%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET108-7 : 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 : n008.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 0.16s 5.56s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 11 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 2 sgn 3 !; 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_33,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_34,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_170,plain,
( ordered_pair(first(A),second(A)) = A
| ~ member(A,cross_product(B,C)) ),
inference(clausify,[status(thm)],[cartesian_product4]) ).
cnf(c_778,plain,
ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) = ordered_pair(y,z),
inference(resolve,[status(thm)],[c_170,c_34]) ).
cnf(c_780,plain,
~ member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_778,c_33]) ).
cnf(c_779,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n008.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 07:09:16 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 3038300 was started by sandbox on n008,
% 0.11/5.39 % Sat Sep 26 07:09:16 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.40
% 0.11/5.40 % From the command line: assign(max_seconds, 300).
% 0.16/5.56
% 0.16/5.56 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.56
% 0.16/5.56 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.16/5.56 % Length of proof is 5.
% 0.16/5.56 % Level of proof is 2.
% 0.16/5.56 % Maximum clause weight is 33.000.
% 0.16/5.56 % Given clauses 96.
% 0.16/5.56
% 0.16/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------