%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET052-6 : 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 : n012.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 08:35:30 AM UTC 2026
% Result : Unsatisfiable 0.04s 25.57s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 5 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_1_to_cartesian_product_2,axiom,
~ member(u,universal_class),
file('theBenchmark.p',prove_corollary_1_to_cartesian_product_2) ).
cnf(c_34,plain,
~ member(u,universal_class),
inference(clausify,[status(thm)],[prove_corollary_1_to_cartesian_product_2]) ).
fof(prove_corollary_1_to_cartesian_product_1,axiom,
member(ordered_pair(u,v),cross_product(x,y)),
file('theBenchmark.p',prove_corollary_1_to_cartesian_product_1) ).
cnf(c_35,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(clausify,[status(thm)],[prove_corollary_1_to_cartesian_product_1]) ).
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_106,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_118,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_121,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_210,plain,
member(u,x),
inference(resolve,[status(thm)],[c_106,c_35]) ).
cnf(c_321,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_319,plain,
~ member(u,A),
inference(resolve,[status(thm)],[c_321,c_34]) ).
cnf(c_320,plain,
$false,
inference(resolve,[status(thm)],[c_319,c_210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET052-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/25.53 % Computer : n012.cluster.edu
% 0.04/25.53 % Model : x86_64 x86_64
% 0.04/25.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/25.53 % Memory : 8046.5625MB
% 0.04/25.53 % OS : Linux 6.8.0-71-generic
% 0.04/25.54 % CPULimit : 300
% 0.04/25.54 % WCLimit : 300
% 0.04/25.54 % DateTime : Sat Sep 26 07:00:06 UTC 2026
% 0.04/25.54 % CPUTime :
% 0.04/25.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/25.54 % Process 4144190 was started by sandbox on n012,
% 0.04/25.54 % Sat Sep 26 07:00:06 2026
% 0.04/25.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/25.54
% 0.04/25.54 % From the command line: assign(max_seconds, 300).
% 0.04/25.57
% 0.04/25.57 % SZS status Unsatisfiable for theBenchmark
% 0.04/25.57
% 0.04/25.57 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.04/25.57 % Length of proof is 8.
% 0.04/25.57 % Level of proof is 2.
% 0.04/25.57 % Maximum clause weight is 20.000.
% 0.04/25.57 % Given clauses 74.
% 0.04/25.57
% 0.04/25.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------