%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU146+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 : n019.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 08:58:11 AM UTC 2026
% Result : Theorem 1.15s 1.48s
% Output : Proof 1.25s
% 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(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
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(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l3_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_zfmisc_1,conjecture,
! [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(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_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] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ( U_3 = U_2
| ~ subset(U_2,U_3)
| ~ subset(U_3,U_2) )
& ( ( subset(U_2,U_3)
& subset(U_3,U_2) )
| U_3 != U_2 ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_7,U_5] :
( U_7 = U_5
| ~ subset(U_5,U_7)
| ~ subset(U_7,U_5) )
& ! [U_6,U_4] :
( ( subset(U_4,U_6)
& subset(U_6,U_4) )
| U_6 != U_4 ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_6,U_4)
| U_6 != U_4 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( subset(U_4,U_6)
| U_6 != U_4 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( U_7 = U_5
| ~ subset(U_5,U_7)
| ~ subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_3_2,plain,
$true,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_k4_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,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[l2_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_9,U_8] :
( ( subset(singleton(U_9),U_8)
| ~ in(U_9,U_8) )
& ( in(U_9,U_8)
| ~ subset(singleton(U_9),U_8) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_13,U_11] :
( subset(singleton(U_13),U_11)
| ~ in(U_13,U_11) )
& ! [U_12,U_10] :
( in(U_12,U_10)
| ~ subset(singleton(U_12),U_10) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( in(U_12,U_10)
| ~ subset(singleton(U_12),U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( subset(singleton(U_13),U_11)
| ~ in(U_13,U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[l3_zfmisc_1]) ).
fof(f_8_2,plain,
! [U_16,U_15,U_14] :
( subset(U_16,set_difference(U_15,singleton(U_14)))
| in(U_14,U_16)
| ~ subset(U_16,U_15) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_16,U_15] :
( ! [U_14] :
( subset(U_16,set_difference(U_15,singleton(U_14)))
| in(U_14,U_16) )
| ~ subset(U_16,U_15) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( subset(U_16,set_difference(U_15,singleton(U_14)))
| in(U_14,U_16)
| ~ subset(U_16,U_15) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negate,[status(cth)],[l4_zfmisc_1]) ).
fof(f_9_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_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_18,U_17] :
( ( ~ subset(U_18,singleton(U_17))
& ( U_18 = singleton(U_17)
| U_18 = empty_set ) )
| ( U_18 != singleton(U_17)
& U_18 != empty_set
& subset(U_18,singleton(U_17)) ) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ? [U_22,U_20] :
( ~ subset(U_22,singleton(U_20))
& ( U_22 = singleton(U_20)
| U_22 = empty_set ) )
| ? [U_21,U_19] :
( U_21 != singleton(U_19)
& U_21 != empty_set
& subset(U_21,singleton(U_19)) ) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ? [U_22,U_20] :
( ~ subset(U_22,singleton(U_20))
& ( U_22 = singleton(U_20)
| U_22 = empty_set ) )
| ? [U_19] :
( sK1 != singleton(U_19)
& sK1 != empty_set
& subset(sK1,singleton(U_19)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_21,sK1)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_22,U_20] :
( ~ subset(U_22,singleton(U_20))
& ( U_22 = singleton(U_20)
| U_22 = empty_set ) )
| ( sK1 != singleton(sK2)
& sK1 != empty_set
& subset(sK1,singleton(sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_19,sK2)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ? [U_20] :
( ~ subset(sK3,singleton(U_20))
& ( sK3 = singleton(U_20)
| sK3 = empty_set ) )
| ( sK1 != singleton(sK2)
& sK1 != empty_set
& subset(sK1,singleton(sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ( ~ subset(sK3,singleton(sK4))
& ( sK3 = singleton(sK4)
| sK3 = empty_set ) )
| ( sK1 != singleton(sK2)
& sK1 != empty_set
& subset(sK1,singleton(sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4)],[f_9_7]) ).
fof(f_9_9,negated_conjecture,
( ( ~ subset(sK3,singleton(sK4))
| ~ sP1 )
& ( sK3 = singleton(sK4)
| sK3 = empty_set
| ~ sP1 )
& ( sK1 != singleton(sK2)
| ~ sP0 )
& ( sK1 != empty_set
| ~ sP0 )
& ( subset(sK1,singleton(sK2))
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_9_8]) ).
cnf(f_9_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_11,negated_conjecture,
( subset(sK1,singleton(sK2))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_12,negated_conjecture,
( sK1 != empty_set
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_13,negated_conjecture,
( sK1 != singleton(sK2)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_14,negated_conjecture,
( sK3 = singleton(sK4)
| sK3 = empty_set
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_15,negated_conjecture,
( ~ subset(sK3,singleton(sK4))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_9]) ).
fof(f_10_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_10_2,plain,
? [U_23] : empty(U_23),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_23,sK5)],[f_10_2]) ).
cnf(f_10_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_11_2,plain,
? [U_24] : ~ empty(U_24),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_24,sK6)],[f_11_2]) ).
cnf(f_11_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_12_2,plain,
! [U_26,U_25] : subset(U_26,U_26),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_26] : subset(U_26,U_26),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
subset(U_26,U_26),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_13_2,plain,
! [U_27] : subset(empty_set,U_27),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
subset(empty_set,U_27),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_29,U_28] :
( ( set_difference(U_29,U_28) = empty_set
| ~ subset(U_29,U_28) )
& ( subset(U_29,U_28)
| set_difference(U_29,U_28) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_33,U_31] :
( set_difference(U_33,U_31) = empty_set
| ~ subset(U_33,U_31) )
& ! [U_32,U_30] :
( subset(U_32,U_30)
| set_difference(U_32,U_30) != empty_set ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( subset(U_32,U_30)
| set_difference(U_32,U_30) != empty_set ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( set_difference(U_33,U_31) = empty_set
| ~ subset(U_33,U_31) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_15_2,plain,
! [U_34] :
( U_34 = empty_set
| ~ subset(U_34,empty_set) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( U_34 = empty_set
| ~ subset(U_34,empty_set) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_3_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_2]) ).
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,
( 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,
( 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(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 : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 23:22:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 1.15/1.48 % SZS status Theorem for theBenchmark
% 1.15/1.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------