%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU143+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 0.09s 0.41s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 96 ( 58 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 111 ( 45 ~; 39 |; 24 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 1 sgn 41 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(l1_zfmisc_1,conjecture,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(f_2_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ( U_4 = singleton(U_5)
| ? [U_3] :
( ( ~ in(U_3,U_4)
& U_3 = U_5 )
| ( U_3 != U_5
& in(U_3,U_4) ) ) )
& ( ! [U_2] :
( ( in(U_2,U_4)
| U_2 != U_5 )
& ( U_2 = U_5
| ~ in(U_2,U_4) ) )
| U_4 != singleton(U_5) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& U_9 = U_13 )
| ? [U_8] :
( U_8 != U_13
& in(U_8,U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& U_9 = U_13 )
| ( sK1(U_13,U_11) != U_13
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_13,U_11))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ( ~ in(sK2(U_13,U_11),U_11)
& sK2(U_13,U_11) = U_13 )
| ( sK1(U_13,U_11) != U_13
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_13,U_11))],[f_2_4]) ).
cnf(f_2_7,plain,
( in(U_7,U_10)
| U_7 != U_12
| U_10 != singleton(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_3_2,plain,
! [U_16] :
( ( U_16 = empty_set
| ? [U_15] : in(U_15,U_16) )
& ( ! [U_14] : ~ in(U_14,U_16)
| U_16 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18] :
( U_18 = empty_set
| ? [U_15] : in(U_15,U_18) )
& ! [U_17] :
( ! [U_14] : ~ in(U_14,U_17)
| U_17 != empty_set ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18] :
( U_18 = empty_set
| in(sK3(U_18),U_18) )
& ! [U_17] :
( ! [U_14] : ~ in(U_14,U_17)
| U_17 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3(U_18))],[f_3_3]) ).
cnf(f_3_5,plain,
( ~ in(U_14,U_17)
| U_17 != empty_set ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_7_1,negated_conjecture,
~ ! [A] : singleton(A) != empty_set,
inference(negate,[status(cth)],[l1_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A] : singleton(A) = empty_set,
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_19] : singleton(U_19) = empty_set,
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
singleton(sK4) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_19,sK4)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
singleton(sK4) = empty_set,
inference(definitional_conversion,[status(esa)],[f_7_4]) ).
cnf(f_7_6,negated_conjecture,
singleton(sK4) = empty_set,
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( ~ in(sK4,singleton(sK4))
| singleton(sK4) != empty_set ),
inference(start,[status(thm),parent(0:0)],[f_3_5]) ).
cnf(t2,plain,
singleton(sK4) = empty_set,
inference(extension,[status(thm),parent(t1:1)],[f_7_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK4 != sK4
| singleton(sK4) != singleton(sK4)
| in(sK4,singleton(sK4)) ),
inference(extension,[status(thm),parent(t1:2)],[f_2_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
singleton(sK4) = singleton(sK4),
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t4:3)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU143+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 23:22:20 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.41 % SZS status Theorem for theBenchmark
% 0.09/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------