%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n008.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 08:57:43 AM UTC 2026
% Result : Theorem 0.38s 0.65s
% Output : Proof 0.38s
% 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(l34_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('theBenchmark.p',l34_zfmisc_1) ).
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(t20_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('theBenchmark.p',t20_zfmisc_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] :
( ( set_difference(singleton(A),B) = singleton(A)
| in(A,B) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[l34_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_15,U_14] :
( ( set_difference(singleton(U_15),U_14) = singleton(U_15)
| in(U_15,U_14) )
& ( ~ in(U_15,U_14)
| set_difference(singleton(U_15),U_14) != singleton(U_15) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_19,U_17] :
( set_difference(singleton(U_19),U_17) = singleton(U_19)
| in(U_19,U_17) )
& ! [U_18,U_16] :
( ~ in(U_18,U_16)
| set_difference(singleton(U_18),U_16) != singleton(U_18) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( ~ in(U_18,U_16)
| set_difference(singleton(U_18),U_16) != singleton(U_18) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( set_difference(singleton(U_19),U_17) = singleton(U_19)
| in(U_19,U_17) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_20] : empty(U_20),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_5_2,plain,
? [U_21] : ~ empty(U_21),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK4),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
inference(negate,[status(cth)],[t20_zfmisc_1]) ).
fof(f_6_2,negated_conjecture,
? [A,B] :
( ( set_difference(singleton(A),singleton(B)) != singleton(A)
& A != B )
| ( A = B
& set_difference(singleton(A),singleton(B)) = singleton(A) ) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_23,U_22] :
( ( set_difference(singleton(U_23),singleton(U_22)) != singleton(U_23)
& U_23 != U_22 )
| ( U_23 = U_22
& set_difference(singleton(U_23),singleton(U_22)) = singleton(U_23) ) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
( ? [U_27,U_25] :
( set_difference(singleton(U_27),singleton(U_25)) != singleton(U_27)
& U_27 != U_25 )
| ? [U_26,U_24] :
( U_26 = U_24
& set_difference(singleton(U_26),singleton(U_24)) = singleton(U_26) ) ),
inference(miniscope,[status(thm)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
( ? [U_27,U_25] :
( set_difference(singleton(U_27),singleton(U_25)) != singleton(U_27)
& U_27 != U_25 )
| ? [U_24] :
( sK5 = U_24
& set_difference(singleton(sK5),singleton(U_24)) = singleton(sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( ? [U_27,U_25] :
( set_difference(singleton(U_27),singleton(U_25)) != singleton(U_27)
& U_27 != U_25 )
| ( sK5 = sK6
& set_difference(singleton(sK5),singleton(sK6)) = singleton(sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_24,sK6)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( ? [U_25] :
( set_difference(singleton(sK7),singleton(U_25)) != singleton(sK7)
& sK7 != U_25 )
| ( sK5 = sK6
& set_difference(singleton(sK5),singleton(sK6)) = singleton(sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7)],[f_6_6]) ).
fof(f_6_8,negated_conjecture,
( ( set_difference(singleton(sK7),singleton(sK8)) != singleton(sK7)
& sK7 != sK8 )
| ( sK5 = sK6
& set_difference(singleton(sK5),singleton(sK6)) = singleton(sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_25,sK8)],[f_6_7]) ).
fof(f_6_9,negated_conjecture,
( ( set_difference(singleton(sK7),singleton(sK8)) != singleton(sK7)
| ~ sP1 )
& ( sK7 != sK8
| ~ sP1 )
& ( sK5 = sK6
| ~ sP0 )
& ( set_difference(singleton(sK5),singleton(sK6)) = singleton(sK5)
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_6_8]) ).
cnf(f_6_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_6_9]) ).
cnf(f_6_11,negated_conjecture,
( set_difference(singleton(sK5),singleton(sK6)) = singleton(sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_6_9]) ).
cnf(f_6_12,negated_conjecture,
( sK5 = sK6
| ~ sP0 ),
inference(clausify,[status(thm)],[f_6_9]) ).
cnf(f_6_13,negated_conjecture,
( sK7 != sK8
| ~ sP1 ),
inference(clausify,[status(thm)],[f_6_9]) ).
cnf(f_6_14,negated_conjecture,
( set_difference(singleton(sK7),singleton(sK8)) != singleton(sK7)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_6_9]) ).
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,
( set_difference(Eq_x_0,Eq_x_1) = set_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,
( 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_9,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 : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:07:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.38/0.65 % SZS status Theorem for theBenchmark
% 0.38/0.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------