TSTP Solution File: SET074+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET074+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 03:32:14 EDT 2022
% Result : Theorem 1.59s 1.79s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 65 ( 22 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 69 ( 34 ~; 21 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 6 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ) ).
fof(null_class_defn,axiom,
! [X] : ~ member(X,null_class) ).
fof(corollary1_2,conjecture,
! [X,Y] :
( member(Y,universal_class)
=> unordered_pair(X,Y) != null_class ) ).
fof(subgoal_0,plain,
! [X,Y] :
( member(Y,universal_class)
=> unordered_pair(X,Y) != null_class ),
inference(strip,[],[corollary1_2]) ).
fof(negate_0_0,plain,
~ ! [X,Y] :
( member(Y,universal_class)
=> unordered_pair(X,Y) != null_class ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y] :
( unordered_pair(X,Y) = null_class
& member(Y,universal_class) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1) = null_class
& member(skolemFOFtoCNF_Y_1,universal_class) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
member(skolemFOFtoCNF_Y_1,universal_class),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
<=> ( ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(canonicalize,[],[unordered_pair_defn]) ).
fof(normalize_0_4,plain,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
<=> ( ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [U,X,Y] :
( ( ~ member(U,unordered_pair(X,Y))
| member(U,universal_class) )
& ( U != X
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( U != Y
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [U,X,Y] :
( U != Y
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1) = null_class,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [X] : ~ member(X,null_class),
inference(canonicalize,[],[null_class_defn]) ).
fof(normalize_0_9,plain,
! [X] : ~ member(X,null_class),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
member(skolemFOFtoCNF_Y_1,universal_class),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( U != Y
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( Y != Y
| ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(Y))]]) ).
cnf(refute_0_3,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_4,plain,
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_Y_1,universal_class)
| member(skolemFOFtoCNF_Y_1,unordered_pair(X_82,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_82)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_6,plain,
member(skolemFOFtoCNF_Y_1,unordered_pair(X_82,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,universal_class) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
member(skolemFOFtoCNF_Y_1,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_0_6:[bind(X_82,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_8,plain,
unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1) = null_class,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1) != null_class
| ~ member(skolemFOFtoCNF_Y_1,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1))
| member(skolemFOFtoCNF_Y_1,null_class) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_Y_1,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)) ),[1],$fot(null_class)]]) ).
cnf(refute_0_10,plain,
( ~ member(skolemFOFtoCNF_Y_1,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1))
| member(skolemFOFtoCNF_Y_1,null_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1),null_class) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
member(skolemFOFtoCNF_Y_1,null_class),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
~ member(X,null_class),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
~ member(skolemFOFtoCNF_Y_1,null_class),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,null_class) )],[refute_0_11,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET074+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 20:53:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.59/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/1.79
% 1.59/1.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.59/1.79
%------------------------------------------------------------------------------