%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n019.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 08:58:12 AM UTC 2026
% Result : Theorem 0.16s 5.71s
% Output : Proof 0.16s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ( U_4 = singleton(U_5)
| ? [U_3] :
( ( ~ in(U_3,U_4)
& U_3 = U_5 )
| ( U_3 != U_5
& in(U_3,U_4) ) ) )
& ( ! [U_2] :
( ( in(U_2,U_4)
| U_2 != U_5 )
& ( U_2 = U_5
| ~ in(U_2,U_4) ) )
| U_4 != singleton(U_5) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& U_9 = U_13 )
| ? [U_8] :
( U_8 != U_13
& in(U_8,U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& U_9 = U_13 )
| ( sK1(U_13,U_11) != U_13
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_13,U_11))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ( ~ in(sK2(U_13,U_11),U_11)
& sK2(U_13,U_11) = U_13 )
| ( sK1(U_13,U_11) != U_13
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_13,U_11))],[f_2_4]) ).
cnf(f_2_6,plain,
( U_6 = U_12
| ~ in(U_6,U_10)
| U_10 != singleton(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( in(U_7,U_10)
| U_7 != U_12
| U_10 != singleton(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( sK2(U_13,U_11) = U_13
| in(sK1(U_13,U_11),U_11)
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( ~ in(sK2(U_13,U_11),U_11)
| in(sK1(U_13,U_11),U_11)
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_10,plain,
( sK2(U_13,U_11) = U_13
| sK1(U_13,U_11) != U_13
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_11,plain,
( ~ in(sK2(U_13,U_11),U_11)
| sK1(U_13,U_11) != U_13
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_17,U_16] :
( ( U_16 = powerset(U_17)
| ? [U_15] :
( ( ~ in(U_15,U_16)
& subset(U_15,U_17) )
| ( ~ subset(U_15,U_17)
& in(U_15,U_16) ) ) )
& ( ! [U_14] :
( ( in(U_14,U_16)
| ~ subset(U_14,U_17) )
& ( subset(U_14,U_17)
| ~ in(U_14,U_16) ) )
| U_16 != powerset(U_17) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_25,U_23] :
( U_23 = powerset(U_25)
| ? [U_21] :
( ~ in(U_21,U_23)
& subset(U_21,U_25) )
| ? [U_20] :
( ~ subset(U_20,U_25)
& in(U_20,U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ~ subset(U_19,U_24) )
& ! [U_18] :
( subset(U_18,U_24)
| ~ in(U_18,U_22) ) )
| U_22 != powerset(U_24) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_25,U_23] :
( U_23 = powerset(U_25)
| ? [U_21] :
( ~ in(U_21,U_23)
& subset(U_21,U_25) )
| ( ~ subset(sK3(U_25,U_23),U_25)
& in(sK3(U_25,U_23),U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ~ subset(U_19,U_24) )
& ! [U_18] :
( subset(U_18,U_24)
| ~ in(U_18,U_22) ) )
| U_22 != powerset(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_25,U_23))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_25,U_23] :
( U_23 = powerset(U_25)
| ( ~ in(sK4(U_25,U_23),U_23)
& subset(sK4(U_25,U_23),U_25) )
| ( ~ subset(sK3(U_25,U_23),U_25)
& in(sK3(U_25,U_23),U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ~ subset(U_19,U_24) )
& ! [U_18] :
( subset(U_18,U_24)
| ~ in(U_18,U_22) ) )
| U_22 != powerset(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4(U_25,U_23))],[f_3_4]) ).
cnf(f_3_6,plain,
( subset(U_18,U_24)
| ~ in(U_18,U_22)
| U_22 != powerset(U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( in(U_19,U_22)
| ~ subset(U_19,U_24)
| U_22 != powerset(U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( subset(sK4(U_25,U_23),U_25)
| in(sK3(U_25,U_23),U_23)
| U_23 = powerset(U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( ~ in(sK4(U_25,U_23),U_23)
| in(sK3(U_25,U_23),U_23)
| U_23 = powerset(U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( subset(sK4(U_25,U_23),U_25)
| ~ subset(sK3(U_25,U_23),U_25)
| U_23 = powerset(U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK4(U_25,U_23),U_23)
| ~ subset(sK3(U_25,U_23),U_25)
| U_23 = powerset(U_25) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_4_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_5_2,plain,
? [U_26] : empty(U_26),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5)],[f_5_2]) ).
cnf(f_5_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_6_2,plain,
? [U_27] : ~ empty(U_27),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_7_2,plain,
! [U_29,U_28] : subset(U_29,U_29),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_29] : subset(U_29,U_29),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
subset(U_29,U_29),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negate,[status(cth)],[t1_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_9_2,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_30] :
( ( ~ in(U_30,U_32)
& in(U_30,U_31) )
| ( ~ in(U_30,U_31)
& in(U_30,U_32) ) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_34] :
( ~ in(U_34,U_32)
& in(U_34,U_31) )
| ? [U_33] :
( ~ in(U_33,U_31)
& in(U_33,U_32) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_34] :
( ~ in(U_34,U_32)
& in(U_34,U_31) )
| ( ~ in(sK7(U_32,U_31),U_31)
& in(sK7(U_32,U_31),U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7(U_32,U_31))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_32,U_31] :
( U_32 = U_31
| ( ~ in(sK8(U_32,U_31),U_32)
& in(sK8(U_32,U_31),U_31) )
| ( ~ in(sK7(U_32,U_31),U_31)
& in(sK7(U_32,U_31),U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_34,sK8(U_32,U_31))],[f_9_4]) ).
cnf(f_9_6,plain,
( in(sK8(U_32,U_31),U_31)
| in(sK7(U_32,U_31),U_32)
| U_32 = U_31 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( ~ in(sK8(U_32,U_31),U_32)
| in(sK7(U_32,U_31),U_32)
| U_32 = U_31 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( in(sK8(U_32,U_31),U_31)
| ~ in(sK7(U_32,U_31),U_31)
| U_32 = U_31 ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ in(sK8(U_32,U_31),U_32)
| ~ in(sK7(U_32,U_31),U_31)
| U_32 = U_31 ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_10_2,plain,
! [U_35] :
( U_35 = empty_set
| ~ subset(U_35,empty_set) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( U_35 = empty_set
| ~ subset(U_35,empty_set) ),
inference(clausify,[status(thm)],[f_10_2]) ).
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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| 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,
( 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_10,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,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_14,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 : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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
% 0.11/5.37 % Computer : n019.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 19 23:22:56 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.16/5.71 % SZS status Theorem for theBenchmark
% 0.16/5.71 % SZS output start Proof for theBenchmark
% See solution above
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