%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET063-7 : 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 : n016.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 08:35:34 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 26 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_of_null_class_is_subclass_2,axiom,
x != null_class,
file('theBenchmark.p',prove_corollary_of_null_class_is_subclass_2) ).
cnf(c_33,plain,
x != null_class,
inference(clausify,[status(thm)],[prove_corollary_of_null_class_is_subclass_2]) ).
fof(prove_corollary_of_null_class_is_subclass_1,axiom,
subclass(x,null_class),
file('theBenchmark.p',prove_corollary_of_null_class_is_subclass_1) ).
cnf(c_34,plain,
subclass(x,null_class),
inference(clausify,[status(thm)],[prove_corollary_of_null_class_is_subclass_1]) ).
fof(null_class_is_subclass,axiom,
! [VAR_0] : subclass(null_class,VAR_0),
file('theBenchmark.p',null_class_is_subclass) ).
cnf(c_35,plain,
subclass(null_class,A),
inference(clausify,[status(thm)],[null_class_is_subclass]) ).
fof(transitivity_of_subclass,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subclass(VAR_0,VAR_2)
| ~ subclass(VAR_1,VAR_2)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_subclass) ).
cnf(c_42,plain,
( subclass(A,C)
| ~ subclass(B,C)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_subclass]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_127,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
cnf(c_469,plain,
( subclass(x,A)
| ~ subclass(null_class,A) ),
inference(resolve,[status(thm)],[c_42,c_34]) ).
cnf(c_160,plain,
subclass(x,A),
inference(resolve,[status(thm)],[c_35,c_469]) ).
cnf(c_312,plain,
( null_class = A
| ~ subclass(A,null_class) ),
inference(resolve,[status(thm)],[c_127,c_35]) ).
cnf(c_470,plain,
null_class = x,
inference(resolve,[status(thm)],[c_312,c_160]) ).
cnf(c_471,plain,
x = null_class,
inference(copy,[status(thm)],[c_470]) ).
cnf(c_468,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:06:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 247921 was started by sandbox on n016,
% 0.10/0.37 % Sat Sep 26 07:06:17 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.42
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.42
% 0.10/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.42 % Length of proof is 8.
% 0.10/0.42 % Level of proof is 2.
% 0.10/0.42 % Maximum clause weight is 14.000.
% 0.10/0.42 % Given clauses 116.
% 0.10/0.42
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------