%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET607+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 : n005.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 08:57:06 AM UTC 2026
% Result : Theorem 3.45s 3.79s
% Output : Proof 3.61s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th79,conjecture,
! [B,C] : union(B,difference(C,B)) = union(B,C),
file('theBenchmark.p',prove_th79) ).
fof(f_1_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_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,union(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,union(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,union(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,union(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ member(U_4,U_8)
| member(U_4,union(U_8,U_6)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( ~ member(U_4,U_6)
| member(U_4,union(U_8,U_6)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_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_2_2,plain,
! [U_11,U_10,U_9] :
( ( member(U_9,difference(U_11,U_10))
| member(U_9,U_10)
| ~ member(U_9,U_11) )
& ( ( ~ member(U_9,U_10)
& member(U_9,U_11) )
| ~ member(U_9,difference(U_11,U_10)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_17,U_15,U_13] :
( member(U_13,difference(U_17,U_15))
| member(U_13,U_15)
| ~ member(U_13,U_17) )
& ! [U_16,U_14,U_12] :
( ( ~ member(U_12,U_14)
& member(U_12,U_16) )
| ~ member(U_12,difference(U_16,U_14)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( member(U_12,U_16)
| ~ member(U_12,difference(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ member(U_12,U_14)
| ~ member(U_12,difference(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( member(U_13,difference(U_17,U_15))
| member(U_13,U_15)
| ~ member(U_13,U_17) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_19,U_18] :
( ( U_19 = U_18
| ~ subset(U_18,U_19)
| ~ subset(U_19,U_18) )
& ( ( subset(U_18,U_19)
& subset(U_19,U_18) )
| U_19 != U_18 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_23,U_21] :
( U_23 = U_21
| ~ subset(U_21,U_23)
| ~ subset(U_23,U_21) )
& ! [U_22,U_20] :
( ( subset(U_20,U_22)
& subset(U_22,U_20) )
| U_22 != U_20 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(U_22,U_20)
| U_22 != U_20 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(U_20,U_22)
| U_22 != U_20 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( U_23 = U_21
| ~ subset(U_21,U_23)
| ~ subset(U_23,U_21) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_4_2,plain,
! [U_25,U_24] : union(U_25,U_24) = union(U_24,U_25),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
union(U_25,U_24) = union(U_24,U_25),
inference(clausify,[status(thm)],[f_4_2]) ).
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_29,U_28] :
( ( subset(U_29,U_28)
| ? [U_27] :
( ~ member(U_27,U_28)
& member(U_27,U_29) ) )
& ( ! [U_26] :
( member(U_26,U_28)
| ~ member(U_26,U_29) )
| ~ subset(U_29,U_28) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_33,U_31] :
( subset(U_33,U_31)
| ? [U_27] :
( ~ member(U_27,U_31)
& member(U_27,U_33) ) )
& ! [U_32,U_30] :
( ! [U_26] :
( member(U_26,U_30)
| ~ member(U_26,U_32) )
| ~ subset(U_32,U_30) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_33,U_31] :
( subset(U_33,U_31)
| ( ~ member(sK1(U_33,U_31),U_31)
& member(sK1(U_33,U_31),U_33) ) )
& ! [U_32,U_30] :
( ! [U_26] :
( member(U_26,U_30)
| ~ member(U_26,U_32) )
| ~ subset(U_32,U_30) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_27,sK1(U_33,U_31))],[f_5_3]) ).
