TSTP Solution File: SET114-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET114-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:32:49 EDT 2022
% Result : Unsatisfiable 1.98s 2.19s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 8 unt; 5 nHn; 17 RR)
% Number of literals : 33 ( 16 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_1st_and_2nd_2,axiom,
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| first(X) = X ) ).
cnf(existence_of_1st_and_2nd_3,axiom,
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| second(X) = X ) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets2_1,negated_conjecture,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ).
cnf(prove_unique_2nd_in_pair_of_non_sets,negated_conjecture,
second(x) != x ).
cnf(refute_0_0,plain,
( second(x) = x
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
inference(subst,[],[existence_of_1st_and_2nd_3:[bind(X,$fot(x))]]) ).
cnf(refute_0_1,plain,
( first(x) = x
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
inference(subst,[],[existence_of_1st_and_2nd_2:[bind(X,$fot(x))]]) ).
cnf(refute_0_2,plain,
first(x) = x,
inference(resolve,[$cnf( member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) )],[refute_0_1,prove_unique_1st_and_2nd_in_pair_of_non_sets2_1]) ).
cnf(refute_0_3,plain,
( first(x) != x
| ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class))
| member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class)) ),
introduced(tautology,[equality,[$cnf( member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),[0,0],$fot(x)]]) ).
cnf(refute_0_4,plain,
( ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class))
| member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class)) ),
inference(resolve,[$cnf( $equal(first(x),x) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( second(x) = x
| member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class)) ),
inference(resolve,[$cnf( member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class)),
inference(resolve,[$cnf( $equal(second(x),x) )],[refute_0_5,prove_unique_2nd_in_pair_of_non_sets]) ).
cnf(refute_0_7,plain,
ordered_pair(first(x),second(x)) = ordered_pair(first(x),second(x)),
introduced(tautology,[refl,[$fot(ordered_pair(first(x),second(x)))]]) ).
cnf(refute_0_8,plain,
( first(x) != x
| ordered_pair(first(x),second(x)) != ordered_pair(first(x),second(x))
| ordered_pair(first(x),second(x)) = ordered_pair(x,second(x)) ),
introduced(tautology,[equality,[$cnf( $equal(ordered_pair(first(x),second(x)),ordered_pair(first(x),second(x))) ),[1,0],$fot(x)]]) ).
cnf(refute_0_9,plain,
( first(x) != x
| ordered_pair(first(x),second(x)) = ordered_pair(x,second(x)) ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),ordered_pair(first(x),second(x))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
ordered_pair(first(x),second(x)) = ordered_pair(x,second(x)),
inference(resolve,[$cnf( $equal(first(x),x) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
( ordered_pair(first(x),second(x)) != ordered_pair(x,second(x))
| ~ member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class))
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
introduced(tautology,[equality,[$cnf( ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),[0],$fot(ordered_pair(x,second(x)))]]) ).
cnf(refute_0_12,plain,
( ~ member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class))
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),ordered_pair(x,second(x))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
~ member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class)),
inference(resolve,[$cnf( member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) )],[refute_0_12,prove_unique_1st_and_2nd_in_pair_of_non_sets2_1]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( member(ordered_pair(x,second(x)),cross_product(universal_class,universal_class)) )],[refute_0_6,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET114-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 03:09:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.98/2.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.98/2.19
% 1.98/2.19 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.98/2.20
%------------------------------------------------------------------------------