%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET606+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 08:57:05 AM UTC 2026
% Result : Theorem 4.26s 4.59s
% Output : Proof 4.36s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(member_equal,axiom,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('theBenchmark.p',member_equal) ).
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(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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(prove_difference_into_intersection,conjecture,
! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
file('theBenchmark.p',prove_difference_into_intersection) ).
fof(f_1_1,plain,
! [B,C] :
( B = C
| ? [D] :
( ( ~ member(D,B)
& member(D,C) )
| ( ~ member(D,C)
& member(D,B) ) ) ),
inference(fof_nnf,[status(thm)],[member_equal]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_2 = U_1
| ? [U_0] :
( ( ~ member(U_0,U_2)
& member(U_0,U_1) )
| ( ~ member(U_0,U_1)
& member(U_0,U_2) ) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_2 = U_1
| ? [U_4] :
( ~ member(U_4,U_2)
& member(U_4,U_1) )
| ? [U_3] :
( ~ member(U_3,U_1)
& member(U_3,U_2) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_2,U_1] :
( U_2 = U_1
| ? [U_4] :
( ~ member(U_4,U_2)
& member(U_4,U_1) )
| ( ~ member(sK1(U_2,U_1),U_1)
& member(sK1(U_2,U_1),U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_2,U_1))],[f_1_3]) ).
fof(f_1_5,plain,
! [U_2,U_1] :
( U_2 = U_1
| ( ~ member(sK2(U_2,U_1),U_2)
& member(sK2(U_2,U_1),U_1) )
| ( ~ member(sK1(U_2,U_1),U_1)
& member(sK1(U_2,U_1),U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2(U_2,U_1))],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK2(U_2,U_1),U_1)
| member(sK1(U_2,U_1),U_2)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( ~ member(sK2(U_2,U_1),U_2)
| member(sK1(U_2,U_1),U_2)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( member(sK2(U_2,U_1),U_1)
| ~ member(sK1(U_2,U_1),U_1)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,plain,
( ~ member(sK2(U_2,U_1),U_2)
| ~ member(sK1(U_2,U_1),U_1)
| U_2 = U_1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_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_2_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_2_1]) ).
fof(f_2_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_2_2]) ).
cnf(f_2_4,plain,
( member(U_8,U_12)
| ~ member(U_8,intersection(U_12,U_10)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( member(U_8,U_10)
| ~ member(U_8,intersection(U_12,U_10)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_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_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_16,U_15,U_14] :
( ( member(U_14,difference(U_16,U_15))
| member(U_14,U_15)
| ~ member(U_14,U_16) )
& ( ( ~ member(U_14,U_15)
& member(U_14,U_16) )
| ~ member(U_14,difference(U_16,U_15)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_22,U_20,U_18] :
( member(U_18,difference(U_22,U_20))
| member(U_18,U_20)
| ~ member(U_18,U_22) )
& ! [U_21,U_19,U_17] :
( ( ~ member(U_17,U_19)
& member(U_17,U_21) )
| ~ member(U_17,difference(U_21,U_19)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( member(U_17,U_21)
| ~ member(U_17,difference(U_21,U_19)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( ~ member(U_17,U_19)
| ~ member(U_17,difference(U_21,U_19)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( member(U_18,difference(U_22,U_20))
| member(U_18,U_20)
| ~ member(U_18,U_22) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_24,U_23] :
( ( U_24 = U_23
| ~ subset(U_23,U_24)
| ~ subset(U_24,U_23) )
& ( ( subset(U_23,U_24)
& subset(U_24,U_23) )
| U_24 != U_23 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_28,U_26] :
( U_28 = U_26
| ~ subset(U_26,U_28)
| ~ subset(U_28,U_26) )
& ! [U_27,U_25] :
( ( subset(U_25,U_27)
& subset(U_27,U_25) )
| U_27 != U_25 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset(U_27,U_25)
| U_27 != U_25 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( subset(U_25,U_27)
| U_27 != U_25 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( U_28 = U_26
| ~ subset(U_26,U_28)
| ~ subset(U_28,U_26) ),
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_30,U_29] : intersection(U_30,U_29) = intersection(U_29,U_30),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
intersection(U_30,U_29) = intersection(U_29,U_30),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_34,U_33] :
( ( U_34 = U_33
| ? [U_32] :
( ( ~ member(U_32,U_34)
& member(U_32,U_33) )
| ( ~ member(U_32,U_33)
& member(U_32,U_34) ) ) )
& ( ! [U_31] :
( ( member(U_31,U_34)
| ~ member(U_31,U_33) )
& ( member(U_31,U_33)
| ~ member(U_31,U_34) ) )
| U_34 != U_33 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_42,U_40] :
