%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET027-6 : 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 : n001.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 08:35:25 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.57s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_transitivity_of_subclass_3,axiom,
~ subclass(x,z),
file('theBenchmark.p',prove_transitivity_of_subclass_3) ).
cnf(c_34,plain,
~ subclass(x,z),
inference(clausify,[status(thm)],[prove_transitivity_of_subclass_3]) ).
fof(prove_transitivity_of_subclass_2,axiom,
subclass(y,z),
file('theBenchmark.p',prove_transitivity_of_subclass_2) ).
cnf(c_35,plain,
subclass(y,z),
inference(clausify,[status(thm)],[prove_transitivity_of_subclass_2]) ).
fof(prove_transitivity_of_subclass_1,axiom,
subclass(x,y),
file('theBenchmark.p',prove_transitivity_of_subclass_1) ).
cnf(c_36,plain,
subclass(x,y),
inference(clausify,[status(thm)],[prove_transitivity_of_subclass_1]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_120,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_121,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_122,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_279,plain,
~ member(not_subclass_element(x,z),z),
inference(resolve,[status(thm)],[c_120,c_34]) ).
cnf(c_300,plain,
member(not_subclass_element(x,z),x),
inference(resolve,[status(thm)],[c_121,c_34]) ).
cnf(c_310,plain,
( member(A,y)
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_122,c_36]) ).
cnf(c_311,plain,
( member(A,z)
| ~ member(A,y) ),
inference(resolve,[status(thm)],[c_122,c_35]) ).
cnf(c_575,plain,
member(not_subclass_element(x,z),y),
inference(resolve,[status(thm)],[c_300,c_310]) ).
cnf(c_602,plain,
~ member(not_subclass_element(x,z),y),
inference(resolve,[status(thm)],[c_311,c_279]) ).
cnf(c_601,plain,
$false,
inference(resolve,[status(thm)],[c_575,c_602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.51 % Computer : n001.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.51 % CPULimit : 300
% 0.08/0.51 % WCLimit : 300
% 0.08/0.51 % DateTime : Sat Sep 26 07:00:27 UTC 2026
% 0.08/0.52 % CPUTime :
% 0.08/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.52 % Process 1177324 was started by sandbox on n001,
% 0.08/0.52 % Sat Sep 26 07:00:27 2026
% 0.08/0.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.52
% 0.08/0.52 % From the command line: assign(max_seconds, 300).
% 0.08/0.57
% 0.08/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.57
% 0.08/0.57 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.08/0.57 % Length of proof is 12.
% 0.08/0.57 % Level of proof is 3.
% 0.08/0.57 % Maximum clause weight is 18.000.
% 0.08/0.57 % Given clauses 137.
% 0.08/0.57
% 0.08/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------