%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET596+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 : 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 08:57:03 AM UTC 2026
% Result : Theorem 1.57s 1.88s
% Output : Proof 1.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('theBenchmark.p',subset_of_empty_set_is_empty_set) ).
fof(intersection_of_subset,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('theBenchmark.p',intersection_of_subset) ).
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_th55,conjecture,
! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,C) )
=> intersection(B,D) = empty_set ),
file('theBenchmark.p',prove_th55) ).
fof(f_1_1,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set) ),
inference(fof_nnf,[status(thm)],[subset_of_empty_set_is_empty_set]) ).
fof(f_1_2,plain,
! [U_0] :
( U_0 = empty_set
| ~ subset(U_0,empty_set) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( U_0 = empty_set
| ~ subset(U_0,empty_set) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C,D] :
( subset(intersection(B,D),intersection(C,D))
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[intersection_of_subset]) ).
fof(f_2_2,plain,
! [U_3,U_2,U_1] :
( subset(intersection(U_3,U_1),intersection(U_2,U_1))
| ~ subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( ! [U_1] : subset(intersection(U_3,U_1),intersection(U_2,U_1))
| ~ subset(U_3,U_2) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(intersection(U_3,U_1),intersection(U_2,U_1))
| ~ subset(U_3,U_2) ),
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_4] : ~ member(U_4,empty_set),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ member(U_4,empty_set),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_7,U_6,U_5] :
( ( member(U_5,intersection(U_7,U_6))
| ~ member(U_5,U_6)
| ~ member(U_5,U_7) )
& ( ( member(U_5,U_6)
& member(U_5,U_7) )
| ~ member(U_5,intersection(U_7,U_6)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_13,U_11,U_9] :
( member(U_9,intersection(U_13,U_11))
| ~ member(U_9,U_11)
| ~ member(U_9,U_13) )
& ! [U_12,U_10,U_8] :
( ( member(U_8,U_10)
& member(U_8,U_12) )
| ~ member(U_8,intersection(U_12,U_10)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_8,U_12)
| ~ member(U_8,intersection(U_12,U_10)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( member(U_8,U_10)
| ~ member(U_8,intersection(U_12,U_10)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( member(U_9,intersection(U_13,U_11))
| ~ member(U_9,U_11)
| ~ member(U_9,U_13) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_17,U_16] :
( ( subset(U_17,U_16)
| ? [U_15] :
( ~ member(U_15,U_16)
& member(U_15,U_17) ) )
& ( ! [U_14] :
( member(U_14,U_16)
| ~ member(U_14,U_17) )
| ~ subset(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ? [U_15] :
( ~ member(U_15,U_19)
& member(U_15,U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( member(U_14,U_18)
| ~ member(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ( ~ member(sK1(U_21,U_19),U_19)
& member(sK1(U_21,U_19),U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( member(U_14,U_18)
| ~ member(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_21,U_19))],[f_5_3]) ).
cnf(f_5_5,plain,
( member(U_14,U_18)
| ~ member(U_14,U_20)
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( member(sK1(U_21,U_19),U_21)
| subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ member(sK1(U_21,U_19),U_19)
| subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_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_6_2,plain,
! [U_23,U_22] :
( ( U_23 = U_22
| ~ subset(U_22,U_23)
| ~ subset(U_23,U_22) )
& ( ( subset(U_22,U_23)
& subset(U_23,U_22) )
| U_23 != U_22 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_27,U_25] :
( U_27 = U_25
| ~ subset(U_25,U_27)
| ~ subset(U_27,U_25) )
& ! [U_26,U_24] :
( ( subset(U_24,U_26)
& subset(U_26,U_24) )
| U_26 != U_24 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( subset(U_26,U_24)
| U_26 != U_24 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( subset(U_24,U_26)
| U_26 != U_24 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( U_27 = U_25
| ~ subset(U_25,U_27)
| ~ subset(U_27,U_25) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_7_2,plain,
! [U_29,U_28] : intersection(U_29,U_28) = intersection(U_28,U_29),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
intersection(U_29,U_28) = intersection(U_28,U_29),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_8_2,plain,
! [U_30] : subset(U_30,U_30),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
subset(U_30,U_30),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_9_2,plain,
! [U_33] :
( ( empty(U_33)
| ? [U_32] : member(U_32,U_33) )
& ( ! [U_31] : ~ member(U_31,U_33)
| ~ empty(U_33) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_35] :
( empty(U_35)
| ? [U_32] : member(U_32,U_35) )
& ! [U_34] :
( ! [U_31] : ~ member(U_31,U_34)
| ~ empty(U_34) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_35] :
( empty(U_35)
| member(sK2(U_35),U_35) )
& ! [U_34] :
( ! [U_31] : ~ member(U_31,U_34)
| ~ empty(U_34) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_32,sK2(U_35))],[f_9_3]) ).
