%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET020-7 : 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 : 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 08:35:21 AM UTC 2026
% Result : Unsatisfiable 113.89s 15.92s
% Output : CNFRefutation 113.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 41 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 8 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_unique_1st_and_2nd_in_pair_of_sets1_2,axiom,
first(ordered_pair(u,v)) != u,
file('theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
cnf(c_33,plain,
first(ordered_pair(u,v)) != u,
inference(clausify,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets1_2]) ).
fof(prove_unique_1st_and_2nd_in_pair_of_sets1_1,axiom,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
cnf(c_34,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets1_1]) ).
fof(existence_of_1st_and_2nd_1,axiom,
! [VAR_0,VAR_1] :
( member(ordered_pair(first(ordered_pair(VAR_0,VAR_1)),second(ordered_pair(VAR_0,VAR_1))),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(universal_class,universal_class)) ),
file('theBenchmark.p',existence_of_1st_and_2nd_1) ).
cnf(c_39,plain,
( member(ordered_pair(first(ordered_pair(A,B)),second(ordered_pair(A,B))),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(A,B),cross_product(universal_class,universal_class)) ),
inference(clausify,[status(thm)],[existence_of_1st_and_2nd_1]) ).
fof(ordered_pair_determines_components1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_2
| ~ member(VAR_0,universal_class)
| ordered_pair(VAR_0,VAR_1) != ordered_pair(VAR_2,VAR_3) ),
file('theBenchmark.p',ordered_pair_determines_components1) ).
cnf(c_41,plain,
( A = C
| ~ member(A,universal_class)
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(clausify,[status(thm)],[ordered_pair_determines_components1]) ).
fof(singleton_is_null_class,axiom,
! [VAR_0] :
( singleton(VAR_0) = null_class
| member(VAR_0,universal_class) ),
file('theBenchmark.p',singleton_is_null_class) ).
cnf(c_74,plain,
( singleton(A) = null_class
| member(A,universal_class) ),
inference(clausify,[status(thm)],[singleton_is_null_class]) ).
fof(corollary_to_set_in_its_singleton,axiom,
! [VAR_0] :
( singleton(VAR_0) != null_class
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',corollary_to_set_in_its_singleton) ).
cnf(c_77,plain,
( singleton(A) != null_class
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[corollary_to_set_in_its_singleton]) ).
fof(cartesian_product4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(first(VAR_0),second(VAR_0)) = VAR_0
| ~ member(VAR_0,cross_product(VAR_1,VAR_2)) ),
file('theBenchmark.p',cartesian_product4) ).
cnf(c_174,plain,
( ordered_pair(first(A),second(A)) = A
| ~ member(A,cross_product(B,C)) ),
inference(clausify,[status(thm)],[cartesian_product4]) ).
fof(cartesian_product1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product1) ).
cnf(c_177,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
cnf(c_219,plain,
member(ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_39,c_34]) ).
cnf(c_309,plain,
( A = C
| ordered_pair(A,B) != ordered_pair(C,D)
| singleton(A) = null_class ),
inference(resolve,[status(thm)],[c_74,c_41]) ).
cnf(c_784,plain,
ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v),
inference(resolve,[status(thm)],[c_174,c_34]) ).
cnf(c_1176,plain,
member(first(ordered_pair(u,v)),universal_class),
inference(resolve,[status(thm)],[c_219,c_177]) ).
cnf(c_4206,plain,
singleton(first(ordered_pair(u,v))) != null_class,
inference(resolve,[status(thm)],[c_1176,c_77]) ).
cnf(c_21756,plain,
( first(ordered_pair(u,v)) = u
| singleton(first(ordered_pair(u,v))) = null_class ),
inference(resolve,[status(thm)],[c_784,c_309]) ).
cnf(c_21757,plain,
first(ordered_pair(u,v)) = u,
inference(resolve,[status(thm)],[c_4206,c_21756]) ).
cnf(c_21755,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_21757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET020-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n015.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 06:56:43 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 3373370 was started by sandbox on n015,
% 0.15/0.42 % Sat Sep 26 06:56:43 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 113.89/15.92
% 113.89/15.92 % given #500 (T,wt=12): 752 -member(null_class,A) | member(null_class,intersection(A,universal_class)). [resolve(168,b,93,a)].
% 113.89/15.92
% 113.89/15.92 % given #1000 (F,wt=16): 5930 unordered_pair(A,not_subclass_element(singleton(null_class),null_class)) != null_class. [resolve(5147,a,83,a)].
% 113.89/15.92
% 113.89/15.92 % given #1500 (A,wt=16): 470 universal_class = null_class | unordered_pair(not_subclass_element(universal_class,null_class),A) != null_class. [resolve(95,b,84,a),flip(a)].
% 113.89/15.92
% 113.89/15.92 % given #2000 (T,wt=12): 13728 -member(omega,u) | member(ordered_pair(omega,u),element_relation). [resolve(13693,a,171,a)].
% 113.89/15.92
% 113.89/15.92 % given #2500 (F,wt=18): 17759 unordered_pair(power_class(sum_class(power_class(null_class))),A) != null_class. [resolve(2482,a,84,a)].
% 113.89/15.92
% 113.89/15.92 % SZS status Unsatisfiable for theBenchmark
% 113.89/15.92
% 113.89/15.92 % Proof 1 at 5.23 (+ 2.10) seconds.
% 113.89/15.92 % Length of proof is 14.
% 113.89/15.92 % Level of proof is 4.
% 113.89/15.92 % Maximum clause weight is 28.000.
% 113.89/15.92 % Given clauses 2869.
% 113.89/15.92
% 113.89/15.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------