%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU160+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n012.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 08:58:16 AM UTC 2026
% Result : Theorem 0.03s 0.31s
% Output : Proof 0.03s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(t39_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(f_1_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_1_2,plain,
? [U_0] : empty(U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_2]) ).
cnf(f_1_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_2_2,plain,
? [U_1] : ~ empty(U_1),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_2_2]) ).
cnf(f_2_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_3_2,plain,
! [U_3,U_2] : subset(U_3,U_3),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_3] : subset(U_3,U_3),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
subset(U_3,U_3),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_6_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negate,[status(cth)],[t39_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [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)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_5,U_4] :
( ( ~ subset(U_5,singleton(U_4))
& ( U_5 = singleton(U_4)
| U_5 = empty_set ) )
| ( U_5 != singleton(U_4)
& U_5 != empty_set
& subset(U_5,singleton(U_4)) ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( ? [U_9,U_7] :
( ~ subset(U_9,singleton(U_7))
& ( U_9 = singleton(U_7)
| U_9 = empty_set ) )
| ? [U_8,U_6] :
( U_8 != singleton(U_6)
& U_8 != empty_set
& subset(U_8,singleton(U_6)) ) ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ? [U_9,U_7] :
( ~ subset(U_9,singleton(U_7))
& ( U_9 = singleton(U_7)
| U_9 = empty_set ) )
| ? [U_6] :
( sK3 != singleton(U_6)
& sK3 != empty_set
& subset(sK3,singleton(U_6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_8,sK3)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ? [U_9,U_7] :
( ~ subset(U_9,singleton(U_7))
& ( U_9 = singleton(U_7)
| U_9 = empty_set ) )
| ( sK3 != singleton(sK4)
& sK3 != empty_set
& subset(sK3,singleton(sK4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( ? [U_7] :
( ~ subset(sK5,singleton(U_7))
& ( sK5 = singleton(U_7)
| sK5 = empty_set ) )
| ( sK3 != singleton(sK4)
& sK3 != empty_set
& subset(sK3,singleton(sK4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_9,sK5)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( ( ~ subset(sK5,singleton(sK6))
& ( sK5 = singleton(sK6)
| sK5 = empty_set ) )
| ( sK3 != singleton(sK4)
& sK3 != empty_set
& subset(sK3,singleton(sK4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_7,sK6)],[f_7_7]) ).
fof(f_7_9,negated_conjecture,
( ( ~ subset(sK5,singleton(sK6))
| ~ sP1 )
& ( sK5 = singleton(sK6)
| sK5 = empty_set
| ~ sP1 )
& ( sK3 != singleton(sK4)
| ~ sP0 )
& ( sK3 != empty_set
| ~ sP0 )
& ( subset(sK3,singleton(sK4))
| ~ 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,
( subset(sK3,singleton(sK4))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_12,negated_conjecture,
( sK3 != empty_set
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_13,negated_conjecture,
( sK3 != singleton(sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_14,negated_conjecture,
( sK5 = singleton(sK6)
| sK5 = empty_set
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_9]) ).
cnf(f_7_15,negated_conjecture,
( ~ subset(sK5,singleton(sK6))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_9]) ).
fof(f_8_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_8_2,plain,
! [U_11,U_10] :
( ( subset(U_11,singleton(U_10))
| ( U_11 != singleton(U_10)
& U_11 != empty_set ) )
& ( U_11 = singleton(U_10)
| U_11 = empty_set
| ~ subset(U_11,singleton(U_10)) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_15,U_13] :
( subset(U_15,singleton(U_13))
| ( U_15 != singleton(U_13)
& U_15 != empty_set ) )
& ! [U_14,U_12] :
( U_14 = singleton(U_12)
| U_14 = empty_set
| ~ subset(U_14,singleton(U_12)) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_14 = singleton(U_12)
| U_14 = empty_set
| ~ subset(U_14,singleton(U_12)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( U_15 != empty_set
| subset(U_15,singleton(U_13)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( U_15 != singleton(U_13)
| subset(U_15,singleton(U_13)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_6,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
% 0.00/0.01 % Problem : SEU160+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 19 23:24:07 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.31 % SZS status Theorem for theBenchmark
% 0.03/0.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------