%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET639+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 : n013.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 08:57:12 AM UTC 2026
% Result : Theorem 0.27s 0.57s
% Output : Proof 0.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('theBenchmark.p',subset_intersection) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_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(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(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_th121,conjecture,
! [B,C] :
( ( intersection(C,B) = empty_set
& subset(B,C) )
=> B = empty_set ),
file('theBenchmark.p',prove_th121) ).
fof(f_1_1,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[subset_intersection]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( intersection(U_1,U_0) = U_1
| ~ subset(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( intersection(U_1,U_0) = U_1
| ~ subset(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_2_2,plain,
! [U_2] : ~ member(U_2,empty_set),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
~ member(U_2,empty_set),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_5,U_4,U_3] :
( ( member(U_3,intersection(U_5,U_4))
| ~ member(U_3,U_4)
| ~ member(U_3,U_5) )
& ( ( member(U_3,U_4)
& member(U_3,U_5) )
| ~ member(U_3,intersection(U_5,U_4)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_11,U_9,U_7] :
( member(U_7,intersection(U_11,U_9))
| ~ member(U_7,U_9)
| ~ member(U_7,U_11) )
& ! [U_10,U_8,U_6] :
( ( member(U_6,U_8)
& member(U_6,U_10) )
| ~ member(U_6,intersection(U_10,U_8)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( member(U_6,U_10)
| ~ member(U_6,intersection(U_10,U_8)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( member(U_6,U_8)
| ~ member(U_6,intersection(U_10,U_8)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( member(U_7,intersection(U_11,U_9))
| ~ member(U_7,U_9)
| ~ member(U_7,U_11) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_15,U_14] :
( ( subset(U_15,U_14)
| ? [U_13] :
( ~ member(U_13,U_14)
& member(U_13,U_15) ) )
& ( ! [U_12] :
( member(U_12,U_14)
| ~ member(U_12,U_15) )
| ~ subset(U_15,U_14) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_19,U_17] :
( subset(U_19,U_17)
| ? [U_13] :
( ~ member(U_13,U_17)
& member(U_13,U_19) ) )
& ! [U_18,U_16] :
( ! [U_12] :
( member(U_12,U_16)
| ~ member(U_12,U_18) )
| ~ subset(U_18,U_16) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_19,U_17] :
( subset(U_19,U_17)
| ( ~ member(sK1(U_19,U_17),U_17)
& member(sK1(U_19,U_17),U_19) ) )
& ! [U_18,U_16] :
( ! [U_12] :
( member(U_12,U_16)
| ~ member(U_12,U_18) )
| ~ subset(U_18,U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_13,sK1(U_19,U_17))],[f_4_3]) ).
cnf(f_4_5,plain,
( member(U_12,U_16)
| ~ member(U_12,U_18)
| ~ subset(U_18,U_16) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( member(sK1(U_19,U_17),U_19)
| subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ member(sK1(U_19,U_17),U_17)
| subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_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_5_2,plain,
! [U_21,U_20] :
( ( U_21 = U_20
| ~ subset(U_20,U_21)
| ~ subset(U_21,U_20) )
& ( ( subset(U_20,U_21)
& subset(U_21,U_20) )
| U_21 != U_20 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_25,U_23] :
( U_25 = U_23
| ~ subset(U_23,U_25)
| ~ subset(U_25,U_23) )
& ! [U_24,U_22] :
( ( subset(U_22,U_24)
& subset(U_24,U_22) )
| U_24 != U_22 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( subset(U_24,U_22)
| U_24 != U_22 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subset(U_22,U_24)
| U_24 != U_22 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_25 = U_23
| ~ subset(U_23,U_25)
| ~ subset(U_25,U_23) ),
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_27,U_26] : intersection(U_27,U_26) = intersection(U_26,U_27),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
intersection(U_27,U_26) = intersection(U_26,U_27),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_7_2,plain,
! [U_28] : subset(U_28,U_28),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
subset(U_28,U_28),
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_31] :
( ( empty(U_31)
| ? [U_30] : member(U_30,U_31) )
& ( ! [U_29] : ~ member(U_29,U_31)
| ~ empty(U_31) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_33] :
( empty(U_33)
| ? [U_30] : member(U_30,U_33) )
& ! [U_32] :
( ! [U_29] : ~ member(U_29,U_32)
| ~ empty(U_32) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_33] :
( empty(U_33)
| member(sK2(U_33),U_33) )
& ! [U_32] :
( ! [U_29] : ~ member(U_29,U_32)
