TSTP Solution File: SET790+4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET790+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:37:14 EDT 2022
% Result : Theorem 0.54s 0.71s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 20 unt; 2 def)
% Number of atoms : 297 ( 34 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 356 ( 136 ~; 116 |; 75 &)
% ( 16 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 169 ( 9 sgn 99 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(order,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ) ).
fof(lower_bound,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ).
fof(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ) ).
fof(thIV2,conjecture,
! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ) ).
fof(definition_0,definition,
! [E,R,X,Y] :
( definitionFOFtoCNF_0(E,R,X,Y)
<=> ( ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| ~ member(X,E)
| ~ member(Y,E)
| X = Y ) ) ).
fof(definition_1,definition,
! [E,R,X] :
( definitionFOFtoCNF_1(E,R,X)
<=> ( ~ member(X,E)
| apply(R,X,X) ) ) ).
fof(subgoal_0,plain,
! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
inference(strip,[],[thIV2]) ).
fof(negate_0_0,plain,
~ ! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E,M,R] :
( least(M,R,E)
& order(R,E)
& ? [X] :
( M != X
& least(X,R,E) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
& order(skolemFOFtoCNF_R,skolemFOFtoCNF_E)
& ? [X] :
( skolemFOFtoCNF_M_2 != X
& least(X,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,M,R] :
( ~ least(M,R,E)
<=> ( ~ member(M,E)
| ? [X] :
( ~ apply(R,M,X)
& member(X,E) ) ) ),
inference(canonicalize,[],[least]) ).
fof(normalize_0_4,plain,
! [E,M,R] :
( ~ lower_bound(M,R,E)
<=> ? [X] :
( ~ apply(R,M,X)
& member(X,E) ) ),
inference(canonicalize,[],[lower_bound]) ).
fof(normalize_0_5,plain,
! [E,M,R] :
( ~ lower_bound(M,R,E)
<=> ? [X] :
( ~ apply(R,M,X)
& member(X,E) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [E,M,R] :
( ~ least(M,R,E)
<=> ( ~ lower_bound(M,R,E)
| ~ member(M,E) ) ),
inference(simplify,[],[normalize_0_3,normalize_0_5]) ).
fof(normalize_0_7,plain,
! [E,M,R] :
( ~ least(M,R,E)
<=> ( ~ lower_bound(M,R,E)
| ~ member(M,E) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [E,M,R] :
( ( ~ least(M,R,E)
| lower_bound(M,R,E) )
& ( ~ least(M,R,E)
| member(M,E) )
& ( ~ lower_bound(M,R,E)
| ~ member(M,E)
| least(M,R,E) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [E,M,R] :
( ~ least(M,R,E)
| member(M,E) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [X] :
( skolemFOFtoCNF_M_2 != X
& least(X,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
( skolemFOFtoCNF_M_2 != skolemFOFtoCNF_X_8
& least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [E,M,R] :
( ~ least(M,R,E)
| lower_bound(M,R,E) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_14,plain,
! [E,M,R,X] :
( ( ~ apply(R,M,skolemFOFtoCNF_X_5(E,M,R))
| lower_bound(M,R,E) )
& ( lower_bound(M,R,E)
| member(skolemFOFtoCNF_X_5(E,M,R),E) )
& ( ~ lower_bound(M,R,E)
| ~ member(X,E)
| apply(R,M,X) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_15,plain,
! [E,M,R,X] :
( ~ lower_bound(M,R,E)
| ~ member(X,E)
| apply(R,M,X) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
order(skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
! [E,R] :
( ~ order(R,E)
<=> ( ? [X] :
( ~ apply(R,X,X)
& member(X,E) )
| ? [X,Y] :
( X != Y
& apply(R,X,Y)
& apply(R,Y,X)
& member(X,E)
& member(Y,E) )
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,X,Y)
& apply(R,Y,Z)
& member(X,E)
& member(Y,E)
& member(Z,E) ) ) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_18,plain,
! [E,R] :
( ~ order(R,E)
<=> ( ? [X] :
( ~ apply(R,X,X)
& member(X,E) )
| ? [X,Y] :
( X != Y
& apply(R,X,Y)
& apply(R,Y,X)
& member(X,E)
& member(Y,E) )
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,X,Y)
& apply(R,Y,Z)
& member(X,E)
& member(Y,E)
& member(Z,E) ) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [E,R,X,Y] :
( ~ definitionFOFtoCNF_0(E,R,X,Y)
<=> ( X != Y
& apply(R,X,Y)
& apply(R,Y,X)
& member(X,E)
& member(Y,E) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_20,plain,
! [E,R] :
( ~ order(R,E)
<=> ( ? [X] :
( ~ apply(R,X,X)
& member(X,E) )
| ? [X,Y] : ~ definitionFOFtoCNF_0(E,R,X,Y)
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,X,Y)
& apply(R,Y,Z)
& member(X,E)
& member(Y,E)
& member(Z,E) ) ) ),
inference(simplify,[],[normalize_0_18,normalize_0_19]) ).
