TSTP Solution File: SET101+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET101+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 03:32:39 EDT 2022
% Result : Theorem 1.21s 1.40s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 21
% Syntax : Number of formulae : 107 ( 50 unt; 0 def)
% Number of atoms : 216 ( 107 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 209 ( 100 ~; 88 |; 14 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 166 ( 11 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ) ).
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X) ).
fof(ordered_pair_defn,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) ).
fof(first_second,axiom,
! [X,Y] :
( ( member(X,universal_class)
& member(Y,universal_class) )
=> ( first(ordered_pair(X,Y)) = X
& second(ordered_pair(X,Y)) = Y ) ) ).
fof(identity_relation,axiom,
! [Z] :
( member(Z,identity_relation)
<=> ? [X] :
( member(X,universal_class)
& Z = ordered_pair(X,X) ) ) ).
fof(singleton_member_of_ordered_pair,conjecture,
! [X,Y] : member(singleton(X),ordered_pair(X,Y)) ).
fof(subgoal_0,plain,
! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
inference(strip,[],[singleton_member_of_ordered_pair]) ).
fof(negate_0_0,plain,
~ ! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y] : ~ member(singleton(X),ordered_pair(X,Y)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ member(singleton(skolemFOFtoCNF_X_2),ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_3,plain,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
<=> ( ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [U,X,Y] :
( U != X
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Z] :
( ~ member(Z,identity_relation)
<=> ! [X] :
( Z != ordered_pair(X,X)
| ~ member(X,universal_class) ) ),
inference(canonicalize,[],[identity_relation]) ).
fof(normalize_0_7,plain,
! [Z] :
( ~ member(Z,identity_relation)
<=> ! [X] :
( Z != ordered_pair(X,X)
| ~ member(X,universal_class) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Z] :
( ( ~ member(Z,identity_relation)
| Z = ordered_pair(skolemFOFtoCNF_X_1(Z),skolemFOFtoCNF_X_1(Z)) )
& ( ~ member(Z,identity_relation)
| member(skolemFOFtoCNF_X_1(Z),universal_class) )
& ( Z != ordered_pair(X,X)
| ~ member(X,universal_class)
| member(Z,identity_relation) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Z] :
( ~ member(Z,identity_relation)
| member(skolemFOFtoCNF_X_1(Z),universal_class) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(canonicalize,[],[unordered_pair]) ).
fof(normalize_0_11,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[singleton_set_defn]) ).
fof(normalize_0_13,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Z] :
( Z != ordered_pair(X,X)
| ~ member(X,universal_class)
| member(Z,identity_relation) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ member(X,universal_class)
| ~ member(Y,universal_class)
| ( first(ordered_pair(X,Y)) = X
& second(ordered_pair(X,Y)) = Y ) ),
inference(canonicalize,[],[first_second]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ member(X,universal_class)
| ~ member(Y,universal_class)
| ( first(ordered_pair(X,Y)) = X
& second(ordered_pair(X,Y)) = Y ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ( ~ member(X,universal_class)
| ~ member(Y,universal_class)
| first(ordered_pair(X,Y)) = X )
& ( ~ member(X,universal_class)
| ~ member(Y,universal_class)
| second(ordered_pair(X,Y)) = Y ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ member(X,universal_class)
| ~ member(Y,universal_class)
| second(ordered_pair(X,Y)) = Y ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [Z] :
( ~ member(Z,identity_relation)
| Z = ordered_pair(skolemFOFtoCNF_X_1(Z),skolemFOFtoCNF_X_1(Z)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_20,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(canonicalize,[],[ordered_pair_defn]) ).
fof(normalize_0_21,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
~ member(singleton(skolemFOFtoCNF_X_2),ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( U != X
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( X != X
| ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(X))]]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),universal_class)
| member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))))]]) ).
cnf(refute_0_6,plain,
( ~ member(Z,identity_relation)
| member(skolemFOFtoCNF_X_1(Z),universal_class) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ member(ordered_pair(singleton(X_70),singleton(X_70)),identity_relation)
| member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),universal_class) ),
inference(subst,[],[refute_0_6:[bind(Z,$fot(ordered_pair(singleton(X_70),singleton(X_70))))]]) ).
