%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM066-1 : 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 : n018.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 08:16:06 AM UTC 2026
% Result : Unsatisfiable 11.92s 2.17s
% Output : CNFRefutation 11.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 23 unt; 0 def)
% Number of atoms : 112 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 129 ( 69 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 4 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_well_ordering_property1_4,axiom,
member(v,least(element_relation,u)),
file('theBenchmark.p',prove_corollary_to_well_ordering_property1_4) ).
cnf(c_53,plain,
member(v,least(element_relation,u)),
inference(clausify,[status(thm)],[prove_corollary_to_well_ordering_property1_4]) ).
fof(prove_corollary_to_well_ordering_property1_3,axiom,
member(v,u),
file('theBenchmark.p',prove_corollary_to_well_ordering_property1_3) ).
cnf(c_54,plain,
member(v,u),
inference(clausify,[status(thm)],[prove_corollary_to_well_ordering_property1_3]) ).
fof(prove_corollary_to_well_ordering_property1_2,axiom,
subclass(u,y),
file('theBenchmark.p',prove_corollary_to_well_ordering_property1_2) ).
cnf(c_55,plain,
subclass(u,y),
inference(clausify,[status(thm)],[prove_corollary_to_well_ordering_property1_2]) ).
fof(prove_corollary_to_well_ordering_property1_1,axiom,
well_ordering(element_relation,y),
file('theBenchmark.p',prove_corollary_to_well_ordering_property1_1) ).
cnf(c_56,plain,
well_ordering(element_relation,y),
inference(clausify,[status(thm)],[prove_corollary_to_well_ordering_property1_1]) ).
fof(well_ordering5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ member(ordered_pair(VAR_3,least(VAR_0,VAR_2)),VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ subclass(VAR_2,VAR_1)
| ~ well_ordering(VAR_0,VAR_1) ),
file('theBenchmark.p',well_ordering5) ).
cnf(c_87,plain,
( ~ member(ordered_pair(D,least(A,C)),A)
| ~ member(D,C)
| ~ subclass(C,B)
| ~ well_ordering(A,B) ),
inference(clausify,[status(thm)],[well_ordering5]) ).
fof(well_ordering3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(least(VAR_0,VAR_2),VAR_2)
| ~ member(VAR_3,VAR_2)
| ~ subclass(VAR_2,VAR_1)
| ~ well_ordering(VAR_0,VAR_1) ),
file('theBenchmark.p',well_ordering3) ).
cnf(c_89,plain,
( member(least(A,C),C)
| ~ member(D,C)
| ~ subclass(C,B)
| ~ well_ordering(A,B) ),
inference(clausify,[status(thm)],[well_ordering3]) ).
fof(element_relation3,axiom,
! [VAR_0,VAR_1] :
( member(ordered_pair(VAR_0,VAR_1),element_relation)
| ~ member(VAR_0,VAR_1)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(universal_class,universal_class)) ),
file('theBenchmark.p',element_relation3) ).
cnf(c_186,plain,
( member(ordered_pair(A,B),element_relation)
| ~ member(A,B)
| ~ member(ordered_pair(A,B),cross_product(universal_class,universal_class)) ),
inference(clausify,[status(thm)],[element_relation3]) ).
fof(cartesian_product3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(ordered_pair(VAR_0,VAR_2),cross_product(VAR_1,VAR_3))
| ~ member(VAR_2,VAR_3)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',cartesian_product3) ).
cnf(c_190,plain,
( member(ordered_pair(A,C),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[cartesian_product3]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_193,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_194,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_193]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_195,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_196,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_195]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_204,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_207,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_7742,plain,
( member(unordered_pair(singleton(A),unordered_pair(A,singleton(C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_194,c_190]) ).
cnf(c_7743,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_196,c_7742]) ).
cnf(c_274,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(C,C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_196,c_7743]) ).
cnf(c_7744,plain,
( member(ordered_pair(A,B),element_relation)
| ~ member(A,B)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_194,c_186]) ).
cnf(c_7745,plain,
( member(ordered_pair(A,B),element_relation)
| ~ member(A,B)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_196,c_7744]) ).
cnf(c_7746,plain,
( member(ordered_pair(A,B),element_relation)
| ~ member(A,B)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_196,c_7745]) ).
cnf(c_7747,plain,
( member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),element_relation)
| ~ member(A,B)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_194,c_7746]) ).
