%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU162+3 : 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 : n010.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 08:58:17 AM UTC 2026
% Result : Theorem 0.13s 0.43s
% 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(l25_zfmisc_1,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t65_zfmisc_1,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_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] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ in(U_3,U_2)
| ~ disjoint(singleton(U_3),U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ in(U_3,U_2)
| ~ disjoint(singleton(U_3),U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_5,U_4] :
( disjoint(singleton(U_5),U_4)
| in(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( disjoint(singleton(U_5),U_4)
| in(U_5,U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_6] : empty(U_6),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK1),
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_7] : ~ empty(U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_7,sK2)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_6_2,plain,
! [U_9,U_8] :
( disjoint(U_8,U_9)
| ~ disjoint(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( disjoint(U_8,U_9)
| ~ disjoint(U_9,U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(negate,[status(cth)],[t65_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B] :
( ( set_difference(A,singleton(B)) != A
& ~ in(B,A) )
| ( in(B,A)
& set_difference(A,singleton(B)) = A ) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_11,U_10] :
( ( set_difference(U_11,singleton(U_10)) != U_11
& ~ in(U_10,U_11) )
| ( in(U_10,U_11)
& set_difference(U_11,singleton(U_10)) = U_11 ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( ? [U_15,U_13] :
( set_difference(U_15,singleton(U_13)) != U_15
& ~ in(U_13,U_15) )
| ? [U_14,U_12] :
( in(U_12,U_14)
& set_difference(U_14,singleton(U_12)) = U_14 ) ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ? [U_15,U_13] :
( set_difference(U_15,singleton(U_13)) != U_15
& ~ in(U_13,U_15) )
| ? [U_12] :
( in(U_12,sK3)
& set_difference(sK3,singleton(U_12)) = sK3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_14,sK3)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ? [U_15,U_13] :
( set_difference(U_15,singleton(U_13)) != U_15
& ~ in(U_13,U_15) )
| ( in(sK4,sK3)
& set_difference(sK3,singleton(sK4)) = sK3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_12,sK4)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( ? [U_13] :
( set_difference(sK5,singleton(U_13)) != sK5
& ~ in(U_13,sK5) )
| ( in(sK4,sK3)
& set_difference(sK3,singleton(sK4)) = sK3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_15,sK5)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( ( set_difference(sK5,singleton(sK6)) != sK5
& ~ in(sK6,sK5) )
| ( in(sK4,sK3)
& set_difference(sK3,singleton(sK4)) = sK3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_13,sK6)],[f_7_7]) ).
fof(f_7_9,negated_conjecture,
( ( set_difference(sK5,singleton(sK6)) != sK5
| ~ sP1 )
& ( ~ in(sK6,sK5)
| ~ sP1 )
& ( in(sK4,sK3)
| ~ sP0 )
& ( set_difference(sK3,singleton(sK4)) = sK3
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_11,negated_conjecture,
( set_difference(sK3,singleton(sK4)) = sK3
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_12,negated_conjecture,
( in(sK4,sK3)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_13,negated_conjecture,
( ~ in(sK6,sK5)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_14,negated_conjecture,
( set_difference(sK5,singleton(sK6)) != sK5
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_9]) ).
fof(f_8_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_8_2,plain,
! [U_17,U_16] :
( ( disjoint(U_17,U_16)
| set_difference(U_17,U_16) != U_17 )
& ( set_difference(U_17,U_16) = U_17
| ~ disjoint(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_21,U_19] :
( disjoint(U_21,U_19)
| set_difference(U_21,U_19) != U_21 )
& ! [U_20,U_18] :
( set_difference(U_20,U_18) = U_20
| ~ disjoint(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( set_difference(U_20,U_18) = U_20
| ~ disjoint(U_20,U_18) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( disjoint(U_21,U_19)
| set_difference(U_21,U_19) != U_21 ),
inference(clausify,[status(thm)],[f_8_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,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,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 : SEU162+3 : 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
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:24:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------