%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET594+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 08:57:03 AM UTC 2026
% Result : Theorem 3.44s 8.98s
% Output : Proof 3.57s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_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(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_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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th53,conjecture,
! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
file('theBenchmark.p',prove_th53) ).
fof(f_1_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_1_2,plain,
! [U_3,U_2] :
( ( subset(U_3,U_2)
| ? [U_1] :
( ~ member(U_1,U_2)
& member(U_1,U_3) ) )
& ( ! [U_0] :
( member(U_0,U_2)
| ~ member(U_0,U_3) )
| ~ subset(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ? [U_1] :
( ~ member(U_1,U_5)
& member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ( ~ member(sK1(U_7,U_5),U_5)
& member(sK1(U_7,U_5),U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subset(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK1(U_7,U_5),U_7)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ member(sK1(U_7,U_5),U_5)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_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_2_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_2_1]) ).
fof(f_2_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_2_2]) ).
cnf(f_2_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_2_3]) ).
cnf(f_2_5,plain,
( ~ member(U_12,U_16)
| member(U_12,union(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( ~ member(U_12,U_14)
| member(U_12,union(U_16,U_14)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
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_19,U_18,U_17] :
( ( member(U_17,intersection(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,intersection(U_19,U_18)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_25,U_23,U_21] :
( member(U_21,intersection(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,intersection(U_24,U_22)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( member(U_20,U_24)
| ~ member(U_20,intersection(U_24,U_22)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( member(U_20,U_22)
| ~ member(U_20,intersection(U_24,U_22)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( member(U_21,intersection(U_25,U_23))
| ~ member(U_21,U_23)
| ~ member(U_21,U_25) ),
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_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_4_1]) ).
fof(f_4_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_4_2]) ).
cnf(f_4_4,plain,
( subset(U_30,U_28)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( subset(U_28,U_30)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_5_2,plain,
! [U_33,U_32] : union(U_33,U_32) = union(U_32,U_33),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
union(U_33,U_32) = union(U_32,U_33),
inference(clausify,[status(thm)],[f_5_2]) ).
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_35,U_34] : intersection(U_35,U_34) = intersection(U_34,U_35),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
intersection(U_35,U_34) = intersection(U_34,U_35),
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_36] : subset(U_36,U_36),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
subset(U_36,U_36),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_40,U_39] :
( ( U_40 = U_39
| ? [U_38] :
( ( ~ member(U_38,U_40)
& member(U_38,U_39) )
| ( ~ member(U_38,U_39)
& member(U_38,U_40) ) ) )
& ( ! [U_37] :
( ( member(U_37,U_40)
| ~ member(U_37,U_39) )
& ( member(U_37,U_39)
| ~ member(U_37,U_40) ) )
| U_40 != U_39 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_48,U_46] :
( U_48 = U_46
| ? [U_44] :
( ~ member(U_44,U_48)
& member(U_44,U_46) )
| ? [U_43] :
( ~ member(U_43,U_46)
& member(U_43,U_48) ) )
& ! [U_47,U_45] :
( ( ! [U_42] :
( member(U_42,U_47)
| ~ member(U_42,U_45) )
& ! [U_41] :
( member(U_41,U_45)
| ~ member(U_41,U_47) ) )
| U_47 != U_45 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_48,U_46] :
( U_48 = U_46
| ? [U_44] :
( ~ member(U_44,U_48)
& member(U_44,U_46) )
| ( ~ member(sK2(U_48,U_46),U_46)
& member(sK2(U_48,U_46),U_48) ) )
& ! [U_47,U_45] :
( ( ! [U_42] :
( member(U_42,U_47)
| ~ member(U_42,U_45) )
& ! [U_41] :
( member(U_41,U_45)
| ~ member(U_41,U_47) ) )
| U_47 != U_45 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_43,sK2(U_48,U_46))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_48,U_46] :
( U_48 = U_46
| ( ~ member(sK3(U_48,U_46),U_48)
& member(sK3(U_48,U_46),U_46) )
| ( ~ member(sK2(U_48,U_46),U_46)
& member(sK2(U_48,U_46),U_48) ) )
& ! [U_47,U_45] :
( ( ! [U_42] :
( member(U_42,U_47)
| ~ member(U_42,U_45) )
& ! [U_41] :
( member(U_41,U_45)
| ~ member(U_41,U_47) ) )
| U_47 != U_45 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_44,sK3(U_48,U_46))],[f_8_4]) ).
cnf(f_8_6,plain,
( member(U_41,U_45)
| ~ member(U_41,U_47)
| U_47 != U_45 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( member(U_42,U_47)
| ~ member(U_42,U_45)
| U_47 != U_45 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( member(sK3(U_48,U_46),U_46)
| member(sK2(U_48,U_46),U_48)
| U_48 = U_46 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( ~ member(sK3(U_48,U_46),U_48)
| member(sK2(U_48,U_46),U_48)
| U_48 = U_46 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_10,plain,
( member(sK3(U_48,U_46),U_46)
| ~ member(sK2(U_48,U_46),U_46)
| U_48 = U_46 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_11,plain,
( ~ member(sK3(U_48,U_46),U_48)
| ~ member(sK2(U_48,U_46),U_46)
| U_48 = U_46 ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_1,negated_conjecture,
~ ! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
inference(negate,[status(cth)],[prove_th53]) ).
fof(f_9_2,negated_conjecture,
? [B,C,D] :
( ~ subset(B,union(C,D))
& union(intersection(B,C),intersection(B,D)) = B ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_51,U_50,U_49] :
( ~ subset(U_51,union(U_50,U_49))
& union(intersection(U_51,U_50),intersection(U_51,U_49)) = U_51 ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_50,U_49] :
( ~ subset(sK4,union(U_50,U_49))
& union(intersection(sK4,U_50),intersection(sK4,U_49)) = sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_51,sK4)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
? [U_49] :
( ~ subset(sK4,union(sK5,U_49))
& union(intersection(sK4,sK5),intersection(sK4,U_49)) = sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_50,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ~ subset(sK4,union(sK5,sK6))
& union(intersection(sK4,sK5),intersection(sK4,sK6)) = sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ~ subset(sK4,union(sK5,sK6))
& union(intersection(sK4,sK5),intersection(sK4,sK6)) = sK4 ),
inference(definitional_conversion,[status(esa)],[f_9_6]) ).
cnf(f_9_8,negated_conjecture,
union(intersection(sK4,sK5),intersection(sK4,sK6)) = sK4,
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
~ subset(sK4,union(sK5,sK6)),
inference(clausify,[status(thm)],[f_9_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,
( 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,
( 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_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,
( 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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594+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
% 0.12/5.59 % Computer : n013.cluster.edu
% 0.12/5.59 % Model : x86_64 x86_64
% 0.12/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.59 % Memory : 8046.5625MB
% 0.12/5.59 % OS : Linux 6.8.0-71-generic
% 0.12/5.59 % CPULimit : 300
% 0.12/5.59 % WCLimit : 300
% 0.12/5.59 % DateTime : Sat Sep 19 22:41:13 UTC 2026
% 0.12/5.59 % CPUTime :
% 3.44/8.98 % SZS status Theorem for theBenchmark
% 3.44/8.98 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------