cnf(c_7748,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))),element_relation)
| ~ member(A,B)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_196,c_7747]) ).
cnf(c_277,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),element_relation)
| ~ member(A,B)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_196,c_7748]) ).
cnf(c_7749,plain,
( ~ member(unordered_pair(singleton(D),unordered_pair(D,singleton(least(A,C)))),A)
| ~ member(D,C)
| ~ subclass(C,B)
| ~ well_ordering(A,B) ),
inference(paramod,[status(thm)],[c_194,c_87]) ).
cnf(c_7750,plain,
( ~ member(unordered_pair(unordered_pair(D,D),unordered_pair(D,singleton(least(A,C)))),A)
| ~ member(D,C)
| ~ subclass(C,B)
| ~ well_ordering(A,B) ),
inference(paramod,[status(thm)],[c_196,c_7749]) ).
cnf(c_289,plain,
( ~ member(unordered_pair(unordered_pair(D,D),unordered_pair(D,unordered_pair(least(A,C),least(A,C)))),A)
| ~ member(D,C)
| ~ subclass(C,B)
| ~ well_ordering(A,B) ),
inference(paramod,[status(thm)],[c_196,c_7750]) ).
cnf(c_297,plain,
( member(least(element_relation,A),A)
| ~ member(B,A)
| ~ subclass(A,y) ),
inference(resolve,[status(thm)],[c_89,c_56]) ).
cnf(c_417,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_207,c_204]) ).
cnf(c_560,plain,
( member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(least(element_relation,u),least(element_relation,u)))),element_relation)
| ~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(least(element_relation,u),least(element_relation,u)))),cross_product(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_277,c_53]) ).
cnf(c_566,plain,
( ~ member(unordered_pair(unordered_pair(B,B),unordered_pair(B,unordered_pair(least(element_relation,A),least(element_relation,A)))),element_relation)
| ~ member(B,A)
| ~ subclass(A,y) ),
inference(resolve,[status(thm)],[c_289,c_56]) ).
cnf(c_7751,plain,
( member(least(element_relation,u),u)
| ~ subclass(u,y) ),
inference(resolve,[status(thm)],[c_297,c_54]) ).
cnf(c_603,plain,
member(least(element_relation,u),u),
inference(resolve,[status(thm)],[c_55,c_7751]) ).
cnf(c_639,plain,
member(v,universal_class),
inference(resolve,[status(thm)],[c_417,c_54]) ).
cnf(c_646,plain,
( member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(A,A))),cross_product(universal_class,B))
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_639,c_274]) ).
cnf(c_816,plain,
member(least(element_relation,u),universal_class),
inference(resolve,[status(thm)],[c_603,c_417]) ).
cnf(c_7752,plain,
( ~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(least(element_relation,u),least(element_relation,u)))),element_relation)
| ~ subclass(u,y) ),
inference(resolve,[status(thm)],[c_566,c_54]) ).
cnf(c_5209,plain,
~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(least(element_relation,u),least(element_relation,u)))),element_relation),
inference(resolve,[status(thm)],[c_55,c_7752]) ).
cnf(c_5211,plain,
~ member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(least(element_relation,u),least(element_relation,u)))),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_5209,c_560]) ).
cnf(c_7753,plain,
member(unordered_pair(unordered_pair(v,v),unordered_pair(v,unordered_pair(least(element_relation,u),least(element_relation,u)))),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_646,c_816]) ).
cnf(c_7741,plain,
$false,
inference(resolve,[status(thm)],[c_5211,c_7753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM066-1 : 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 : n018.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 02:00:51 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 3449182 was started by sandbox on n018,
% 0.10/0.37 % Sat Sep 26 02:00:51 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).
% 11.92/2.17
% 11.92/2.17 % given #500 (T,wt=18): 2080 -subclass(intersection(y,universal_class),A) | member(v,A). [resolve(2055,a,207,b)].
% 11.92/2.17
% 11.92/2.17 % SZS status Unsatisfiable for theBenchmark
% 11.92/2.17
% 11.92/2.17 % Proof 1 at 1.45 (+ 0.29) seconds.
% 11.92/2.17 % Length of proof is 28.
% 11.92/2.17 % Level of proof is 6.
% 11.92/2.17 % Maximum clause weight is 87.000.
% 11.92/2.17 % Given clauses 884.
% 11.92/2.17
% 11.92/2.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------