%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET577+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 : n009.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 08:57:00 AM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Proof 0.13s
% 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(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_th18,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) )
=> B = union(C,D) ),
file('theBenchmark.p',prove_th18) ).
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] :
( ( 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_2_2,plain,
! [U_10,U_9] :
( ( U_10 = U_9
| ~ subset(U_9,U_10)
| ~ subset(U_10,U_9) )
& ( ( subset(U_9,U_10)
& subset(U_10,U_9) )
| U_10 != U_9 ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_14,U_12] :
( U_14 = U_12
| ~ subset(U_12,U_14)
| ~ subset(U_14,U_12) )
& ! [U_13,U_11] :
( ( subset(U_11,U_13)
& subset(U_13,U_11) )
| U_13 != U_11 ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_13,U_11)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( subset(U_11,U_13)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( U_14 = U_12
| ~ subset(U_12,U_14)
| ~ subset(U_14,U_12) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B,C] : union(B,C) = union(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_union]) ).
fof(f_3_2,plain,
! [U_16,U_15] : union(U_16,U_15) = union(U_15,U_16),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
union(U_16,U_15) = union(U_15,U_16),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_20,U_19] :
( ( subset(U_20,U_19)
| ? [U_18] :
( ~ member(U_18,U_19)
& member(U_18,U_20) ) )
& ( ! [U_17] :
( member(U_17,U_19)
| ~ member(U_17,U_20) )
| ~ subset(U_20,U_19) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_24,U_22] :
( subset(U_24,U_22)
| ? [U_18] :
( ~ member(U_18,U_22)
& member(U_18,U_24) ) )
& ! [U_23,U_21] :
( ! [U_17] :
( member(U_17,U_21)
| ~ member(U_17,U_23) )
| ~ subset(U_23,U_21) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_24,U_22] :
( subset(U_24,U_22)
| ( ~ member(sK1(U_24,U_22),U_22)
& member(sK1(U_24,U_22),U_24) ) )
& ! [U_23,U_21] :
( ! [U_17] :
( member(U_17,U_21)
| ~ member(U_17,U_23) )
| ~ subset(U_23,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_18,sK1(U_24,U_22))],[f_4_3]) ).
cnf(f_4_5,plain,
( member(U_17,U_21)
| ~ member(U_17,U_23)
| ~ subset(U_23,U_21) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( member(sK1(U_24,U_22),U_24)
| subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ member(sK1(U_24,U_22),U_22)
| subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_5_2,plain,
! [U_25] : subset(U_25,U_25),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
subset(U_25,U_25),
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_29,U_28] :
( ( U_29 = U_28
| ? [U_27] :
( ( ~ member(U_27,U_29)
& member(U_27,U_28) )
| ( ~ member(U_27,U_28)
& member(U_27,U_29) ) ) )
& ( ! [U_26] :
( ( member(U_26,U_29)
| ~ member(U_26,U_28) )
& ( member(U_26,U_28)
| ~ member(U_26,U_29) ) )
| U_29 != U_28 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ? [U_33] :
( ~ member(U_33,U_37)
& member(U_33,U_35) )
| ? [U_32] :
( ~ member(U_32,U_35)
& member(U_32,U_37) ) )
& ! [U_36,U_34] :
( ( ! [U_31] :
( member(U_31,U_36)
| ~ member(U_31,U_34) )
& ! [U_30] :
( member(U_30,U_34)
| ~ member(U_30,U_36) ) )
| U_36 != U_34 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ? [U_33] :
( ~ member(U_33,U_37)
& member(U_33,U_35) )
| ( ~ member(sK2(U_37,U_35),U_35)
& member(sK2(U_37,U_35),U_37) ) )
& ! [U_36,U_34] :
( ( ! [U_31] :
( member(U_31,U_36)
| ~ member(U_31,U_34) )
& ! [U_30] :
( member(U_30,U_34)
| ~ member(U_30,U_36) ) )
| U_36 != U_34 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_32,sK2(U_37,U_35))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ( ~ member(sK3(U_37,U_35),U_37)
& member(sK3(U_37,U_35),U_35) )
| ( ~ member(sK2(U_37,U_35),U_35)
& member(sK2(U_37,U_35),U_37) ) )
& ! [U_36,U_34] :
( ( ! [U_31] :
( member(U_31,U_36)
| ~ member(U_31,U_34) )
& ! [U_30] :
( member(U_30,U_34)
| ~ member(U_30,U_36) ) )
| U_36 != U_34 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_33,sK3(U_37,U_35))],[f_6_4]) ).
