%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET882+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 : n003.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 08:57:44 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.13s
% 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(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('theBenchmark.p',l39_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(t23_zfmisc_1,conjecture,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
file('theBenchmark.p',t23_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] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_7,U_6] :
( ( U_6 = singleton(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& U_5 = U_7 )
| ( U_5 != U_7
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| U_4 != U_7 )
& ( U_4 = U_7
| ~ in(U_4,U_6) ) )
| U_6 != singleton(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ? [U_10] :
( U_10 != U_15
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_15,U_13))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& sK2(U_15,U_13) = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15,U_13))],[f_3_4]) ).
cnf(f_3_6,plain,
( U_8 = U_14
| ~ in(U_8,U_12)
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( in(U_9,U_12)
| U_9 != U_14
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( sK2(U_15,U_13) = U_15
| in(sK1(U_15,U_13),U_13)
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( ~ in(sK2(U_15,U_13),U_13)
| in(sK1(U_15,U_13),U_13)
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( sK2(U_15,U_13) = U_15
| sK1(U_15,U_13) != U_15
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK2(U_15,U_13),U_13)
| sK1(U_15,U_13) != U_15
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A)
| ( A != B
& ~ in(B,C) )
| in(A,C) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[l39_zfmisc_1]) ).
fof(f_4_2,plain,
! [U_18,U_17,U_16] :
( ( set_difference(unordered_pair(U_18,U_17),U_16) = singleton(U_18)
| ( U_18 != U_17
& ~ in(U_17,U_16) )
| in(U_18,U_16) )
& ( ( ( U_18 = U_17
| in(U_17,U_16) )
& ~ in(U_18,U_16) )
| set_difference(unordered_pair(U_18,U_17),U_16) != singleton(U_18) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_24,U_22,U_20] :
( set_difference(unordered_pair(U_24,U_22),U_20) = singleton(U_24)
| ( U_24 != U_22
& ~ in(U_22,U_20) )
| in(U_24,U_20) )
& ! [U_23,U_21,U_19] :
( ( ( U_23 = U_21
| in(U_21,U_19) )
& ~ in(U_23,U_19) )
| set_difference(unordered_pair(U_23,U_21),U_19) != singleton(U_23) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ in(U_23,U_19)
| set_difference(unordered_pair(U_23,U_21),U_19) != singleton(U_23) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( U_23 = U_21
| in(U_21,U_19)
| set_difference(unordered_pair(U_23,U_21),U_19) != singleton(U_23) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( ~ in(U_22,U_20)
| in(U_24,U_20)
| set_difference(unordered_pair(U_24,U_22),U_20) = singleton(U_24) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( U_24 != U_22
| in(U_24,U_20)
| set_difference(unordered_pair(U_24,U_22),U_20) = singleton(U_24) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_5_2,plain,
? [U_25] : empty(U_25),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
empty(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3)],[f_5_2]) ).
cnf(f_5_4,plain,
empty(sK3),
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_26] : ~ empty(U_26),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
~ empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK4),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
inference(negate,[status(cth)],[t23_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B] :
( set_difference(unordered_pair(A,B),singleton(B)) != singleton(A)
& A != B ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_28,U_27] :
( set_difference(unordered_pair(U_28,U_27),singleton(U_27)) != singleton(U_28)
& U_28 != U_27 ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_27] :
( set_difference(unordered_pair(sK5,U_27),singleton(U_27)) != singleton(sK5)
& sK5 != U_27 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_28,sK5)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( set_difference(unordered_pair(sK5,sK6),singleton(sK6)) != singleton(sK5)
& sK5 != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( set_difference(unordered_pair(sK5,sK6),singleton(sK6)) != singleton(sK5)
& sK5 != sK6 ),
inference(definitional_conversion,[status(esa)],[f_7_5]) ).
cnf(f_7_7,negated_conjecture,
sK5 != sK6,
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,negated_conjecture,
set_difference(unordered_pair(sK5,sK6),singleton(sK6)) != singleton(sK5),
inference(clausify,[status(thm)],[f_7_6]) ).
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,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,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_8,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_9,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_10,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 : SET882+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
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:08:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------