cnf(f_9_5,plain,
( ~ member(U_31,U_34)
| ~ empty(U_34) ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( empty(U_35)
| member(sK2(U_35),U_35) ),
inference(clausify,[status(thm)],[f_9_4]) ).
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_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_10_1]) ).
fof(f_10_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_10_2]) ).
fof(f_10_4,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ? [U_43] :
( ~ member(U_43,U_47)
& member(U_43,U_45) )
| ( ~ member(sK3(U_47,U_45),U_45)
& member(sK3(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_42,sK3(U_47,U_45))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ( ~ member(sK4(U_47,U_45),U_47)
& member(sK4(U_47,U_45),U_45) )
| ( ~ member(sK3(U_47,U_45),U_45)
& member(sK3(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,[sK4]),skolemize(U_43,sK4(U_47,U_45))],[f_10_4]) ).
cnf(f_10_6,plain,
( member(U_40,U_44)
| ~ member(U_40,U_46)
| U_46 != U_44 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( member(U_41,U_46)
| ~ member(U_41,U_44)
| U_46 != U_44 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( member(sK4(U_47,U_45),U_45)
| member(sK3(U_47,U_45),U_47)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( ~ member(sK4(U_47,U_45),U_47)
| member(sK3(U_47,U_45),U_47)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( member(sK4(U_47,U_45),U_45)
| ~ member(sK3(U_47,U_45),U_45)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( ~ member(sK4(U_47,U_45),U_47)
| ~ member(sK3(U_47,U_45),U_45)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,C) )
=> intersection(B,D) = empty_set ),
inference(negate,[status(cth)],[prove_th55]) ).
fof(f_11_2,negated_conjecture,
? [B,C,D] :
( intersection(B,D) != empty_set
& intersection(C,D) = empty_set
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_50,U_49,U_48] :
( intersection(U_50,U_48) != empty_set
& intersection(U_49,U_48) = empty_set
& subset(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_49,U_48] :
( intersection(sK5,U_48) != empty_set
& intersection(U_49,U_48) = empty_set
& subset(sK5,U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_50,sK5)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
? [U_48] :
( intersection(sK5,U_48) != empty_set
& intersection(sK6,U_48) = empty_set
& subset(sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( intersection(sK5,sK7) != empty_set
& intersection(sK6,sK7) = empty_set
& subset(sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_48,sK7)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( intersection(sK5,sK7) != empty_set
& intersection(sK6,sK7) = empty_set
& subset(sK5,sK6) ),
inference(definitional_conversion,[status(esa)],[f_11_6]) ).
cnf(f_11_8,negated_conjecture,
subset(sK5,sK6),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,negated_conjecture,
intersection(sK6,sK7) = empty_set,
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,negated_conjecture,
intersection(sK5,sK7) != empty_set,
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,
( 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
% 0.00/0.03 % Problem : SET596+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
% 0.09/0.34 % Computer : n026.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 19 22:44:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 1.57/1.88 % SZS status Theorem for theBenchmark
% 1.57/1.88 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------