%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET203-6 : 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 : n005.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 08:36:02 AM UTC 2026
% Result : Unsatisfiable 0.22s 5.61s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 21 unt; 0 def)
% Number of atoms : 48 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 22 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_X_product_property1_3,axiom,
~ member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_corollary_to_X_product_property1_3) ).
cnf(c_36,plain,
~ member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_corollary_to_X_product_property1_3]) ).
fof(prove_corollary_to_X_product_property1_2,axiom,
member(v,y),
file('theBenchmark.p',prove_corollary_to_X_product_property1_2) ).
cnf(c_37,plain,
member(v,y),
inference(clausify,[status(thm)],[prove_corollary_to_X_product_property1_2]) ).
fof(prove_corollary_to_X_product_property1_1,axiom,
member(u,x),
file('theBenchmark.p',prove_corollary_to_X_product_property1_1) ).
cnf(c_38,plain,
member(u,x),
inference(clausify,[status(thm)],[prove_corollary_to_X_product_property1_1]) ).
fof(cartesian_product3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(ordered_pair(VAR_0,VAR_2),cross_product(VAR_1,VAR_3))
| ~ member(VAR_2,VAR_3)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',cartesian_product3) ).
cnf(c_129,plain,
( member(ordered_pair(A,C),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[cartesian_product3]) ).
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_132,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_133,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_132]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_134,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_135,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_134]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_143,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_146,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_579,plain,
( member(unordered_pair(singleton(A),unordered_pair(A,singleton(C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_133,c_129]) ).
cnf(c_580,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_135,c_579]) ).
cnf(c_237,plain,
( member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(C,C))),cross_product(B,D))
| ~ member(C,D)
| ~ member(A,B) ),
inference(paramod,[status(thm)],[c_135,c_580]) ).
cnf(c_581,plain,
~ member(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_133,c_36]) ).
cnf(c_582,plain,
~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,singleton(v))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_135,c_581]) ).
cnf(c_252,plain,
~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_135,c_582]) ).
cnf(c_583,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_146,c_143]) ).
cnf(c_348,plain,
member(u,universal_class),
inference(resolve,[status(thm)],[c_583,c_38]) ).
cnf(c_584,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_146,c_143]) ).
cnf(c_349,plain,
member(v,universal_class),
inference(resolve,[status(thm)],[c_584,c_37]) ).
cnf(c_585,plain,
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(A,A))),cross_product(universal_class,B))
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_237,c_348]) ).
cnf(c_586,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_585,c_349]) ).
cnf(c_578,plain,
$false,
inference(resolve,[status(thm)],[c_252,c_586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET203-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.42 % Computer : n005.cluster.edu
% 0.17/5.42 % Model : x86_64 x86_64
% 0.17/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.42 % Memory : 8046.5625MB
% 0.17/5.42 % OS : Linux 6.8.0-71-generic
% 0.17/5.42 % CPULimit : 300
% 0.17/5.42 % WCLimit : 300
% 0.17/5.42 % DateTime : Sat Sep 26 07:19:22 UTC 2026
% 0.17/5.42 % CPUTime :
% 0.17/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.42 % Process 1542177 was started by sandbox on n005,
% 0.17/5.42 % Sat Sep 26 07:19:22 2026
% 0.17/5.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.44
% 0.17/5.44 % From the command line: assign(max_seconds, 300).
% 0.22/5.61
% 0.22/5.61 % SZS status Unsatisfiable for theBenchmark
% 0.22/5.61
% 0.22/5.61 % Proof 1 at 0.12 (+ 0.03) seconds.
% 0.22/5.61 % Length of proof is 15.
% 0.22/5.61 % Level of proof is 3.
% 0.22/5.61 % Maximum clause weight is 54.000.
% 0.22/5.61 % Given clauses 132.
% 0.22/5.61
% 0.22/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------