y_1)
| ~ not_equal(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 : SET637+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 : n017.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 22:39:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 258.54/258.81 % SZS status Theorem for theBenchmark
% 258.54/258.81 % SZS output start Proof for theBenchmark
% See solution above
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