%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:57:48 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% 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(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(t67_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('theBenchmark.p',t67_zfmisc_1) ).
fof(l34_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('theBenchmark.p',l34_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] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_2_2,plain,
? [U_2] : empty(U_2),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_2_2]) ).
cnf(f_2_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_3_2,plain,
? [U_3] : ~ empty(U_3),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2)],[f_3_2]) ).
cnf(f_3_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
inference(negate,[status(cth)],[t67_zfmisc_1]) ).
fof(f_4_2,negated_conjecture,
? [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)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_5,U_4] :
( ( set_difference(singleton(U_5),U_4) != singleton(U_5)
& ~ in(U_5,U_4) )
| ( in(U_5,U_4)
& set_difference(singleton(U_5),U_4) = singleton(U_5) ) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
( ? [U_9,U_7] :
( set_difference(singleton(U_9),U_7) != singleton(U_9)
& ~ in(U_9,U_7) )
| ? [U_8,U_6] :
( in(U_8,U_6)
& set_difference(singleton(U_8),U_6) = singleton(U_8) ) ),
inference(miniscope,[status(thm)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
( ? [U_9,U_7] :
( set_difference(singleton(U_9),U_7) != singleton(U_9)
& ~ in(U_9,U_7) )
| ? [U_6] :
( in(sK3,U_6)
& set_difference(singleton(sK3),U_6) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_8,sK3)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( ? [U_9,U_7] :
( set_difference(singleton(U_9),U_7) != singleton(U_9)
& ~ in(U_9,U_7) )
| ( in(sK3,sK4)
& set_difference(singleton(sK3),sK4) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4)],[f_4_5]) ).
fof(f_4_7,negated_conjecture,
( ? [U_7] :
( set_difference(singleton(sK5),U_7) != singleton(sK5)
& ~ in(sK5,U_7) )
| ( in(sK3,sK4)
& set_difference(singleton(sK3),sK4) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_9,sK5)],[f_4_6]) ).
fof(f_4_8,negated_conjecture,
( ( set_difference(singleton(sK5),sK6) != singleton(sK5)
& ~ in(sK5,sK6) )
| ( in(sK3,sK4)
& set_difference(singleton(sK3),sK4) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_7,sK6)],[f_4_7]) ).
fof(f_4_9,negated_conjecture,
( ( set_difference(singleton(sK5),sK6) != singleton(sK5)
| ~ sP1 )
& ( ~ in(sK5,sK6)
| ~ sP1 )
& ( in(sK3,sK4)
| ~ sP0 )
& ( set_difference(singleton(sK3),sK4) = singleton(sK3)
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_4_8]) ).
cnf(f_4_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_4_9]) ).
cnf(f_4_11,negated_conjecture,
( set_difference(singleton(sK3),sK4) = singleton(sK3)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_4_9]) ).
cnf(f_4_12,negated_conjecture,
( in(sK3,sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_4_9]) ).
cnf(f_4_13,negated_conjecture,
( ~ in(sK5,sK6)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_4_9]) ).
cnf(f_4_14,negated_conjecture,
( set_difference(singleton(sK5),sK6) != singleton(sK5)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_4_9]) ).
fof(f_5_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_5_2,plain,
! [U_11,U_10] :
( ( set_difference(singleton(U_11),U_10) = singleton(U_11)
| in(U_11,U_10) )
& ( ~ in(U_11,U_10)
| set_difference(singleton(U_11),U_10) != singleton(U_11) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_15,U_13] :
( set_difference(singleton(U_15),U_13) = singleton(U_15)
| in(U_15,U_13) )
& ! [U_14,U_12] :
( ~ in(U_14,U_12)
| set_difference(singleton(U_14),U_12) != singleton(U_14) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( ~ in(U_14,U_12)
| set_difference(singleton(U_14),U_12) != singleton(U_14) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( set_difference(singleton(U_15),U_13) = singleton(U_15)
| in(U_15,U_13) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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,
( 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_7,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 : SET924+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.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 23:09:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------