( U_42 = U_40
| ? [U_38] :
( ~ member(U_38,U_42)
& member(U_38,U_40) )
| ? [U_37] :
( ~ member(U_37,U_40)
& member(U_37,U_42) ) )
& ! [U_41,U_39] :
( ( ! [U_36] :
( member(U_36,U_41)
| ~ member(U_36,U_39) )
& ! [U_35] :
( member(U_35,U_39)
| ~ member(U_35,U_41) ) )
| U_41 != U_39 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_42,U_40] :
( U_42 = U_40
| ? [U_38] :
( ~ member(U_38,U_42)
& member(U_38,U_40) )
| ( ~ member(sK3(U_42,U_40),U_40)
& member(sK3(U_42,U_40),U_42) ) )
& ! [U_41,U_39] :
( ( ! [U_36] :
( member(U_36,U_41)
| ~ member(U_36,U_39) )
& ! [U_35] :
( member(U_35,U_39)
| ~ member(U_35,U_41) ) )
| U_41 != U_39 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_37,sK3(U_42,U_40))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_42,U_40] :
( U_42 = U_40
| ( ~ member(sK4(U_42,U_40),U_42)
& member(sK4(U_42,U_40),U_40) )
| ( ~ member(sK3(U_42,U_40),U_40)
& member(sK3(U_42,U_40),U_42) ) )
& ! [U_41,U_39] :
( ( ! [U_36] :
( member(U_36,U_41)
| ~ member(U_36,U_39) )
& ! [U_35] :
( member(U_35,U_39)
| ~ member(U_35,U_41) ) )
| U_41 != U_39 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_38,sK4(U_42,U_40))],[f_6_4]) ).
cnf(f_6_6,plain,
( member(U_35,U_39)
| ~ member(U_35,U_41)
| U_41 != U_39 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( member(U_36,U_41)
| ~ member(U_36,U_39)
| U_41 != U_39 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( member(sK4(U_42,U_40),U_40)
| member(sK3(U_42,U_40),U_42)
| U_42 = U_40 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( ~ member(sK4(U_42,U_40),U_42)
| member(sK3(U_42,U_40),U_42)
| U_42 = U_40 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( member(sK4(U_42,U_40),U_40)
| ~ member(sK3(U_42,U_40),U_40)
| U_42 = U_40 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_11,plain,
( ~ member(sK4(U_42,U_40),U_42)
| ~ member(sK3(U_42,U_40),U_40)
| U_42 = U_40 ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_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_7_2,plain,
! [U_46,U_45] :
( ( subset(U_46,U_45)
| ? [U_44] :
( ~ member(U_44,U_45)
& member(U_44,U_46) ) )
& ( ! [U_43] :
( member(U_43,U_45)
| ~ member(U_43,U_46) )
| ~ subset(U_46,U_45) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_50,U_48] :
( subset(U_50,U_48)
| ? [U_44] :
( ~ member(U_44,U_48)
& member(U_44,U_50) ) )
& ! [U_49,U_47] :
( ! [U_43] :
( member(U_43,U_47)
| ~ member(U_43,U_49) )
| ~ subset(U_49,U_47) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_50,U_48] :
( subset(U_50,U_48)
| ( ~ member(sK5(U_50,U_48),U_48)
& member(sK5(U_50,U_48),U_50) ) )
& ! [U_49,U_47] :
( ! [U_43] :
( member(U_43,U_47)
| ~ member(U_43,U_49) )
| ~ subset(U_49,U_47) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5(U_50,U_48))],[f_7_3]) ).
cnf(f_7_5,plain,
( member(U_43,U_47)
| ~ member(U_43,U_49)
| ~ subset(U_49,U_47) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( member(sK5(U_50,U_48),U_50)
| subset(U_50,U_48) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
( ~ member(sK5(U_50,U_48),U_48)
| subset(U_50,U_48) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_8_2,plain,
! [U_51] : subset(U_51,U_51),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
subset(U_51,U_51),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,negated_conjecture,
~ ! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
inference(negate,[status(cth)],[prove_difference_into_intersection]) ).
fof(f_9_2,negated_conjecture,
? [B,C] : difference(B,intersection(B,C)) != difference(B,C),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_53,U_52] : difference(U_53,intersection(U_53,U_52)) != difference(U_53,U_52),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_52] : difference(sK6,intersection(sK6,U_52)) != difference(sK6,U_52),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_53,sK6)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
difference(sK6,intersection(sK6,sK7)) != difference(sK6,sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_52,sK7)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
difference(sK6,intersection(sK6,sK7)) != difference(sK6,sK7),
inference(definitional_conversion,[status(esa)],[f_9_5]) ).
cnf(f_9_7,negated_conjecture,
difference(sK6,intersection(sK6,sK7)) != difference(sK6,sK7),
inference(clausify,[status(thm)],[f_9_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,
( 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_10,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET606+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
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 22:48:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 4.26/4.59 % SZS status Theorem for theBenchmark
% 4.26/4.59 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------