%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET057-6 : 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 : n005.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 08:35:31 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 28 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_equality2_3,axiom,
~ member(not_subclass_element(y,x),y),
file('theBenchmark.p',prove_equality2_3) ).
cnf(c_34,plain,
~ member(not_subclass_element(y,x),y),
inference(clausify,[status(thm)],[prove_equality2_3]) ).
fof(prove_equality2_2,axiom,
x != y,
file('theBenchmark.p',prove_equality2_2) ).
cnf(c_35,plain,
x != y,
inference(clausify,[status(thm)],[prove_equality2_2]) ).
fof(prove_equality2_1,axiom,
member(not_subclass_element(x,y),y),
file('theBenchmark.p',prove_equality2_1) ).
cnf(c_36,plain,
member(not_subclass_element(x,y),y),
inference(clausify,[status(thm)],[prove_equality2_1]) ).
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_116,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
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]) ).
cnf(c_253,plain,
subclass(x,y),
inference(resolve,[status(thm)],[c_120,c_36]) ).
cnf(c_389,plain,
( y = x
| ~ subclass(y,x) ),
inference(resolve,[status(thm)],[c_253,c_116]) ).
cnf(c_390,plain,
( x = y
| ~ subclass(y,x) ),
inference(copy,[status(thm)],[c_389]) ).
cnf(c_364,plain,
~ subclass(y,x),
inference(resolve,[status(thm)],[c_35,c_390]) ).
cnf(c_391,plain,
member(not_subclass_element(y,x),y),
inference(resolve,[status(thm)],[c_364,c_121]) ).
cnf(c_388,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET057-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:00:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1498058 was started by sandbox on n005,
% 0.11/0.37 % Sat Sep 26 07:00:18 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.43
% 0.11/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.43
% 0.11/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.11/0.43 % Length of proof is 9.
% 0.11/0.43 % Level of proof is 3.
% 0.11/0.43 % Maximum clause weight is 9.000.
% 0.11/0.43 % Given clauses 110.
% 0.11/0.43
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------