%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET093-7 : 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 : n014.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 08:35:44 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 2 ( 1 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_singletons_are_sets_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_corollary_2_to_singletons_are_sets_2) ).
cnf(c_33,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_2_to_singletons_are_sets_2]) ).
fof(prove_corollary_2_to_singletons_are_sets_1,axiom,
singleton(member_of(x)) = x,
file('theBenchmark.p',prove_corollary_2_to_singletons_are_sets_1) ).
cnf(c_34,plain,
singleton(member_of(x)) = x,
inference(clausify,[status(thm)],[prove_corollary_2_to_singletons_are_sets_1]) ).
fof(singletons_are_sets,axiom,
! [VAR_0] : member(singleton(VAR_0),universal_class),
file('theBenchmark.p',singletons_are_sets) ).
cnf(c_52,plain,
member(singleton(A),universal_class),
inference(clausify,[status(thm)],[singletons_are_sets]) ).
cnf(c_236,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_34,c_52]) ).
cnf(c_235,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET093-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 07:05:31 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2462538 was started by sandbox on n014,
% 0.09/0.38 % Sat Sep 26 07:05:31 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.42
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.42
% 0.09/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.42 % Length of proof is 4.
% 0.09/0.42 % Level of proof is 1.
% 0.09/0.42 % Maximum clause weight is 20.000.
% 0.09/0.42 % Given clauses 24.
% 0.09/0.42
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------