%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:35:43 AM UTC 2026
% Result : Unsatisfiable 0.66s 0.48s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 25 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_member_of_singleton_is_unique_2,axiom,
member_of(singleton(u)) != u,
file('theBenchmark.p',prove_member_of_singleton_is_unique_2) ).
cnf(c_33,plain,
member_of(singleton(u)) != u,
inference(clausify,[status(thm)],[prove_member_of_singleton_is_unique_2]) ).
fof(prove_member_of_singleton_is_unique_1,axiom,
member(u,universal_class),
file('theBenchmark.p',prove_member_of_singleton_is_unique_1) ).
cnf(c_34,plain,
member(u,universal_class),
inference(clausify,[status(thm)],[prove_member_of_singleton_is_unique_1]) ).
fof(member_exists2,axiom,
! [VAR_0] :
( singleton(member_of(singleton(VAR_0))) = singleton(VAR_0)
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',member_exists2) ).
cnf(c_37,plain,
( singleton(member_of(singleton(A))) = singleton(A)
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[member_exists2]) ).
fof(singleton_identified_by_element2,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ member(VAR_1,universal_class)
| singleton(VAR_0) != singleton(VAR_1) ),
file('theBenchmark.p',singleton_identified_by_element2) ).
cnf(c_41,plain,
( A = B
| ~ member(B,universal_class)
| singleton(A) != singleton(B) ),
inference(clausify,[status(thm)],[singleton_identified_by_element2]) ).
cnf(c_194,plain,
singleton(member_of(singleton(u))) = singleton(u),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_1558,plain,
( A = u
| singleton(A) != singleton(u) ),
inference(resolve,[status(thm)],[c_41,c_34]) ).
cnf(c_1559,plain,
( A = u
| singleton(u) != singleton(A) ),
inference(copy,[status(thm)],[c_1558]) ).
cnf(c_205,plain,
( u = A
| singleton(u) != singleton(A) ),
inference(copy,[status(thm)],[c_1559]) ).
cnf(c_1560,plain,
singleton(u) = singleton(member_of(singleton(u))),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_1561,plain,
u = member_of(singleton(u)),
inference(resolve,[status(thm)],[c_205,c_1560]) ).
cnf(c_1562,plain,
member_of(singleton(u)) = u,
inference(copy,[status(thm)],[c_1561]) ).
cnf(c_1557,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_1562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:04:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 627879 was started by sandbox on n006,
% 0.09/0.36 % Sat Sep 26 07:04:59 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.66/0.48
% 0.66/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.66/0.48
% 0.66/0.48 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.66/0.48 % Length of proof is 7.
% 0.66/0.48 % Level of proof is 2.
% 0.66/0.48 % Maximum clause weight is 30.000.
% 0.66/0.48 % Given clauses 215.
% 0.66/0.48
% 0.66/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------