%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET162+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 : n014.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 08:56:29 AM UTC 2026
% Result : Theorem 0.32s 0.60s
% Output : Proof 0.32s
% 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(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_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(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('theBenchmark.p',empty_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_union_empty_set,conjecture,
! [B] : union(B,empty_set) = B,
file('theBenchmark.p',prove_union_empty_set) ).
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] : ~ member(B,empty_set),
inference(fof_nnf,[status(thm)],[empty_set_defn]) ).
fof(f_2_2,plain,
! [U_9] : ~ member(U_9,empty_set),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
~ member(U_9,empty_set),
inference(clausify,[status(thm)],[f_2_2]) ).
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_11,U_10] :
( ( U_11 = U_10
| ~ subset(U_10,U_11)
| ~ subset(U_11,U_10) )
& ( ( subset(U_10,U_11)
& subset(U_11,U_10) )
| U_11 != U_10 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( ( subset(U_12,U_14)
& subset(U_14,U_12) )
| U_14 != U_12 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(U_14,U_12)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(U_12,U_14)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) ),
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_17,U_16] : union(U_17,U_16) = union(U_16,U_17),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
union(U_17,U_16) = union(U_16,U_17),
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_21,U_20] :
( ( subset(U_21,U_20)
| ? [U_19] :
( ~ member(U_19,U_20)
& member(U_19,U_21) ) )
& ( ! [U_18] :
( member(U_18,U_20)
| ~ member(U_18,U_21) )
| ~ subset(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_25,U_23] :
( subset(U_25,U_23)
| ? [U_19] :
( ~ member(U_19,U_23)
& member(U_19,U_25) ) )
& ! [U_24,U_22] :
( ! [U_18] :
( member(U_18,U_22)
| ~ member(U_18,U_24) )
| ~ subset(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_25,U_23] :
( subset(U_25,U_23)
| ( ~ member(sK1(U_25,U_23),U_23)
& member(sK1(U_25,U_23),U_25) ) )
& ! [U_24,U_22] :
( ! [U_18] :
( member(U_18,U_22)
| ~ member(U_18,U_24) )
| ~ subset(U_24,U_22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1(U_25,U_23))],[f_5_3]) ).
cnf(f_5_5,plain,
( member(U_18,U_22)
| ~ member(U_18,U_24)
| ~ subset(U_24,U_22) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( member(sK1(U_25,U_23),U_25)
| subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ member(sK1(U_25,U_23),U_23)
| subset(U_25,U_23) ),
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_26] : subset(U_26,U_26),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
subset(U_26,U_26),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B] :
( ( empty(B)
| ? [C] : member(C,B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(fof_nnf,[status(thm)],[empty_defn]) ).
fof(f_7_2,plain,
! [U_29] :
( ( empty(U_29)
| ? [U_28] : member(U_28,U_29) )
& ( ! [U_27] : ~ member(U_27,U_29)
| ~ empty(U_29) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_31] :
( empty(U_31)
| ? [U_28] : member(U_28,U_31) )
& ! [U_30] :
( ! [U_27] : ~ member(U_27,U_30)
| ~ empty(U_30) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_31] :
( empty(U_31)
| member(sK2(U_31),U_31) )
& ! [U_30] :
( ! [U_27] : ~ member(U_27,U_30)
| ~ empty(U_30) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_28,sK2(U_31))],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ member(U_27,U_30)
| ~ empty(U_30) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( empty(U_31)
| member(sK2(U_31),U_31) ),
inference(clausify,[status(thm)],[f_7_4]) ).
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_35,U_34] :
( ( U_35 = U_34
| ? [U_33] :
( ( ~ member(U_33,U_35)
& member(U_33,U_34) )
| ( ~ member(U_33,U_34)
& member(U_33,U_35) ) ) )
& ( ! [U_32] :
( ( member(U_32,U_35)
| ~ member(U_32,U_34) )
& ( member(U_32,U_34)
| ~ member(U_32,U_35) ) )
| U_35 != U_34 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_43,U_41] :
( U_43 = U_41
| ? [U_39] :
( ~ member(U_39,U_43)
& member(U_39,U_41) )
| ? [U_38] :
( ~ member(U_38,U_41)
& member(U_38,U_43) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( member(U_37,U_42)
| ~ member(U_37,U_40) )
& ! [U_36] :
( member(U_36,U_40)
| ~ member(U_36,U_42) ) )
| U_42 != U_40 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_43,U_41] :
( U_43 = U_41
| ? [U_39] :
( ~ member(U_39,U_43)
& member(U_39,U_41) )
| ( ~ member(sK3(U_43,U_41),U_41)
& member(sK3(U_43,U_41),U_43) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( member(U_37,U_42)
| ~ member(U_37,U_40) )
& ! [U_36] :
( member(U_36,U_40)
| ~ member(U_36,U_42) ) )
| U_42 != U_40 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_38,sK3(U_43,U_41))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_43,U_41] :
( U_43 = U_41
| ( ~ member(sK4(U_43,U_41),U_43)
& member(sK4(U_43,U_41),U_41) )
| ( ~ member(sK3(U_43,U_41),U_41)
& member(sK3(U_43,U_41),U_43) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( member(U_37,U_42)
| ~ member(U_37,U_40) )
& ! [U_36] :
( member(U_36,U_40)
| ~ member(U_36,U_42) ) )
| U_42 != U_40 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_39,sK4(U_43,U_41))],[f_8_4]) ).
cnf(f_8_6,plain,
( member(U_36,U_40)
| ~ member(U_36,U_42)
| U_42 != U_40 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( member(U_37,U_42)
| ~ member(U_37,U_40)
| U_42 != U_40 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( member(sK4(U_43,U_41),U_41)
| member(sK3(U_43,U_41),U_43)
| U_43 = U_41 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( ~ member(sK4(U_43,U_41),U_43)
| member(sK3(U_43,U_41),U_43)
| U_43 = U_41 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_10,plain,
( member(sK4(U_43,U_41),U_41)
| ~ member(sK3(U_43,U_41),U_41)
| U_43 = U_41 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_11,plain,
( ~ member(sK4(U_43,U_41),U_43)
| ~ member(sK3(U_43,U_41),U_41)
| U_43 = U_41 ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_1,negated_conjecture,
~ ! [B] : union(B,empty_set) = B,
inference(negate,[status(cth)],[prove_union_empty_set]) ).
fof(f_9_2,negated_conjecture,
? [B] : union(B,empty_set) != B,
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_44] : union(U_44,empty_set) != U_44,
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
union(sK5,empty_set) != sK5,
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
union(sK5,empty_set) != sK5,
inference(definitional_conversion,[status(esa)],[f_9_4]) ).
cnf(f_9_6,negated_conjecture,
union(sK5,empty_set) != sK5,
inference(clausify,[status(thm)],[f_9_5]) ).
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) = sK2(Eq_y_0)
| 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,
( 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_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(equality_11,axiom,
( empty(Eq_y_0)
| ~ empty(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 : SET162+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
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 21:52:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.32/0.60 % SZS status Theorem for theBenchmark
% 0.32/0.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------