cnf(refute_0_8,plain,
member(unordered_pair(X,Y),universal_class),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
member(unordered_pair(X_8,X_8),universal_class),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_8)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_10,plain,
singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
singleton(X_8) = unordered_pair(X_8,X_8),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( singleton(X_8) != unordered_pair(X_8,X_8)
| unordered_pair(X_8,X_8) = singleton(X_8) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(singleton(X_8))),bind(Y0,$fot(unordered_pair(X_8,X_8)))]]) ).
cnf(refute_0_16,plain,
unordered_pair(X_8,X_8) = singleton(X_8),
inference(resolve,[$cnf( $equal(singleton(X_8),unordered_pair(X_8,X_8)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( unordered_pair(X_8,X_8) != singleton(X_8)
| ~ member(unordered_pair(X_8,X_8),universal_class)
| member(singleton(X_8),universal_class) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(X_8,X_8),universal_class) ),[0],$fot(singleton(X_8))]]) ).
cnf(refute_0_18,plain,
( ~ member(unordered_pair(X_8,X_8),universal_class)
| member(singleton(X_8),universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_8,X_8),singleton(X_8)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
member(singleton(X_8),universal_class),
inference(resolve,[$cnf( member(unordered_pair(X_8,X_8),universal_class) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
( Z != ordered_pair(X,X)
| ~ member(X,universal_class)
| member(Z,identity_relation) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_21,plain,
( ordered_pair(X,X) != ordered_pair(X,X)
| ~ member(X,universal_class)
| member(ordered_pair(X,X),identity_relation) ),
inference(subst,[],[refute_0_20:[bind(Z,$fot(ordered_pair(X,X)))]]) ).
cnf(refute_0_22,plain,
ordered_pair(X,X) = ordered_pair(X,X),
introduced(tautology,[refl,[$fot(ordered_pair(X,X))]]) ).
cnf(refute_0_23,plain,
( ~ member(X,universal_class)
| member(ordered_pair(X,X),identity_relation) ),
inference(resolve,[$cnf( $equal(ordered_pair(X,X),ordered_pair(X,X)) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( ~ member(singleton(X_8),universal_class)
| member(ordered_pair(singleton(X_8),singleton(X_8)),identity_relation) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(singleton(X_8)))]]) ).
cnf(refute_0_25,plain,
member(ordered_pair(singleton(X_8),singleton(X_8)),identity_relation),
inference(resolve,[$cnf( member(singleton(X_8),universal_class) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
member(ordered_pair(singleton(X_70),singleton(X_70)),identity_relation),
inference(subst,[],[refute_0_25:[bind(X_8,$fot(X_70))]]) ).
cnf(refute_0_27,plain,
member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),universal_class),
inference(resolve,[$cnf( member(ordered_pair(singleton(X_70),singleton(X_70)),identity_relation) )],[refute_0_26,refute_0_7]) ).
cnf(refute_0_28,plain,
member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),universal_class),
inference(subst,[],[refute_0_27:[bind(X_70,$fot(X_99))]]) ).
cnf(refute_0_29,plain,
member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),universal_class) )],[refute_0_28,refute_0_5]) ).
cnf(refute_0_30,plain,
( ~ member(X,universal_class)
| ~ member(Y,universal_class)
| second(ordered_pair(X,Y)) = Y ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_31,plain,
( ~ member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),universal_class)
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),bind(Y,$fot(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))))]]) ).
cnf(refute_0_32,plain,
second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),universal_class) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ member(singleton(X_8),universal_class)
| second(ordered_pair(singleton(X_8),singleton(X_8))) = singleton(X_8) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(singleton(X_8))),bind(Y,$fot(singleton(X_8)))]]) ).
cnf(refute_0_34,plain,
second(ordered_pair(singleton(X_8),singleton(X_8))) = singleton(X_8),
inference(resolve,[$cnf( member(singleton(X_8),universal_class) )],[refute_0_19,refute_0_33]) ).
