%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET479-6 : 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 : n003.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 08:36:22 AM UTC 2026
% Result : Unsatisfiable 62.72s 9.43s
% Output : CNFRefutation 62.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_replacement_property1_2,axiom,
~ member(domain_of(x),universal_class),
file('theBenchmark.p',prove_replacement_property1_2) ).
cnf(c_36,plain,
~ member(domain_of(x),universal_class),
inference(clausify,[status(thm)],[prove_replacement_property1_2]) ).
fof(prove_replacement_property1_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_replacement_property1_1) ).
cnf(c_37,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_replacement_property1_1]) ).
fof(definition_of_domain_relation3,axiom,
! [VAR_0] :
( member(ordered_pair(VAR_0,domain_of(VAR_0)),domain_relation)
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',definition_of_domain_relation3) ).
cnf(c_51,plain,
( member(ordered_pair(A,domain_of(A)),domain_relation)
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[definition_of_domain_relation3]) ).
fof(definition_of_domain_relation1,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('theBenchmark.p',definition_of_domain_relation1) ).
cnf(c_53,plain,
subclass(domain_relation,cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[definition_of_domain_relation1]) ).
fof(cartesian_product2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,VAR_3)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product2) ).
cnf(c_129,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product2]) ).
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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_181,plain,
member(ordered_pair(x,domain_of(x)),domain_relation),
inference(resolve,[status(thm)],[c_51,c_37]) ).
cnf(c_343,plain,
( member(A,cross_product(universal_class,universal_class))
| ~ member(A,domain_relation) ),
inference(resolve,[status(thm)],[c_145,c_53]) ).
cnf(c_1357,plain,
member(ordered_pair(x,domain_of(x)),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_343,c_181]) ).
cnf(c_9741,plain,
member(domain_of(x),universal_class),
inference(resolve,[status(thm)],[c_1357,c_129]) ).
cnf(c_9740,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_9741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET479-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n003.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:49:24 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2360206 was started by sandbox on n003,
% 0.19/0.45 % Sat Sep 26 07:49:24 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 62.72/9.43
% 62.72/9.43 % given #500 (T,wt=13): 1554 member(null_class,intersection(universal_class,unordered_pair(A,null_class))). [resolve(480,a,476,a)].
% 62.72/9.43
% 62.72/9.43 % SZS status Unsatisfiable for theBenchmark
% 62.72/9.43
% 62.72/9.43 % Proof 1 at 0.66 (+ 0.23) seconds.
% 62.72/9.43 % Length of proof is 10.
% 62.72/9.43 % Level of proof is 3.
% 62.72/9.43 % Maximum clause weight is 15.000.
% 62.72/9.43 % Given clauses 651.
% 62.72/9.43
% 62.72/9.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------