| ~ empty(U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2(U_33))],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ member(U_29,U_32)
| ~ empty(U_32) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( empty(U_33)
| member(sK2(U_33),U_33) ),
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_37,U_36] :
( ( U_37 = U_36
| ? [U_35] :
( ( ~ member(U_35,U_37)
& member(U_35,U_36) )
| ( ~ member(U_35,U_36)
& member(U_35,U_37) ) ) )
& ( ! [U_34] :
( ( member(U_34,U_37)
| ~ member(U_34,U_36) )
& ( member(U_34,U_36)
| ~ member(U_34,U_37) ) )
| U_37 != U_36 ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_45,U_43] :
( U_45 = U_43
| ? [U_41] :
( ~ member(U_41,U_45)
& member(U_41,U_43) )
| ? [U_40] :
( ~ member(U_40,U_43)
& member(U_40,U_45) ) )
& ! [U_44,U_42] :
( ( ! [U_39] :
( member(U_39,U_44)
| ~ member(U_39,U_42) )
& ! [U_38] :
( member(U_38,U_42)
| ~ member(U_38,U_44) ) )
| U_44 != U_42 ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_45,U_43] :
( U_45 = U_43
| ? [U_41] :
( ~ member(U_41,U_45)
& member(U_41,U_43) )
| ( ~ member(sK3(U_45,U_43),U_43)
& member(sK3(U_45,U_43),U_45) ) )
& ! [U_44,U_42] :
( ( ! [U_39] :
( member(U_39,U_44)
| ~ member(U_39,U_42) )
& ! [U_38] :
( member(U_38,U_42)
| ~ member(U_38,U_44) ) )
| U_44 != U_42 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_40,sK3(U_45,U_43))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_45,U_43] :
( U_45 = U_43
| ( ~ member(sK4(U_45,U_43),U_45)
& member(sK4(U_45,U_43),U_43) )
| ( ~ member(sK3(U_45,U_43),U_43)
& member(sK3(U_45,U_43),U_45) ) )
& ! [U_44,U_42] :
( ( ! [U_39] :
( member(U_39,U_44)
| ~ member(U_39,U_42) )
& ! [U_38] :
( member(U_38,U_42)
| ~ member(U_38,U_44) ) )
| U_44 != U_42 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_41,sK4(U_45,U_43))],[f_9_4]) ).
cnf(f_9_6,plain,
( member(U_38,U_42)
| ~ member(U_38,U_44)
| U_44 != U_42 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( member(U_39,U_44)
| ~ member(U_39,U_42)
| U_44 != U_42 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( member(sK4(U_45,U_43),U_43)
| member(sK3(U_45,U_43),U_45)
| U_45 = U_43 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ member(sK4(U_45,U_43),U_45)
| member(sK3(U_45,U_43),U_45)
| U_45 = U_43 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( member(sK4(U_45,U_43),U_43)
| ~ member(sK3(U_45,U_43),U_43)
| U_45 = U_43 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ member(sK4(U_45,U_43),U_45)
| ~ member(sK3(U_45,U_43),U_43)
| U_45 = U_43 ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,negated_conjecture,
~ ! [B,C] :
( ( intersection(C,B) = empty_set
& subset(B,C) )
=> B = empty_set ),
inference(negate,[status(cth)],[prove_th121]) ).
fof(f_10_2,negated_conjecture,
? [B,C] :
( B != empty_set
& intersection(C,B) = empty_set
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_10_1]) ).
fof(f_10_3,negated_conjecture,
? [U_47,U_46] :
( U_47 != empty_set
& intersection(U_46,U_47) = empty_set
& subset(U_47,U_46) ),
inference(variable_rename,[status(thm)],[f_10_2]) ).
fof(f_10_4,negated_conjecture,
? [U_47] :
( ? [U_46] :
( intersection(U_46,U_47) = empty_set
& subset(U_47,U_46) )
& U_47 != empty_set ),
inference(miniscope,[status(thm)],[f_10_3]) ).
fof(f_10_5,negated_conjecture,
( ? [U_46] :
( intersection(U_46,sK5) = empty_set
& subset(sK5,U_46) )
& sK5 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_47,sK5)],[f_10_4]) ).
fof(f_10_6,negated_conjecture,
( intersection(sK6,sK5) = empty_set
& subset(sK5,sK6)
& sK5 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6)],[f_10_5]) ).
fof(f_10_7,negated_conjecture,
( intersection(sK6,sK5) = empty_set
& subset(sK5,sK6)
& sK5 != empty_set ),
inference(definitional_conversion,[status(esa)],[f_10_6]) ).
cnf(f_10_8,negated_conjecture,
sK5 != empty_set,
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,negated_conjecture,
subset(sK5,sK6),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,negated_conjecture,
intersection(sK6,sK5) = empty_set,
inference(clausify,[status(thm)],[f_10_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,
( 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) = sK2(Eq_y_0)
| 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,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_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(equality_11,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
% 0.00/0.02 % Problem : SET639+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
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 22:43:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.27/0.57 % SZS status Theorem for theBenchmark
% 0.27/0.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------