cnf(f_6_6,plain,
( member(U_30,U_34)
| ~ member(U_30,U_36)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( member(U_31,U_36)
| ~ member(U_31,U_34)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( member(sK3(U_37,U_35),U_35)
| member(sK2(U_37,U_35),U_37)
| U_37 = U_35 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( ~ member(sK3(U_37,U_35),U_37)
| member(sK2(U_37,U_35),U_37)
| U_37 = U_35 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( member(sK3(U_37,U_35),U_35)
| ~ member(sK2(U_37,U_35),U_35)
| U_37 = U_35 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_11,plain,
( ~ member(sK3(U_37,U_35),U_37)
| ~ member(sK2(U_37,U_35),U_35)
| U_37 = U_35 ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) )
=> B = union(C,D) ),
inference(negate,[status(cth)],[prove_th18]) ).
fof(f_7_2,negated_conjecture,
? [B,C,D] :
( B != union(C,D)
& ! [E] :
( ( member(E,B)
| ( ~ member(E,D)
& ~ member(E,C) ) )
& ( member(E,D)
| member(E,C)
| ~ member(E,B) ) ) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_41,U_40,U_39] :
( U_41 != union(U_40,U_39)
& ! [U_38] :
( ( member(U_38,U_41)
| ( ~ member(U_38,U_39)
& ~ member(U_38,U_40) ) )
& ( member(U_38,U_39)
| member(U_38,U_40)
| ~ member(U_38,U_41) ) ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_41,U_40,U_39] :
( U_41 != union(U_40,U_39)
& ! [U_43] :
( member(U_43,U_41)
| ( ~ member(U_43,U_39)
& ~ member(U_43,U_40) ) )
& ! [U_42] :
( member(U_42,U_39)
| member(U_42,U_40)
| ~ member(U_42,U_41) ) ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
? [U_40,U_39] :
( sK4 != union(U_40,U_39)
& ! [U_43] :
( member(U_43,sK4)
| ( ~ member(U_43,U_39)
& ~ member(U_43,U_40) ) )
& ! [U_42] :
( member(U_42,U_39)
| member(U_42,U_40)
| ~ member(U_42,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_41,sK4)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
? [U_39] :
( sK4 != union(sK5,U_39)
& ! [U_43] :
( member(U_43,sK4)
| ( ~ member(U_43,U_39)
& ~ member(U_43,sK5) ) )
& ! [U_42] :
( member(U_42,U_39)
| member(U_42,sK5)
| ~ member(U_42,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_40,sK5)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( sK4 != union(sK5,sK6)
& ! [U_43] :
( member(U_43,sK4)
| ( ~ member(U_43,sK6)
& ~ member(U_43,sK5) ) )
& ! [U_42] :
( member(U_42,sK6)
| member(U_42,sK5)
| ~ member(U_42,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( ! [U_43] :
( ~ member(U_43,sK6)
| ~ sP0(U_43) )
& ! [U_43] :
( ~ member(U_43,sK5)
| ~ sP0(U_43) )
& sK4 != union(sK5,sK6)
& ! [U_43] :
( member(U_43,sK4)
| sP0(U_43) )
& ! [U_42] :
( member(U_42,sK6)
| member(U_42,sK5)
| ~ member(U_42,sK4) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
( member(U_42,sK6)
| member(U_42,sK5)
| ~ member(U_42,sK4) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
( member(U_43,sK4)
| sP0(U_43) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,negated_conjecture,
sK4 != union(sK5,sK6),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_12,negated_conjecture,
( ~ member(U_43,sK5)
| ~ sP0(U_43) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_13,negated_conjecture,
( ~ member(U_43,sK6)
| ~ sP0(U_43) ),
inference(clausify,[status(thm)],[f_7_8]) ).
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,
( 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,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_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,
( 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_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,
( sP0(Eq_y_0)
| ~ sP0(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 : SET577+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
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 22:40:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------