%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET183-6 : 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 : n015.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 08:35:59 AM UTC 2026
% Result : Unsatisfiable 26.49s 3.79s
% Output : CNFRefutation 26.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 60 ( 7 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subclass_property1_2,axiom,
intersection(x,y) != x,
file('theBenchmark.p',prove_subclass_property1_2) ).
cnf(c_36,plain,
intersection(x,y) != x,
inference(clausify,[status(thm)],[prove_subclass_property1_2]) ).
fof(prove_subclass_property1_1,axiom,
subclass(x,y),
file('theBenchmark.p',prove_subclass_property1_1) ).
cnf(c_37,plain,
subclass(x,y),
inference(clausify,[status(thm)],[prove_subclass_property1_1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_121,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
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_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_139,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_143,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_144,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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_337,plain,
( member(not_subclass_element(intersection(A,B),C),A)
| subclass(intersection(A,B),C) ),
inference(resolve,[status(thm)],[c_144,c_123]) ).
cnf(c_340,plain,
( member(not_subclass_element(A,B),intersection(A,C))
| ~ member(not_subclass_element(A,B),C)
| subclass(A,B) ),
inference(resolve,[status(thm)],[c_144,c_121]) ).
cnf(c_365,plain,
( member(A,y)
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_145,c_37]) ).
cnf(c_449,plain,
( subclass(x,A)
| member(not_subclass_element(x,A),y) ),
inference(resolve,[status(thm)],[c_365,c_144]) ).
cnf(c_22015,plain,
( subclass(intersection(A,B),A)
| subclass(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_337,c_143]) ).
cnf(c_7308,plain,
subclass(intersection(A,B),A),
inference(copy,[status(thm)],[c_22015]) ).
cnf(c_22016,plain,
( A = intersection(A,B)
| ~ subclass(A,intersection(A,B)) ),
inference(resolve,[status(thm)],[c_7308,c_139]) ).
cnf(c_7368,plain,
( intersection(A,B) = A
| ~ subclass(A,intersection(A,B)) ),
inference(copy,[status(thm)],[c_22016]) ).
cnf(c_22017,plain,
( subclass(x,A)
| member(not_subclass_element(x,A),intersection(x,y))
| subclass(x,A) ),
inference(resolve,[status(thm)],[c_340,c_449]) ).
cnf(c_7422,plain,
( member(not_subclass_element(x,A),intersection(x,y))
| subclass(x,A) ),
inference(copy,[status(thm)],[c_22017]) ).
cnf(c_22018,plain,
( subclass(x,intersection(x,y))
| subclass(x,intersection(x,y)) ),
inference(resolve,[status(thm)],[c_7422,c_143]) ).
cnf(c_22013,plain,
subclass(x,intersection(x,y)),
inference(copy,[status(thm)],[c_22018]) ).
cnf(c_22019,plain,
intersection(x,y) = x,
inference(resolve,[status(thm)],[c_22013,c_7368]) ).
cnf(c_22014,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_22019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET183-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:20:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3423452 was started by sandbox2 on n015,
% 0.09/0.36 % Sat Sep 26 07:20:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 26.49/3.79
% 26.49/3.79 % given #500 (A,wt=38): 312 subclass(range(A,B,C),second(not_subclass_element(restrict(A,singleton(B),C),null_class))). [resolve(140,a,96,a(flip))].
% 26.49/3.79
% 26.49/3.79 % given #1000 (T,wt=19): 11354 member(sum_class(omega),complement(A)) | member(regular(A),universal_class). [resolve(6068,a,355,a)].
% 26.49/3.79
% 26.49/3.79 % given #1500 (W,wt=19): 21808 member(regular(identity_relation),intersection(universal_class,subset_relation)) | subclass(identity_relation,null_class). [resolve(21558,a,7458,a)].
% 26.49/3.79
% 26.49/3.79 % SZS status Unsatisfiable for theBenchmark
% 26.49/3.79
% 26.49/3.79 % Proof 1 at 2.71 (+ 0.67) seconds.
% 26.49/3.79 % Length of proof is 17.
% 26.49/3.79 % Level of proof is 5.
% 26.49/3.79 % Maximum clause weight is 27.000.
% 26.49/3.79 % Given clauses 1509.
% 26.49/3.79
% 26.49/3.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------