cnf(refute_0_35,plain,
second(ordered_pair(singleton(X_99),singleton(X_99))) = singleton(X_99),
inference(subst,[],[refute_0_34:[bind(X_8,$fot(X_99))]]) ).
cnf(refute_0_36,plain,
( ~ member(Z,identity_relation)
| Z = ordered_pair(skolemFOFtoCNF_X_1(Z),skolemFOFtoCNF_X_1(Z)) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_37,plain,
( ~ member(ordered_pair(singleton(X_70),singleton(X_70)),identity_relation)
| ordered_pair(singleton(X_70),singleton(X_70)) = ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70)))) ),
inference(subst,[],[refute_0_36:[bind(Z,$fot(ordered_pair(singleton(X_70),singleton(X_70))))]]) ).
cnf(refute_0_38,plain,
ordered_pair(singleton(X_70),singleton(X_70)) = ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70)))),
inference(resolve,[$cnf( member(ordered_pair(singleton(X_70),singleton(X_70)),identity_relation) )],[refute_0_26,refute_0_37]) ).
cnf(refute_0_39,plain,
( ordered_pair(singleton(X_70),singleton(X_70)) != ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))))
| ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70)))) = ordered_pair(singleton(X_70),singleton(X_70)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(ordered_pair(singleton(X_70),singleton(X_70)))),bind(Y0,$fot(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))))))]]) ).
cnf(refute_0_40,plain,
ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70)))) = ordered_pair(singleton(X_70),singleton(X_70)),
inference(resolve,[$cnf( $equal(ordered_pair(singleton(X_70),singleton(X_70)),ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_70),singleton(X_70))))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))) = ordered_pair(singleton(X_99),singleton(X_99)),
inference(subst,[],[refute_0_40:[bind(X_70,$fot(X_99))]]) ).
cnf(refute_0_42,plain,
second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),
introduced(tautology,[refl,[$fot(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))))]]) ).
cnf(refute_0_43,plain,
( ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))) != ordered_pair(singleton(X_99),singleton(X_99))
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) != second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))))
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = second(ordered_pair(singleton(X_99),singleton(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))))) ),[1,0],$fot(ordered_pair(singleton(X_99),singleton(X_99)))]]) ).
cnf(refute_0_44,plain,
( ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))) != ordered_pair(singleton(X_99),singleton(X_99))
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = second(ordered_pair(singleton(X_99),singleton(X_99))) ),
inference(resolve,[$cnf( $equal(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = second(ordered_pair(singleton(X_99),singleton(X_99))),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))),ordered_pair(singleton(X_99),singleton(X_99))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_47,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_14,refute_0_46]) ).
cnf(refute_0_48,plain,
( second(ordered_pair(singleton(X_99),singleton(X_99))) != singleton(X_99)
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) != second(ordered_pair(singleton(X_99),singleton(X_99)))
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = singleton(X_99) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))))),bind(Y0,$fot(second(ordered_pair(singleton(X_99),singleton(X_99))))),bind(Z0,$fot(singleton(X_99)))]]) ).
cnf(refute_0_49,plain,
( second(ordered_pair(singleton(X_99),singleton(X_99))) != singleton(X_99)
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = singleton(X_99) ),
inference(resolve,[$cnf( $equal(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),second(ordered_pair(singleton(X_99),singleton(X_99)))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) = singleton(X_99),
inference(resolve,[$cnf( $equal(second(ordered_pair(singleton(X_99),singleton(X_99))),singleton(X_99)) )],[refute_0_35,refute_0_49]) ).
cnf(refute_0_51,plain,
( second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) != singleton(X_99)
| second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) != skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))
| singleton(X_99) = skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) ),
introduced(tautology,[equality,[$cnf( $equal(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))) ),[0],$fot(singleton(X_99))]]) ).
cnf(refute_0_52,plain,
( second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))) != skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))
| singleton(X_99) = skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) ),
inference(resolve,[$cnf( $equal(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),singleton(X_99)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
singleton(X_99) = skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),
inference(resolve,[$cnf( $equal(second(ordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))))),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))) )],[refute_0_32,refute_0_52]) ).
