%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET187-6 : 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 : n006.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 08:36:00 AM UTC 2026
% Result : Unsatisfiable 19.62s 3.29s
% Output : CNFRefutation 19.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 37 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subclass_property5_2,axiom,
intersection(complement(y),x) != null_class,
file('theBenchmark.p',prove_subclass_property5_2) ).
cnf(c_36,plain,
intersection(complement(y),x) != null_class,
inference(clausify,[status(thm)],[prove_subclass_property5_2]) ).
fof(prove_subclass_property5_1,axiom,
subclass(x,y),
file('theBenchmark.p',prove_subclass_property5_1) ).
cnf(c_37,plain,
subclass(x,y),
inference(clausify,[status(thm)],[prove_subclass_property5_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_76,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_77,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_76]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_120,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_122,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_123,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_11984,plain,
null_class != intersection(complement(y),x),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_184,plain,
member(regular(intersection(complement(y),x)),intersection(complement(y),x)),
inference(resolve,[status(thm)],[c_77,c_11984]) ).
cnf(c_367,plain,
( member(A,y)
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_145,c_37]) ).
cnf(c_461,plain,
member(regular(intersection(complement(y),x)),complement(y)),
inference(resolve,[status(thm)],[c_184,c_123]) ).
cnf(c_462,plain,
member(regular(intersection(complement(y),x)),x),
inference(resolve,[status(thm)],[c_184,c_122]) ).
cnf(c_11982,plain,
~ member(regular(intersection(complement(y),x)),y),
inference(resolve,[status(thm)],[c_461,c_120]) ).
cnf(c_11985,plain,
member(regular(intersection(complement(y),x)),y),
inference(resolve,[status(thm)],[c_462,c_367]) ).
cnf(c_11983,plain,
$false,
inference(resolve,[status(thm)],[c_11982,c_11985]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET187-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n006.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 07:17:55 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 665943 was started by sandbox2 on n006,
% 0.17/0.43 % Sat Sep 26 07:17:55 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 19.62/3.29
% 19.62/3.29 % given #500 (A,wt=38): 314 subclass(range(A,B,C),second(not_subclass_element(restrict(A,singleton(B),C),null_class))). [resolve(140,a,96,a(flip))].
% 19.62/3.29
% 19.62/3.29 % SZS status Unsatisfiable for theBenchmark
% 19.62/3.29
% 19.62/3.29 % Proof 1 at 2.25 (+ 0.51) seconds.
% 19.62/3.29 % Length of proof is 14.
% 19.62/3.29 % Level of proof is 5.
% 19.62/3.29 % Maximum clause weight is 30.000.
% 19.62/3.29 % Given clauses 764.
% 19.62/3.29
% 19.62/3.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------