%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU143+2 : 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 : n006.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 169.03s 169.76s
% Output : Proof 169.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 18 unt; 0 def)
% Number of atoms : 99 ( 61 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 1 sgn 44 !; 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(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(f_7_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_7_2,plain,
! [U_19,U_18] :
( ( U_18 = singleton(U_19)
| ? [U_17] :
( ( ~ in(U_17,U_18)
& U_17 = U_19 )
| ( U_17 != U_19
& in(U_17,U_18) ) ) )
& ( ! [U_16] :
( ( in(U_16,U_18)
| U_16 != U_19 )
& ( U_16 = U_19
| ~ in(U_16,U_18) ) )
| U_18 != singleton(U_19) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& U_23 = U_27 )
| ? [U_22] :
( U_22 != U_27
& in(U_22,U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& U_23 = U_27 )
| ( sK1(U_27,U_25) != U_27
& in(sK1(U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_22,sK1(U_27,U_25))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ( ~ in(sK2(U_27,U_25),U_25)
& sK2(U_27,U_25) = U_27 )
| ( sK1(U_27,U_25) != U_27
& in(sK1(U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_23,sK2(U_27,U_25))],[f_7_4]) ).
cnf(f_7_7,plain,
( in(U_21,U_24)
| U_21 != U_26
| U_24 != singleton(U_26) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_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_8_2,plain,
! [U_30] :
( ( U_30 = empty_set
| ? [U_29] : in(U_29,U_30) )
& ( ! [U_28] : ~ in(U_28,U_30)
| U_30 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_32] :
( U_32 = empty_set
| ? [U_29] : in(U_29,U_32) )
& ! [U_31] :
( ! [U_28] : ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_32] :
( U_32 = empty_set
| in(sK3(U_32),U_32) )
& ! [U_31] :
( ! [U_28] : ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3(U_32))],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ in(U_28,U_31)
| U_31 != empty_set ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_28_1,negated_conjecture,
~ ! [A] : singleton(A) != empty_set,
inference(negate,[status(cth)],[l1_zfmisc_1]) ).
fof(f_28_2,negated_conjecture,
? [A] : singleton(A) = empty_set,
inference(fof_nnf,[status(thm)],[f_28_1]) ).
fof(f_28_3,negated_conjecture,
? [U_123] : singleton(U_123) = empty_set,
inference(variable_rename,[status(thm)],[f_28_2]) ).
fof(f_28_4,negated_conjecture,
singleton(sK13) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_123,sK13)],[f_28_3]) ).
cnf(f_28_5,negated_conjecture,
singleton(sK13) = empty_set,
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_48_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_48_2,plain,
! [U_172] : set_difference(U_172,empty_set) = U_172,
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
set_difference(U_172,empty_set) = U_172,
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
singleton(sK13) = empty_set,
inference(start,[status(thm),parent(0:0)],[f_28_5]) ).
cnf(t2,plain,
( ~ in(set_difference(sK13,empty_set),singleton(sK13))
| singleton(sK13) != empty_set ),
inference(extension,[status(thm),parent(t1:1)],[f_8_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( set_difference(sK13,empty_set) != sK13
| singleton(sK13) != singleton(sK13)
| in(set_difference(sK13,empty_set),singleton(sK13)) ),
inference(extension,[status(thm),parent(t2:2)],[f_7_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
singleton(sK13) = singleton(sK13),
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,
set_difference(sK13,empty_set) = sK13,
inference(extension,[status(thm),parent(t4:3)],[f_48_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU143+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.78 % Computer : n006.cluster.edu
% 0.09/0.78 % Model : x86_64 x86_64
% 0.09/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.78 % Memory : 8046.5625MB
% 0.09/0.78 % OS : Linux 6.8.0-71-generic
% 0.09/0.78 % CPULimit : 300
% 0.09/0.78 % WCLimit : 300
% 0.09/0.78 % DateTime : Sat Sep 19 23:22:15 UTC 2026
% 0.09/0.78 % CPUTime :
% 169.03/169.76 % SZS status Theorem for theBenchmark
% 169.03/169.76 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------