cnf(f_5_5,plain,
( member(U_26,U_30)
| ~ member(U_26,U_32)
| ~ subset(U_32,U_30) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( member(sK1(U_33,U_31),U_33)
| subset(U_33,U_31) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ member(sK1(U_33,U_31),U_31)
| subset(U_33,U_31) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_6_2,plain,
! [U_34] : subset(U_34,U_34),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
subset(U_34,U_34),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_38,U_37] :
( ( U_38 = U_37
| ? [U_36] :
( ( ~ member(U_36,U_38)
& member(U_36,U_37) )
| ( ~ member(U_36,U_37)
& member(U_36,U_38) ) ) )
& ( ! [U_35] :
( ( member(U_35,U_38)
| ~ member(U_35,U_37) )
& ( member(U_35,U_37)
| ~ member(U_35,U_38) ) )
| U_38 != U_37 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_46,U_44] :
( U_46 = U_44
| ? [U_42] :
( ~ member(U_42,U_46)
& member(U_42,U_44) )
| ? [U_41] :
( ~ member(U_41,U_44)
& member(U_41,U_46) ) )
& ! [U_45,U_43] :
( ( ! [U_40] :
( member(U_40,U_45)
| ~ member(U_40,U_43) )
& ! [U_39] :
( member(U_39,U_43)
| ~ member(U_39,U_45) ) )
| U_45 != U_43 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_46,U_44] :
( U_46 = U_44
| ? [U_42] :
( ~ member(U_42,U_46)
& member(U_42,U_44) )
| ( ~ member(sK2(U_46,U_44),U_44)
& member(sK2(U_46,U_44),U_46) ) )
& ! [U_45,U_43] :
( ( ! [U_40] :
( member(U_40,U_45)
| ~ member(U_40,U_43) )
& ! [U_39] :
( member(U_39,U_43)
| ~ member(U_39,U_45) ) )
| U_45 != U_43 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_41,sK2(U_46,U_44))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_46,U_44] :
( U_46 = U_44
| ( ~ member(sK3(U_46,U_44),U_46)
& member(sK3(U_46,U_44),U_44) )
| ( ~ member(sK2(U_46,U_44),U_44)
& member(sK2(U_46,U_44),U_46) ) )
& ! [U_45,U_43] :
( ( ! [U_40] :
( member(U_40,U_45)
| ~ member(U_40,U_43) )
& ! [U_39] :
( member(U_39,U_43)
| ~ member(U_39,U_45) ) )
| U_45 != U_43 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_42,sK3(U_46,U_44))],[f_7_4]) ).
cnf(f_7_6,plain,
( member(U_39,U_43)
| ~ member(U_39,U_45)
| U_45 != U_43 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( member(U_40,U_45)
| ~ member(U_40,U_43)
| U_45 != U_43 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( member(sK3(U_46,U_44),U_44)
| member(sK2(U_46,U_44),U_46)
| U_46 = U_44 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( ~ member(sK3(U_46,U_44),U_46)
| member(sK2(U_46,U_44),U_46)
| U_46 = U_44 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( member(sK3(U_46,U_44),U_44)
| ~ member(sK2(U_46,U_44),U_44)
| U_46 = U_44 ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ member(sK3(U_46,U_44),U_46)
| ~ member(sK2(U_46,U_44),U_44)
| U_46 = U_44 ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,negated_conjecture,
~ ! [B,C] : union(B,difference(C,B)) = union(B,C),
inference(negate,[status(cth)],[prove_th79]) ).
fof(f_8_2,negated_conjecture,
? [B,C] : union(B,difference(C,B)) != union(B,C),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_48,U_47] : union(U_48,difference(U_47,U_48)) != union(U_48,U_47),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_47] : union(sK4,difference(U_47,sK4)) != union(sK4,U_47),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_48,sK4)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
union(sK4,difference(sK5,sK4)) != union(sK4,sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_47,sK5)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
union(sK4,difference(sK5,sK4)) != union(sK4,sK5),
inference(definitional_conversion,[status(esa)],[f_8_5]) ).
cnf(f_8_7,negated_conjecture,
union(sK4,difference(sK5,sK4)) != union(sK4,sK5),
inference(clausify,[status(thm)],[f_8_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,
( 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_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,
( 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,
( 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 : SET607+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 : n005.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 22:42:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.45/3.79 % SZS status Theorem for theBenchmark
% 3.45/3.79 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------