cnf(refute_0_54,plain,
( singleton(X_99) != skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))
| skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) = singleton(X_99) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(singleton(X_99))),bind(Y0,$fot(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))))]]) ).
cnf(refute_0_55,plain,
skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) = singleton(X_99),
inference(resolve,[$cnf( $equal(singleton(X_99),skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) != singleton(X_99)
| ~ member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y))
| member(singleton(X_99),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) ),[0],$fot(singleton(X_99))]]) ).
cnf(refute_0_57,plain,
( ~ member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y))
| member(singleton(X_99),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),singleton(X_99)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y) = unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y))]]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) != singleton(X_99)
| unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y) != unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)
| unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y) = unordered_pair(singleton(X_99),Y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) ),[1,0],$fot(singleton(X_99))]]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))) != singleton(X_99)
| unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y) = unordered_pair(singleton(X_99),Y) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y) = unordered_pair(singleton(X_99),Y),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),singleton(X_99)) )],[refute_0_55,refute_0_60]) ).
cnf(refute_0_62,plain,
( unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y) != unordered_pair(singleton(X_99),Y)
| ~ member(singleton(X_99),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y))
| member(singleton(X_99),unordered_pair(singleton(X_99),Y)) ),
introduced(tautology,[equality,[$cnf( member(singleton(X_99),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) ),[1],$fot(unordered_pair(singleton(X_99),Y))]]) ).
cnf(refute_0_63,plain,
( ~ member(singleton(X_99),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y))
| member(singleton(X_99),unordered_pair(singleton(X_99),Y)) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y),unordered_pair(singleton(X_99),Y)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y))
| member(singleton(X_99),unordered_pair(singleton(X_99),Y)) ),
inference(resolve,[$cnf( member(singleton(X_99),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) )],[refute_0_57,refute_0_63]) ).
cnf(refute_0_65,plain,
member(singleton(X_99),unordered_pair(singleton(X_99),Y)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),unordered_pair(skolemFOFtoCNF_X_1(ordered_pair(singleton(X_99),singleton(X_99))),Y)) )],[refute_0_29,refute_0_64]) ).
cnf(refute_0_66,plain,
member(singleton(X_101),unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y)))),
inference(subst,[],[refute_0_65:[bind(Y,$fot(unordered_pair(X_101,singleton(Y)))),bind(X_99,$fot(X_101))]]) ).
cnf(refute_0_67,plain,
ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_68,plain,
ordered_pair(X_101,Y) = unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_101))]]) ).
cnf(refute_0_69,plain,
( ordered_pair(X_101,Y) != unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y)))
| unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))) = ordered_pair(X_101,Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(ordered_pair(X_101,Y))),bind(Y0,$fot(unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y)))))]]) ).
cnf(refute_0_70,plain,
unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))) = ordered_pair(X_101,Y),
inference(resolve,[$cnf( $equal(ordered_pair(X_101,Y),unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))) != ordered_pair(X_101,Y)
| ~ member(singleton(X_101),unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))))
| member(singleton(X_101),ordered_pair(X_101,Y)) ),
introduced(tautology,[equality,[$cnf( member(singleton(X_101),unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y)))) ),[1],$fot(ordered_pair(X_101,Y))]]) ).
cnf(refute_0_72,plain,
( ~ member(singleton(X_101),unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))))
| member(singleton(X_101),ordered_pair(X_101,Y)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y))),ordered_pair(X_101,Y)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
member(singleton(X_101),ordered_pair(X_101,Y)),
inference(resolve,[$cnf( member(singleton(X_101),unordered_pair(singleton(X_101),unordered_pair(X_101,singleton(Y)))) )],[refute_0_66,refute_0_72]) ).
cnf(refute_0_74,plain,
member(singleton(skolemFOFtoCNF_X_2),ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_0_73:[bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(X_101,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( member(singleton(skolemFOFtoCNF_X_2),ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1)) )],[refute_0_74,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET101+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 07:16:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.21/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/1.40
% 1.21/1.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.21/1.42
%------------------------------------------------------------------------------