%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET621+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 : n018.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 08:57:08 AM UTC 2026
% Result : Theorem 120.46s 120.79s
% Output : Proof 121.04s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',symmetric_difference_defn) ).
fof(difference_difference_union,axiom,
! [B,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)),
file('theBenchmark.p',difference_difference_union) ).
fof(difference_distributes_over_union,axiom,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
file('theBenchmark.p',difference_distributes_over_union) ).
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_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_union,axiom,
! [B,C] : union(B,C) = union(C,B),
file('theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_symmetric_difference,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('theBenchmark.p',commutativity_of_symmetric_difference) ).
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_th97,conjecture,
! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
file('theBenchmark.p',prove_th97) ).
fof(f_1_1,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(fof_nnf,[status(thm)],[symmetric_difference_defn]) ).
fof(f_1_2,plain,
! [U_1,U_0] : symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)),
inference(fof_nnf,[status(thm)],[difference_difference_union]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] : difference(difference(U_4,U_3),U_2) = difference(U_4,union(U_3,U_2)),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
difference(difference(U_4,U_3),U_2) = difference(U_4,union(U_3,U_2)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
inference(fof_nnf,[status(thm)],[difference_distributes_over_union]) ).
fof(f_3_2,plain,
! [U_7,U_6,U_5] : difference(union(U_7,U_6),U_5) = union(difference(U_7,U_5),difference(U_6,U_5)),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
difference(union(U_7,U_6),U_5) = union(difference(U_7,U_5),difference(U_6,U_5)),
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_10,U_9,U_8] :
( ( member(U_8,union(U_10,U_9))
| ( ~ member(U_8,U_9)
& ~ member(U_8,U_10) ) )
& ( member(U_8,U_9)
| member(U_8,U_10)
| ~ member(U_8,union(U_10,U_9)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_16,U_14,U_12] :
( member(U_12,union(U_16,U_14))
| ( ~ member(U_12,U_14)
& ~ member(U_12,U_16) ) )
& ! [U_15,U_13,U_11] :
( member(U_11,U_13)
| member(U_11,U_15)
| ~ member(U_11,union(U_15,U_13)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_11,U_13)
| member(U_11,U_15)
| ~ member(U_11,union(U_15,U_13)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ member(U_12,U_16)
| member(U_12,union(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( ~ member(U_12,U_14)
| member(U_12,union(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_19,U_18,U_17] :
( ( member(U_17,difference(U_19,U_18))
| member(U_17,U_18)
| ~ member(U_17,U_19) )
& ( ( ~ member(U_17,U_18)
& member(U_17,U_19) )
| ~ member(U_17,difference(U_19,U_18)) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_25,U_23,U_21] :
( member(U_21,difference(U_25,U_23))
| member(U_21,U_23)
| ~ member(U_21,U_25) )
& ! [U_24,U_22,U_20] :
( ( ~ member(U_20,U_22)
& member(U_20,U_24) )
| ~ member(U_20,difference(U_24,U_22)) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( member(U_20,U_24)
| ~ member(U_20,difference(U_24,U_22)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( ~ member(U_20,U_22)
| ~ member(U_20,difference(U_24,U_22)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( member(U_21,difference(U_25,U_23))
| member(U_21,U_23)
| ~ member(U_21,U_25) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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_27,U_26] :
( ( U_27 = U_26
| ~ subset(U_26,U_27)
| ~ subset(U_27,U_26) )
& ( ( subset(U_26,U_27)
& subset(U_27,U_26) )
| U_27 != U_26 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_31,U_29] :
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) )
& ! [U_30,U_28] :
( ( subset(U_28,U_30)
& subset(U_30,U_28) )
| U_30 != U_28 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( subset(U_30,U_28)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( subset(U_28,U_30)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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_33,U_32] : union(U_33,U_32) = union(U_32,U_33),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
union(U_33,U_32) = union(U_32,U_33),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_symmetric_difference]) ).
fof(f_8_2,plain,
! [U_35,U_34] : symmetric_difference(U_35,U_34) = symmetric_difference(U_34,U_35),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
symmetric_difference(U_35,U_34) = symmetric_difference(U_34,U_35),
inference(clausify,[status(thm)],[f_8_2]) ).
