%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET900+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 : n017.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 08:57:45 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : Proof 0.08s
% 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(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(t41_zfmisc_1,conjecture,
! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
file('theBenchmark.p',t41_zfmisc_1) ).
fof(l45_zfmisc_1,axiom,
! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
file('theBenchmark.p',l45_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,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_2_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_3_2,plain,
? [U_2] : empty(U_2),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_3_2]) ).
cnf(f_3_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_4_2,plain,
? [U_3] : ~ empty(U_3),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2)],[f_4_2]) ).
cnf(f_4_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,negated_conjecture,
~ ! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
inference(negate,[status(cth)],[t41_zfmisc_1]) ).
fof(f_5_2,negated_conjecture,
? [A,B] :
( ! [C] :
( C = B
| ~ in(C,A) )
& A != empty_set
& A != singleton(B) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_6,U_5] :
( ! [U_4] :
( U_4 = U_5
| ~ in(U_4,U_6) )
& U_6 != empty_set
& U_6 != singleton(U_5) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
? [U_6] :
( ? [U_5] :
( ! [U_4] :
( U_4 = U_5
| ~ in(U_4,U_6) )
& U_6 != singleton(U_5) )
& U_6 != empty_set ),
inference(miniscope,[status(thm)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
( ? [U_5] :
( ! [U_4] :
( U_4 = U_5
| ~ in(U_4,sK3) )
& sK3 != singleton(U_5) )
& sK3 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_6,sK3)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
( ! [U_4] :
( U_4 = sK4
| ~ in(U_4,sK3) )
& sK3 != singleton(sK4)
& sK3 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_5,sK4)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( ! [U_4] :
( U_4 = sK4
| ~ in(U_4,sK3) )
& sK3 != singleton(sK4)
& sK3 != empty_set ),
inference(definitional_conversion,[status(esa)],[f_5_6]) ).
cnf(f_5_8,negated_conjecture,
sK3 != empty_set,
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,negated_conjecture,
sK3 != singleton(sK4),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,negated_conjecture,
( U_4 = sK4
| ~ in(U_4,sK3) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_1,plain,
! [A,B] :
( ? [C] :
( C != B
& in(C,A) )
| A = empty_set
| A = singleton(B) ),
inference(fof_nnf,[status(thm)],[l45_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_9,U_8] :
( ? [U_7] :
( U_7 != U_8
& in(U_7,U_9) )
| U_9 = empty_set
| U_9 = singleton(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_9] :
( ! [U_8] :
( ? [U_7] :
( U_7 != U_8
& in(U_7,U_9) )
| U_9 = singleton(U_8) )
| U_9 = empty_set ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_9] :
( ! [U_8] :
( ( sK5(U_9,U_8) != U_8
& in(sK5(U_9,U_8),U_9) )
| U_9 = singleton(U_8) )
| U_9 = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_7,sK5(U_9,U_8))],[f_6_3]) ).
cnf(f_6_5,plain,
( in(sK5(U_9,U_8),U_9)
| U_9 = singleton(U_8)
| U_9 = empty_set ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( sK5(U_9,U_8) != U_8
| U_9 = singleton(U_8)
| U_9 = empty_set ),
inference(clausify,[status(thm)],[f_6_4]) ).
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,
( sK5(Eq_x_0,Eq_x_1) = sK5(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 : SET900+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
% 0.08/0.36 % Computer : n017.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 23:02:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------