fof(normalize_0_21,plain,
! [E,R,X] :
( ~ definitionFOFtoCNF_1(E,R,X)
<=> ( ~ apply(R,X,X)
& member(X,E) ) ),
inference(canonicalize,[],[definition_1]) ).
fof(normalize_0_22,plain,
! [E,R] :
( ~ order(R,E)
<=> ( ? [X] : ~ definitionFOFtoCNF_1(E,R,X)
| ? [X,Y] : ~ definitionFOFtoCNF_0(E,R,X,Y)
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,X,Y)
& apply(R,Y,Z)
& member(X,E)
& member(Y,E)
& member(Z,E) ) ) ),
inference(simplify,[],[normalize_0_20,normalize_0_21]) ).
fof(normalize_0_23,plain,
! [E,R,X,Y,Z] :
( ( ~ order(R,E)
| definitionFOFtoCNF_0(E,R,X,Y) )
& ( ~ order(R,E)
| definitionFOFtoCNF_1(E,R,X) )
& ( ~ apply(R,skolemFOFtoCNF_X_2(E,R),skolemFOFtoCNF_Z(E,R))
| ~ definitionFOFtoCNF_0(E,R,skolemFOFtoCNF_X_1(E,R),skolemFOFtoCNF_Y(E,R))
| ~ definitionFOFtoCNF_1(E,R,skolemFOFtoCNF_X(E,R))
| order(R,E) )
& ( ~ definitionFOFtoCNF_0(E,R,skolemFOFtoCNF_X_1(E,R),skolemFOFtoCNF_Y(E,R))
| ~ definitionFOFtoCNF_1(E,R,skolemFOFtoCNF_X(E,R))
| apply(R,skolemFOFtoCNF_X_2(E,R),skolemFOFtoCNF_Y_1(E,R))
| order(R,E) )
& ( ~ definitionFOFtoCNF_0(E,R,skolemFOFtoCNF_X_1(E,R),skolemFOFtoCNF_Y(E,R))
| ~ definitionFOFtoCNF_1(E,R,skolemFOFtoCNF_X(E,R))
| apply(R,skolemFOFtoCNF_Y_1(E,R),skolemFOFtoCNF_Z(E,R))
| order(R,E) )
& ( ~ definitionFOFtoCNF_0(E,R,skolemFOFtoCNF_X_1(E,R),skolemFOFtoCNF_Y(E,R))
| ~ definitionFOFtoCNF_1(E,R,skolemFOFtoCNF_X(E,R))
| member(skolemFOFtoCNF_X_2(E,R),E)
| order(R,E) )
& ( ~ definitionFOFtoCNF_0(E,R,skolemFOFtoCNF_X_1(E,R),skolemFOFtoCNF_Y(E,R))
| ~ definitionFOFtoCNF_1(E,R,skolemFOFtoCNF_X(E,R))
| member(skolemFOFtoCNF_Y_1(E,R),E)
| order(R,E) )
& ( ~ definitionFOFtoCNF_0(E,R,skolemFOFtoCNF_X_1(E,R),skolemFOFtoCNF_Y(E,R))
| ~ definitionFOFtoCNF_1(E,R,skolemFOFtoCNF_X(E,R))
| member(skolemFOFtoCNF_Z(E,R),E)
| order(R,E) )
& ( ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| ~ member(X,E)
| ~ member(Y,E)
| ~ member(Z,E)
| ~ order(R,E)
| apply(R,X,Z) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [E,R,X,Y] :
( ~ order(R,E)
| definitionFOFtoCNF_0(E,R,X,Y) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [E,R,X,Y] :
( ( X != Y
| definitionFOFtoCNF_0(E,R,X,Y) )
& ( apply(R,X,Y)
| definitionFOFtoCNF_0(E,R,X,Y) )
& ( apply(R,Y,X)
| definitionFOFtoCNF_0(E,R,X,Y) )
& ( definitionFOFtoCNF_0(E,R,X,Y)
| member(X,E) )
& ( definitionFOFtoCNF_0(E,R,X,Y)
| member(Y,E) )
& ( ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| ~ definitionFOFtoCNF_0(E,R,X,Y)
| ~ member(X,E)
| ~ member(Y,E)
| X = Y ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_26,plain,
! [E,R,X,Y] :
( ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| ~ definitionFOFtoCNF_0(E,R,X,Y)
| ~ member(X,E)
| ~ member(Y,E)
| X = Y ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
skolemFOFtoCNF_M_2 != skolemFOFtoCNF_X_8,
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ least(M,R,E)
| member(M,E) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
( ~ least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_3,plain,
member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E),
inference(resolve,[$cnf( least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_5,plain,
( ~ least(M,R,E)
| lower_bound(M,R,E) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_6,plain,
( ~ least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| lower_bound(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_5:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_X_8)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_7,plain,
lower_bound(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(resolve,[$cnf( least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ lower_bound(M,R,E)
| ~ member(X,E)
| apply(R,M,X) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_9,plain,
( ~ lower_bound(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| ~ member(X_161,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_8,X_161) ),
inference(subst,[],[refute_0_8:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_X_8)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_161))]]) ).
