%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET553-6 : 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 : n019.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 08:36:28 AM UTC 2026
% Result : Unsatisfiable 11.51s 1.99s
% Output : CNFRefutation 11.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 32 ( 9 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 : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_cantor_class_alternate_defn_1,axiom,
~ subclass(cantor(x),domain_of(x)),
file('theBenchmark.p',prove_cantor_class_alternate_defn_1) ).
cnf(c_36,plain,
~ subclass(cantor(x),domain_of(x)),
inference(clausify,[status(thm)],[prove_cantor_class_alternate_defn_1]) ).
fof(cantor_class,axiom,
! [VAR_0] : intersection(domain_of(VAR_0),diagonalise(compose(inverse(element_relation),VAR_0))) = cantor(VAR_0),
file('theBenchmark.p',cantor_class) ).
cnf(c_63,plain,
intersection(domain_of(A),diagonalise(compose(inverse(element_relation),A))) = cantor(A),
inference(clausify,[status(thm)],[cantor_class]) ).
cnf(c_64,plain,
cantor(A) = intersection(domain_of(A),diagonalise(compose(inverse(element_relation),A))),
inference(copy,[status(thm)],[c_63]) ).
fof(diagonalisation,axiom,
! [VAR_0] : complement(domain_of(intersection(VAR_0,identity_relation))) = diagonalise(VAR_0),
file('theBenchmark.p',diagonalisation) ).
cnf(c_65,plain,
complement(domain_of(intersection(A,identity_relation))) = diagonalise(A),
inference(clausify,[status(thm)],[diagonalisation]) ).
cnf(c_66,plain,
diagonalise(A) = complement(domain_of(intersection(A,identity_relation))),
inference(copy,[status(thm)],[c_65]) ).
fof(inverse,axiom,
! [VAR_0] : domain_of(flip(cross_product(VAR_0,universal_class))) = inverse(VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_100,plain,
domain_of(flip(cross_product(A,universal_class))) = inverse(A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_101,plain,
inverse(A) = domain_of(flip(cross_product(A,universal_class))),
inference(copy,[status(thm)],[c_100]) ).
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_122,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_142,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_143,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_181,plain,
~ subclass(intersection(domain_of(x),diagonalise(compose(inverse(element_relation),x))),domain_of(x)),
inference(paramod,[status(thm)],[c_64,c_36]) ).
cnf(c_336,plain,
( member(not_subclass_element(intersection(A,B),C),A)
| subclass(intersection(A,B),C) ),
inference(resolve,[status(thm)],[c_143,c_122]) ).
cnf(c_422,plain,
~ subclass(intersection(domain_of(x),complement(domain_of(intersection(compose(inverse(element_relation),x),identity_relation)))),domain_of(x)),
inference(paramod,[status(thm)],[c_66,c_181]) ).
cnf(c_425,plain,
~ subclass(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),
inference(paramod,[status(thm)],[c_101,c_422]) ).
cnf(c_7377,plain,
( subclass(intersection(A,B),A)
| subclass(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_336,c_142]) ).
cnf(c_7375,plain,
subclass(intersection(A,B),A),
inference(copy,[status(thm)],[c_7377]) ).
cnf(c_7376,plain,
$false,
inference(resolve,[status(thm)],[c_7375,c_425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET553-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n019.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Sat Sep 26 07:54:37 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 778083 was started by sandbox on n019,
% 0.19/0.44 % Sat Sep 26 07:54:37 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 11.51/1.99
% 11.51/1.99 % given #500 (A,wt=38): 310 subclass(domain(A,B,C),first(not_subclass_element(restrict(A,B,singleton(C)),null_class))). [resolve(139,a,97,a(flip))].
% 11.51/1.99
% 11.51/1.99 % SZS status Unsatisfiable for theBenchmark
% 11.51/1.99
% 11.51/1.99 % Proof 1 at 1.23 (+ 0.28) seconds.
% 11.51/1.99 % Length of proof is 16.
% 11.51/1.99 % Level of proof is 5.
% 11.51/1.99 % Maximum clause weight is 62.000.
% 11.51/1.99 % Given clauses 556.
% 11.51/1.99
% 11.51/1.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------