%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET108-6 : 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 : n009.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 08:35:48 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.54s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 25 unt; 0 def)
% Number of atoms : 35 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 17 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 8 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_existence_of_1st_and_2nd_1_2,axiom,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
cnf(c_34,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_existence_of_1st_and_2nd_1_2]) ).
fof(prove_existence_of_1st_and_2nd_1_1,axiom,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
cnf(c_35,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_existence_of_1st_and_2nd_1_1]) ).
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_103,plain,
( ordered_pair(first(A),second(A)) = A
| ~ member(A,cross_product(B,C)) ),
inference(clausify,[status(thm)],[cartesian_product4]) ).
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_107,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_108,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_107]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_109,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_110,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_337,plain,
( unordered_pair(singleton(first(A)),unordered_pair(first(A),singleton(second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_108,c_103]) ).
cnf(c_338,plain,
( unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),singleton(second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_110,c_337]) ).
cnf(c_188,plain,
( unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),unordered_pair(second(A),second(A)))) = A
| ~ member(A,cross_product(B,C)) ),
inference(paramod,[status(thm)],[c_110,c_338]) ).
cnf(c_339,plain,
member(unordered_pair(singleton(y),unordered_pair(y,singleton(z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_108,c_35]) ).
cnf(c_340,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,singleton(z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_339]) ).
cnf(c_195,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_340]) ).
cnf(c_341,plain,
~ member(ordered_pair(first(unordered_pair(singleton(y),unordered_pair(y,singleton(z)))),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_108,c_34]) ).
cnf(c_342,plain,
~ member(ordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,singleton(z)))),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_341]) ).
cnf(c_343,plain,
~ member(ordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_342]) ).
cnf(c_344,plain,
~ member(ordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(singleton(y),unordered_pair(y,singleton(z))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_108,c_343]) ).
cnf(c_345,plain,
~ member(ordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,singleton(z))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_344]) ).
cnf(c_346,plain,
~ member(ordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_345]) ).
cnf(c_347,plain,
~ member(unordered_pair(singleton(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),singleton(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_108,c_346]) ).
cnf(c_348,plain,
~ member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),singleton(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_347]) ).
cnf(c_196,plain,
~ member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_110,c_348]) ).
cnf(c_324,plain,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))) = unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),
inference(resolve,[status(thm)],[c_195,c_188]) ).
cnf(c_349,plain,
~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_324,c_196]) ).
cnf(c_336,plain,
$false,
inference(resolve,[status(thm)],[c_195,c_349]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET108-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n009.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 07:08:30 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 3644801 was started by sandbox on n009,
% 0.15/0.44 % Sat Sep 26 07:08:30 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 0.15/0.54
% 0.15/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.54
% 0.15/0.54 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.15/0.54 % Length of proof is 12.
% 0.15/0.54 % Level of proof is 4.
% 0.15/0.54 % Maximum clause weight is 64.000.
% 0.15/0.54 % Given clauses 95.
% 0.15/0.54
% 0.15/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------