%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET923+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 : n015.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 0.10s 0.39s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t66_zfmisc_1,conjecture,
! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
file('theBenchmark.p',t66_zfmisc_1) ).
fof(f_1_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_1_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1]) ).
fof(f_2_2,plain,
! [U_1,U_0] :
( ( subset(U_1,singleton(U_0))
| ( U_1 != singleton(U_0)
& U_1 != empty_set ) )
& ( U_1 = singleton(U_0)
| U_1 = empty_set
| ~ subset(U_1,singleton(U_0)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_5,U_3] :
( subset(U_5,singleton(U_3))
| ( U_5 != singleton(U_3)
& U_5 != empty_set ) )
& ! [U_4,U_2] :
( U_4 = singleton(U_2)
| U_4 = empty_set
| ~ subset(U_4,singleton(U_2)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( U_4 = singleton(U_2)
| U_4 = empty_set
| ~ subset(U_4,singleton(U_2)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( U_5 != empty_set
| subset(U_5,singleton(U_3)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( U_5 != singleton(U_3)
| subset(U_5,singleton(U_3)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_3_2,plain,
? [U_6] : empty(U_6),
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_6,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_7] : ~ empty(U_7),
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_7,sK2)],[f_4_2]) ).
cnf(f_4_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_5_2,plain,
! [U_9,U_8] : subset(U_9,U_9),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_9] : subset(U_9,U_9),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
subset(U_9,U_9),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_6_2,plain,
! [U_11,U_10] :
( ( set_difference(U_11,U_10) = empty_set
| ~ subset(U_11,U_10) )
& ( subset(U_11,U_10)
| set_difference(U_11,U_10) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_15,U_13] :
( set_difference(U_15,U_13) = empty_set
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( subset(U_14,U_12)
| set_difference(U_14,U_12) != empty_set ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( subset(U_14,U_12)
| set_difference(U_14,U_12) != empty_set ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( set_difference(U_15,U_13) = empty_set
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B] :
~ ( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(negate,[status(cth)],[t66_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B] :
( A != singleton(B)
& A != empty_set
& set_difference(A,singleton(B)) = empty_set ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_17,U_16] :
( U_17 != singleton(U_16)
& U_17 != empty_set
& set_difference(U_17,singleton(U_16)) = empty_set ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_17] :
( ? [U_16] :
( U_17 != singleton(U_16)
& set_difference(U_17,singleton(U_16)) = empty_set )
& U_17 != empty_set ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ? [U_16] :
( sK3 != singleton(U_16)
& set_difference(sK3,singleton(U_16)) = empty_set )
& sK3 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( sK3 != singleton(sK4)
& set_difference(sK3,singleton(sK4)) = empty_set
& sK3 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( sK3 != singleton(sK4)
& set_difference(sK3,singleton(sK4)) = empty_set
& sK3 != empty_set ),
inference(definitional_conversion,[status(esa)],[f_7_6]) ).
cnf(f_7_8,negated_conjecture,
sK3 != empty_set,
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
set_difference(sK3,singleton(sK4)) = empty_set,
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,negated_conjecture,
sK3 != singleton(sK4),
inference(clausify,[status(thm)],[f_7_7]) ).
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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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 : SET923+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
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:10:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------