%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:35:42 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.35s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 36 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_identified_by_element2_3,axiom,
x != y,
file('theBenchmark.p',prove_singleton_identified_by_element2_3) ).
cnf(c_33,plain,
x != y,
inference(clausify,[status(thm)],[prove_singleton_identified_by_element2_3]) ).
cnf(c_34,plain,
y != x,
inference(copy,[status(thm)],[c_33]) ).
fof(prove_singleton_identified_by_element2_2,axiom,
member(y,universal_class),
file('theBenchmark.p',prove_singleton_identified_by_element2_2) ).
cnf(c_35,plain,
member(y,universal_class),
inference(clausify,[status(thm)],[prove_singleton_identified_by_element2_2]) ).
fof(prove_singleton_identified_by_element2_1,axiom,
singleton(x) = singleton(y),
file('theBenchmark.p',prove_singleton_identified_by_element2_1) ).
cnf(c_36,plain,
singleton(x) = singleton(y),
inference(clausify,[status(thm)],[prove_singleton_identified_by_element2_1]) ).
cnf(c_37,plain,
singleton(y) = singleton(x),
inference(copy,[status(thm)],[c_36]) ).
fof(singleton_is_null_class,axiom,
! [VAR_0] :
( singleton(VAR_0) = null_class
| member(VAR_0,universal_class) ),
file('theBenchmark.p',singleton_is_null_class) ).
cnf(c_38,plain,
( singleton(A) = null_class
| member(A,universal_class) ),
inference(clausify,[status(thm)],[singleton_is_null_class]) ).
fof(only_member_in_singleton,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ member(VAR_0,singleton(VAR_1)) ),
file('theBenchmark.p',only_member_in_singleton) ).
cnf(c_39,plain,
( A = B
| ~ member(A,singleton(B)) ),
inference(clausify,[status(thm)],[only_member_in_singleton]) ).
fof(corollary_to_set_in_its_singleton,axiom,
! [VAR_0] :
( singleton(VAR_0) != null_class
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',corollary_to_set_in_its_singleton) ).
cnf(c_41,plain,
( singleton(A) != null_class
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[corollary_to_set_in_its_singleton]) ).
fof(set_in_its_singleton,axiom,
! [VAR_0] :
( member(VAR_0,singleton(VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',set_in_its_singleton) ).
cnf(c_42,plain,
( member(A,singleton(A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[set_in_its_singleton]) ).
cnf(c_762,plain,
( A = y
| ~ member(A,singleton(x)) ),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_187,plain,
( y = A
| ~ member(A,singleton(x)) ),
inference(copy,[status(thm)],[c_762]) ).
cnf(c_188,plain,
singleton(y) != null_class,
inference(resolve,[status(thm)],[c_41,c_35]) ).
cnf(c_189,plain,
( singleton(A) = null_class
| member(A,singleton(A)) ),
inference(resolve,[status(thm)],[c_42,c_38]) ).
cnf(c_758,plain,
singleton(x) != null_class,
inference(paramod,[status(thm)],[c_37,c_188]) ).
cnf(c_763,plain,
( y = x
| singleton(x) = null_class ),
inference(resolve,[status(thm)],[c_189,c_187]) ).
cnf(c_764,plain,
y = x,
inference(resolve,[status(thm)],[c_758,c_763]) ).
cnf(c_761,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.30 % Computer : n012.cluster.edu
% 0.06/0.30 % Model : x86_64 x86_64
% 0.06/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.30 % Memory : 8046.5625MB
% 0.06/0.30 % OS : Linux 6.8.0-71-generic
% 0.06/0.30 % CPULimit : 300
% 0.06/0.30 % WCLimit : 300
% 0.06/0.30 % DateTime : Sat Sep 26 07:04:04 UTC 2026
% 0.06/0.30 % CPUTime :
% 0.06/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.30 % Process 4153362 was started by sandbox2 on n012,
% 0.06/0.30 % Sat Sep 26 07:04:04 2026
% 0.06/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.31
% 0.06/0.31 % From the command line: assign(max_seconds, 300).
% 0.23/0.35
% 0.23/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.35
% 0.23/0.35 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.23/0.35 % Length of proof is 14.
% 0.23/0.35 % Level of proof is 3.
% 0.23/0.35 % Maximum clause weight is 18.000.
% 0.23/0.35 % Given clauses 138.
% 0.23/0.35
% 0.23/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------