%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET451-6 : 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 : n010.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 08:36:20 AM UTC 2026
% Result : Unsatisfiable 8.10s 1.57s
% Output : CNFRefutation 8.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 21 unt; 0 def)
% Number of atoms : 37 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_relation_alternate_defn1_1,axiom,
~ subclass(subset_relation,cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_subset_relation_alternate_defn1_1) ).
cnf(c_36,plain,
~ subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_subset_relation_alternate_defn1_1]) ).
fof(subset_relation,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('theBenchmark.p',subset_relation) ).
cnf(c_68,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(clausify,[status(thm)],[subset_relation]) ).
cnf(c_69,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),
inference(copy,[status(thm)],[c_68]) ).
fof(inverse,axiom,
! [VAR_0] : domain_of(flip(cross_product(VAR_0,universal_class))) = inverse(VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_101,plain,
domain_of(flip(cross_product(A,universal_class))) = inverse(A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_102,plain,
inverse(A) = domain_of(flip(cross_product(A,universal_class))),
inference(copy,[status(thm)],[c_101]) ).
fof(restriction2,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(cross_product(VAR_0,VAR_1),VAR_2) = restrict(VAR_2,VAR_0,VAR_1),
file('theBenchmark.p',restriction2) ).
cnf(c_111,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_112,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_111]) ).
fof(restriction1,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(VAR_0,cross_product(VAR_1,VAR_2)) = restrict(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',restriction1) ).
cnf(c_113,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_114,plain,
restrict(A,B,C) = intersection(A,cross_product(B,C)),
inference(copy,[status(thm)],[c_113]) ).
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(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]) ).
cnf(c_183,plain,
~ subclass(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_69,c_36]) ).
cnf(c_7410,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_114,c_112]) ).
cnf(c_220,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_7410]) ).
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_427,plain,
~ subclass(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_102,c_183]) ).
cnf(c_1392,plain,
~ subclass(intersection(cross_product(universal_class,universal_class),intersection(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),cross_product(universal_class,universal_class))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_220,c_427]) ).
cnf(c_7411,plain,
( subclass(intersection(A,B),A)
| subclass(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_337,c_143]) ).
cnf(c_7408,plain,
subclass(intersection(A,B),A),
inference(copy,[status(thm)],[c_7411]) ).
cnf(c_7409,plain,
$false,
inference(resolve,[status(thm)],[c_7408,c_1392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET451-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:45:16 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2836136 was started by sandbox2 on n010,
% 0.08/0.36 % Sat Sep 26 07:45:16 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 8.10/1.57
% 8.10/1.57 % given #500 (T,wt=19): 5123 member(regular(omega),intersection(omega,universal_class)) | omega = null_class. [resolve(5096,a,228,a),flip(b)].
% 8.10/1.57
% 8.10/1.57 % SZS status Unsatisfiable for theBenchmark
% 8.10/1.57
% 8.10/1.57 % Proof 1 at 0.97 (+ 0.22) seconds.
% 8.10/1.57 % Length of proof is 19.
% 8.10/1.57 % Level of proof is 5.
% 8.10/1.57 % Maximum clause weight is 61.000.
% 8.10/1.57 % Given clauses 560.
% 8.10/1.57
% 8.10/1.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------