%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM042-1 : 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 08:16:05 AM UTC 2026
% Result : Unsatisfiable 159.26s 21.94s
% Output : CNFRefutation 159.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 54 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 3 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_43,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
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_44,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
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_45,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
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_71,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : complement(intersection(complement(VAR_0),complement(VAR_1))) = union(VAR_0,VAR_1),
file('theBenchmark.p',union) ).
cnf(c_76,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_77,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_76]) ).
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_80,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_81,plain,
restrict(A,B,C) = intersection(A,cross_product(B,C)),
inference(copy,[status(thm)],[c_80]) ).
fof(inverse,axiom,
! [VAR_0] : domain_of(flip(cross_product(VAR_0,universal_class))) = inverse(VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_98,plain,
domain_of(flip(cross_product(A,universal_class))) = inverse(A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_99,plain,
inverse(A) = domain_of(flip(cross_product(A,universal_class))),
inference(copy,[status(thm)],[c_98]) ).
fof(symmetrization,axiom,
! [VAR_0] : union(VAR_0,inverse(VAR_0)) = symmetrization_of(VAR_0),
file('theBenchmark.p',symmetrization) ).
cnf(c_189,plain,
union(A,inverse(A)) = symmetrization_of(A),
inference(clausify,[status(thm)],[symmetrization]) ).
cnf(c_19349,plain,
union(A,domain_of(flip(cross_product(A,universal_class)))) = symmetrization_of(A),
inference(paramod,[status(thm)],[c_99,c_189]) ).
cnf(c_19350,plain,
complement(intersection(complement(A),complement(domain_of(flip(cross_product(A,universal_class)))))) = symmetrization_of(A),
inference(paramod,[status(thm)],[c_77,c_19349]) ).
cnf(c_190,plain,
symmetrization_of(A) = complement(intersection(complement(A),complement(domain_of(flip(cross_product(A,universal_class)))))),
inference(copy,[status(thm)],[c_19350]) ).
fof(irreflexive2,axiom,
! [VAR_0,VAR_1] :
( irreflexive(VAR_0,VAR_1)
| ~ subclass(restrict(VAR_0,VAR_1,VAR_1),complement(identity_relation)) ),
file('theBenchmark.p',irreflexive2) ).
cnf(c_193,plain,
( irreflexive(A,B)
| ~ subclass(restrict(A,B,B),complement(identity_relation)) ),
inference(clausify,[status(thm)],[irreflexive2]) ).
cnf(c_194,plain,
( irreflexive(A,B)
| ~ subclass(intersection(A,cross_product(B,B)),complement(identity_relation)) ),
inference(paramod,[status(thm)],[c_81,c_193]) ).
fof(prove_irreflexive_class_property4_1,axiom,
subclass(x,complement(identity_relation)),
file('theBenchmark.p',prove_irreflexive_class_property4_1) ).
cnf(c_243,plain,
subclass(x,complement(identity_relation)),
inference(clausify,[status(thm)],[prove_irreflexive_class_property4_1]) ).
fof(prove_irreflexive_class_property4_2,axiom,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('theBenchmark.p',prove_irreflexive_class_property4_2) ).
cnf(c_244,plain,
~ irreflexive(x,domain_of(symmetrization_of(x))),
inference(clausify,[status(thm)],[prove_irreflexive_class_property4_2]) ).
cnf(c_245,plain,
~ irreflexive(x,domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),
inference(paramod,[status(thm)],[c_190,c_244]) ).
cnf(c_291,plain,
( subclass(intersection(A,B),C)
| member(not_subclass_element(intersection(A,B),C),A) ),
inference(resolve,[status(thm)],[c_71,c_44]) ).
cnf(c_430,plain,
( member(A,complement(identity_relation))
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_243,c_43]) ).
cnf(c_1100,plain,
( member(not_subclass_element(intersection(x,A),B),complement(identity_relation))
| subclass(intersection(x,A),B) ),
inference(resolve,[status(thm)],[c_291,c_430]) ).
cnf(c_19351,plain,
( subclass(intersection(x,A),complement(identity_relation))
| subclass(intersection(x,A),complement(identity_relation)) ),
inference(resolve,[status(thm)],[c_1100,c_45]) ).
cnf(c_19343,plain,
subclass(intersection(x,A),complement(identity_relation)),
inference(copy,[status(thm)],[c_19351]) ).
cnf(c_19347,plain,
irreflexive(x,A),
inference(resolve,[status(thm)],[c_19343,c_194]) ).
cnf(c_19348,plain,
$false,
inference(resolve,[status(thm)],[c_19347,c_245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 01:55:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 939696 was started by sandbox on n005,
% 0.10/0.37 % Sat Sep 26 01:55:46 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 159.26/21.94
% 159.26/21.94 % given #500 (W,wt=20): 3396 member(regular(element_relation),cross_product(universal_class,universal_class)) | element_relation = complement(universal_class). [back_rewrite(1010),rewrite([2656(8)])].
% 159.26/21.94
% 159.26/21.94 % SZS status Unsatisfiable for theBenchmark
% 159.26/21.94
% 159.26/21.94 % Proof 1 at 4.55 (+ 0.74) seconds.
% 159.26/21.94 % Length of proof is 23.
% 159.26/21.94 % Level of proof is 5.
% 159.26/21.94 % Maximum clause weight is 53.000.
% 159.26/21.94 % Given clauses 892.
% 159.26/21.94
% 159.26/21.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------