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_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_9_1]) ).
fof(f_9_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_9_2]) ).
fof(f_9_4,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ? [U_43] :
( ~ member(U_43,U_47)
& member(U_43,U_45) )
| ( ~ member(sK1(U_47,U_45),U_45)
& member(sK1(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,[sK1]),skolemize(U_42,sK1(U_47,U_45))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_47,U_45] :
( U_47 = U_45
| ( ~ member(sK2(U_47,U_45),U_47)
& member(sK2(U_47,U_45),U_45) )
| ( ~ member(sK1(U_47,U_45),U_45)
& member(sK1(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,[sK2]),skolemize(U_43,sK2(U_47,U_45))],[f_9_4]) ).
cnf(f_9_6,plain,
( member(U_40,U_44)
| ~ member(U_40,U_46)
| U_46 != U_44 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( member(U_41,U_46)
| ~ member(U_41,U_44)
| U_46 != U_44 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( member(sK2(U_47,U_45),U_45)
| member(sK1(U_47,U_45),U_47)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ member(sK2(U_47,U_45),U_47)
| member(sK1(U_47,U_45),U_47)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( member(sK2(U_47,U_45),U_45)
| ~ member(sK1(U_47,U_45),U_45)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ member(sK2(U_47,U_45),U_47)
| ~ member(sK1(U_47,U_45),U_45)
| U_47 = U_45 ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_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_10_2,plain,
! [U_51,U_50] :
( ( subset(U_51,U_50)
| ? [U_49] :
( ~ member(U_49,U_50)
& member(U_49,U_51) ) )
& ( ! [U_48] :
( member(U_48,U_50)
| ~ member(U_48,U_51) )
| ~ subset(U_51,U_50) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_55,U_53] :
( subset(U_55,U_53)
| ? [U_49] :
( ~ member(U_49,U_53)
& member(U_49,U_55) ) )
& ! [U_54,U_52] :
( ! [U_48] :
( member(U_48,U_52)
| ~ member(U_48,U_54) )
| ~ subset(U_54,U_52) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_55,U_53] :
( subset(U_55,U_53)
| ( ~ member(sK3(U_55,U_53),U_53)
& member(sK3(U_55,U_53),U_55) ) )
& ! [U_54,U_52] :
( ! [U_48] :
( member(U_48,U_52)
| ~ member(U_48,U_54) )
| ~ subset(U_54,U_52) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_49,sK3(U_55,U_53))],[f_10_3]) ).
cnf(f_10_5,plain,
( member(U_48,U_52)
| ~ member(U_48,U_54)
| ~ subset(U_54,U_52) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( member(sK3(U_55,U_53),U_55)
| subset(U_55,U_53) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_7,plain,
( ~ member(sK3(U_55,U_53),U_53)
| subset(U_55,U_53) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_11_2,plain,
! [U_56] : subset(U_56,U_56),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
subset(U_56,U_56),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,negated_conjecture,
~ ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(negate,[status(cth)],[prove_th97]) ).
fof(f_12_2,negated_conjecture,
? [B,C,D] : difference(symmetric_difference(B,C),D) != union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_59,U_58,U_57] : difference(symmetric_difference(U_59,U_58),U_57) != union(difference(U_59,union(U_58,U_57)),difference(U_58,union(U_59,U_57))),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_58,U_57] : difference(symmetric_difference(sK4,U_58),U_57) != union(difference(sK4,union(U_58,U_57)),difference(U_58,union(sK4,U_57))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_59,sK4)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
? [U_57] : difference(symmetric_difference(sK4,sK5),U_57) != union(difference(sK4,union(sK5,U_57)),difference(sK5,union(sK4,U_57))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_58,sK5)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
difference(symmetric_difference(sK4,sK5),sK6) != union(difference(sK4,union(sK5,sK6)),difference(sK5,union(sK4,sK6))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_57,sK6)],[f_12_5]) ).
fof(f_12_7,negated_conjecture,
difference(symmetric_difference(sK4,sK5),sK6) != union(difference(sK4,union(sK5,sK6)),difference(sK5,union(sK4,sK6))),
inference(definitional_conversion,[status(esa)],[f_12_6]) ).
cnf(f_12_8,negated_conjecture,
difference(symmetric_difference(sK4,sK5),sK6) != union(difference(sK4,union(sK5,sK6)),difference(sK5,union(sK4,sK6))),
inference(clausify,[status(thm)],[f_12_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,
( symmetric_difference(Eq_x_0,Eq_x_1) = symmetric_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_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,
( 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_7,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_8,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_9,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_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,
( 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
% 0.00/0.02 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n018.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 19 22:45:41 UTC 2026
% 0.07/0.33 % CPUTime :
% 120.46/120.79 % SZS status Theorem for theBenchmark
% 120.46/120.79 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------