cnf(refute_0_10,plain,
( ~ member(X_161,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_8,X_161) ),
inference(resolve,[$cnf( lower_bound(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_8,skolemFOFtoCNF_M_2) ),
inference(subst,[],[refute_0_10:[bind(X_161,$fot(skolemFOFtoCNF_M_2))]]) ).
cnf(refute_0_12,plain,
apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_8,skolemFOFtoCNF_M_2),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
order(skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
( ~ order(R,E)
| definitionFOFtoCNF_0(E,R,X,Y) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_15,plain,
( ~ order(skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_57,X_58) ),
inference(subst,[],[refute_0_14:[bind(E,$fot(skolemFOFtoCNF_E)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_57)),bind(Y,$fot(X_58))]]) ).
cnf(refute_0_16,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_57,X_58),
inference(resolve,[$cnf( order(skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_857,X_858),
inference(subst,[],[refute_0_16:[bind(X_57,$fot(X_857)),bind(X_58,$fot(X_858))]]) ).
cnf(refute_0_18,plain,
( ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| ~ definitionFOFtoCNF_0(E,R,X,Y)
| ~ member(X,E)
| ~ member(Y,E)
| X = Y ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_19,plain,
( ~ apply(skolemFOFtoCNF_R,X_857,X_858)
| ~ apply(skolemFOFtoCNF_R,X_858,X_857)
| ~ definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_857,X_858)
| ~ member(X_857,skolemFOFtoCNF_E)
| ~ member(X_858,skolemFOFtoCNF_E)
| X_857 = X_858 ),
inference(subst,[],[refute_0_18:[bind(E,$fot(skolemFOFtoCNF_E)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_857)),bind(Y,$fot(X_858))]]) ).
cnf(refute_0_20,plain,
( ~ apply(skolemFOFtoCNF_R,X_857,X_858)
| ~ apply(skolemFOFtoCNF_R,X_858,X_857)
| ~ member(X_857,skolemFOFtoCNF_E)
| ~ member(X_858,skolemFOFtoCNF_E)
| X_857 = X_858 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_857,X_858) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_8)
| ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_8,skolemFOFtoCNF_M_2)
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_8 = skolemFOFtoCNF_M_2 ),
inference(subst,[],[refute_0_20:[bind(X_857,$fot(skolemFOFtoCNF_X_8)),bind(X_858,$fot(skolemFOFtoCNF_M_2))]]) ).
cnf(refute_0_22,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_8)
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_8 = skolemFOFtoCNF_M_2 ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_8,skolemFOFtoCNF_M_2) )],[refute_0_12,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_X_8)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_24,plain,
member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E),
inference(resolve,[$cnf( least(skolemFOFtoCNF_X_8,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_5:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_26,plain,
lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(resolve,[$cnf( least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_0,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| ~ member(X_161,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,X_161) ),
inference(subst,[],[refute_0_8:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_161))]]) ).
cnf(refute_0_28,plain,
( ~ member(X_161,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,X_161) ),
inference(resolve,[$cnf( lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_8) ),
inference(subst,[],[refute_0_28:[bind(X_161,$fot(skolemFOFtoCNF_X_8))]]) ).
cnf(refute_0_30,plain,
apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_8),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_8 = skolemFOFtoCNF_M_2 ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_8) )],[refute_0_30,refute_0_22]) ).
cnf(refute_0_32,plain,
( ~ member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_8 = skolemFOFtoCNF_M_2 ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_3,refute_0_31]) ).
cnf(refute_0_33,plain,
skolemFOFtoCNF_X_8 = skolemFOFtoCNF_M_2,
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_8,skolemFOFtoCNF_E) )],[refute_0_24,refute_0_32]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_M_2 != skolemFOFtoCNF_X_8,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_35,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_36,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_37,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_X_8 != skolemFOFtoCNF_M_2
| skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_8 ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(skolemFOFtoCNF_X_8)),bind(Y0,$fot(skolemFOFtoCNF_M_2))]]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_X_8 != skolemFOFtoCNF_M_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_8) )],[refute_0_38,refute_0_34]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_8,skolemFOFtoCNF_M_2) )],[refute_0_33,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET790+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.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 09:13:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.54/0.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.71
% 0.54/0.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.54/0.71
%------------------------------------------------------------------------------