TSTP Solution File: SET116-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET116-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 03:32:50 EDT 2022
% Result : Unsatisfiable 2.19s 2.37s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 9 unt; 6 nHn; 21 RR)
% Number of literals : 42 ( 41 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_1st_and_2nd_4,axiom,
( ordered_pair(first(X),second(X)) = X
| first(X) = X ) ).
cnf(existence_of_1st_and_2nd_5,axiom,
( ordered_pair(first(X),second(X)) = X
| second(X) = X ) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets4_1,negated_conjecture,
ordered_pair(first(x),second(x)) != x ).
cnf(prove_unique_2nd_in_pair_of_non_sets,negated_conjecture,
second(x) != x ).
cnf(refute_0_0,plain,
( ordered_pair(first(x),second(x)) = x
| second(x) = x ),
inference(subst,[],[existence_of_1st_and_2nd_5:[bind(X,$fot(x))]]) ).
cnf(refute_0_1,plain,
( first(x) = x
| ordered_pair(first(x),second(x)) = x ),
inference(subst,[],[existence_of_1st_and_2nd_4:[bind(X,$fot(x))]]) ).
cnf(refute_0_2,plain,
( ordered_pair(first(x),second(x)) != x
| x != x
| ordered_pair(first(x),second(x)) = x ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(first(x),second(x)),x) ),[0],$fot(x)]]) ).
cnf(refute_0_3,plain,
( x != x
| first(x) = x
| ordered_pair(first(x),second(x)) = x ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( x != x
| first(x) = x ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[refute_0_3,prove_unique_1st_and_2nd_in_pair_of_non_sets4_1]) ).
cnf(refute_0_5,plain,
x = x,
introduced(tautology,[refl,[$fot(x)]]) ).
cnf(refute_0_6,plain,
first(x) = x,
inference(resolve,[$cnf( $equal(x,x) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( first(x) != x
| ordered_pair(first(x),second(x)) != x
| ordered_pair(x,second(x)) = x ),
introduced(tautology,[equality,[$cnf( $equal(ordered_pair(first(x),second(x)),x) ),[0,0],$fot(x)]]) ).
cnf(refute_0_8,plain,
( ordered_pair(first(x),second(x)) != x
| ordered_pair(x,second(x)) = x ),
inference(resolve,[$cnf( $equal(first(x),x) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ordered_pair(x,second(x)) = x
| second(x) = x ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
ordered_pair(first(x),second(x)) = ordered_pair(first(x),second(x)),
introduced(tautology,[refl,[$fot(ordered_pair(first(x),second(x)))]]) ).
cnf(refute_0_11,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_12,plain,
( first(x) != x
| ordered_pair(first(x),second(x)) = ordered_pair(x,second(x)) ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),ordered_pair(first(x),second(x))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
ordered_pair(first(x),second(x)) = ordered_pair(x,second(x)),
inference(resolve,[$cnf( $equal(first(x),x) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
( ordered_pair(first(x),second(x)) != ordered_pair(x,second(x))
| ordered_pair(x,second(x)) != x
| ordered_pair(first(x),second(x)) = x ),
introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(first(x),second(x)),x) ),[0],$fot(ordered_pair(x,second(x)))]]) ).
cnf(refute_0_15,plain,
( ordered_pair(x,second(x)) != x
| ordered_pair(first(x),second(x)) = x ),
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),ordered_pair(x,second(x))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
ordered_pair(x,second(x)) != x,
inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[refute_0_15,prove_unique_1st_and_2nd_in_pair_of_non_sets4_1]) ).
cnf(refute_0_17,plain,
second(x) = x,
inference(resolve,[$cnf( $equal(ordered_pair(x,second(x)),x) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( $equal(second(x),x) )],[refute_0_17,prove_unique_2nd_in_pair_of_non_sets]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET116-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 18:35:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.19/2.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.19/2.37
% 2.19/2.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.19/2.37
%------------------------------------------------------------------------------