%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU143+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 : Sun Sep 27 08:45:09 AM UTC 2026
% Result : Theorem 0.17s 5.41s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 25 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 5 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 20 ( 4 sgn 7 !; 1 ?)
% 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(l1_zfmisc_1_neg,negated_conjecture,
~ ! [A] : singleton(A) != empty_set,
inference(assume_negation,[status(cth)],[l1_zfmisc_1]) ).
cnf(c_11,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_14,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
fof(nnf_8,plain,
? [A] : singleton(A) = empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1_neg]) ).
fof(sk_l1_zfmisc_1_neg,plain,
singleton(sK0) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_8]) ).
cnf(c_19,negated_conjecture,
singleton(sK0) = empty_set,
inference(split_conjunct,[status(thm)],[sk_l1_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
empty_set = singleton(sK0),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_25,plain,
( ~ in(B,A)
| singleton(sK0) != A ),
inference(paramod,[status(thm)],[c_20,c_14]) ).
cnf(c_26,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_41,negated_conjecture,
singleton(sK0) = empty_set,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_42,negated_conjecture,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_25,c_41]) ).
cnf(c_36,negated_conjecture,
~ in(A,singleton(sK0)),
inference(paramod,[status(thm)],[c_20,c_42]) ).
cnf(c_39,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_26]) ).
cnf(c_40,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU143+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.39 % Computer : n006.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Sat Sep 26 08:39:35 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 842322 was started by sandbox2 on n006,
% 0.10/5.39 % Sat Sep 26 08:39:35 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.40
% 0.17/5.40 % From the command line: assign(max_seconds, 300).
% 0.17/5.41
% 0.17/5.41 % SZS status Theorem for theBenchmark
% 0.17/5.41
% 0.17/5.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/5.41 % Length of proof is 12.
% 0.17/5.41 % Level of proof is 5.
% 0.17/5.41 % Maximum clause weight is 10.000.
% 0.17/5.41 % Given clauses 13.
% 0.17/5.41
% 0.17/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------