%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU153+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 08:45:12 AM UTC 2026
% Result : Theorem 0.23s 20.72s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 49 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 21 ~; 12 |; 5 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn 17 !; 2 ?)
% 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(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(l25_zfmisc_1,conjecture,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l25_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
inference(assume_negation,[status(cth)],[l25_zfmisc_1]) ).
cnf(c_18,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_21,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_25,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_29,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_35,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(nnf_14,plain,
? [A,B] :
( in(A,B)
& disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1_neg]) ).
fof(sk_l25_zfmisc_1_neg,plain,
( in(sK0,sK1)
& disjoint(singleton(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_14]) ).
cnf(c_36,negated_conjecture,
disjoint(singleton(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_l25_zfmisc_1_neg]) ).
cnf(c_37,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l25_zfmisc_1_neg]) ).
cnf(c_46,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_18]) ).
cnf(c_59,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_21]) ).
cnf(c_137,plain,
disjoint(sK1,singleton(sK0)),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_208,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_46]) ).
cnf(c_261,plain,
set_intersection2(sK1,singleton(sK0)) = empty_set,
inference(resolve,[status(thm)],[c_137,c_29]) ).
cnf(c_272,plain,
( ~ in(C,B)
| ~ in(C,A)
| set_intersection2(A,B) != empty_set ),
inference(resolve,[status(thm)],[c_25,c_59]) ).
cnf(c_273,negated_conjecture,
( ~ in(sK0,A)
| set_intersection2(sK1,A) != empty_set ),
inference(resolve,[status(thm)],[c_272,c_37]) ).
cnf(c_274,negated_conjecture,
set_intersection2(sK1,singleton(sK0)) != empty_set,
inference(resolve,[status(thm)],[c_273,c_208]) ).
cnf(c_271,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_261,c_274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU153+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/20.68 % Computer : n006.cluster.edu
% 0.18/20.68 % Model : x86_64 x86_64
% 0.18/20.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/20.68 % Memory : 8046.5625MB
% 0.18/20.68 % OS : Linux 6.8.0-71-generic
% 0.18/20.68 % CPULimit : 300
% 0.18/20.68 % WCLimit : 300
% 0.18/20.68 % DateTime : Sat Sep 26 08:41:17 UTC 2026
% 0.18/20.68 % CPUTime :
% 0.18/20.68 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/20.68 % Process 844337 was started by sandbox2 on n006,
% 0.18/20.68 % Sat Sep 26 08:41:17 2026
% 0.18/20.68 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/20.69
% 0.18/20.69 % From the command line: assign(max_seconds, 300).
% 0.23/20.72
% 0.23/20.72 % SZS status Theorem for theBenchmark
% 0.23/20.72
% 0.23/20.72 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.23/20.72 % Length of proof is 19.
% 0.23/20.72 % Level of proof is 4.
% 0.23/20.72 % Maximum clause weight is 24.000.
% 0.23/20.72 % Given clauses 41.
% 0.23/20.72
% 0.23/20.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------