TSTP Solution File: SET791+4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 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 03:37:15 EDT 2022
% Result : Theorem 0.49s 0.66s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 86 ( 14 unt; 2 def)
% Number of atoms : 352 ( 34 equ)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 424 ( 158 ~; 155 |; 81 &)
% ( 19 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 199 ( 9 sgn 119 !; 32 ?)
% 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(upper_bound,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ).
fof(greatest,axiom,
! [R,E,M] :
( greatest(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,X,M) ) ) ) ).
fof(max,axiom,
! [R,E,M] :
( max(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,M,X) )
=> M = X ) ) ) ).
fof(thIV3,conjecture,
! [R,E,M] :
( ( order(R,E)
& greatest(M,R,E) )
=> max(M,R,E) ) ).
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)
& greatest(M,R,E) )
=> max(M,R,E) ),
inference(strip,[],[thIV3]) ).
fof(negate_0_0,plain,
~ ! [R,E,M] :
( ( order(R,E)
& greatest(M,R,E) )
=> max(M,R,E) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [E,M,R] :
( ~ max(M,R,E)
<=> ( ~ member(M,E)
| ? [X] :
( M != X
& apply(R,M,X)
& member(X,E) ) ) ),
inference(canonicalize,[],[max]) ).
fof(normalize_0_1,plain,
! [E,M,R] :
( ~ max(M,R,E)
<=> ( ~ member(M,E)
| ? [X] :
( M != X
& apply(R,M,X)
& member(X,E) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [E,M,R,X] :
( ( ~ max(M,R,E)
| member(M,E) )
& ( M != skolemFOFtoCNF_X_6(E,M,R)
| ~ member(M,E)
| max(M,R,E) )
& ( ~ member(M,E)
| apply(R,M,skolemFOFtoCNF_X_6(E,M,R))
| max(M,R,E) )
& ( ~ member(M,E)
| max(M,R,E)
| member(skolemFOFtoCNF_X_6(E,M,R),E) )
& ( ~ apply(R,M,X)
| ~ max(M,R,E)
| ~ member(X,E)
| M = X ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,M,R] :
( M != skolemFOFtoCNF_X_6(E,M,R)
| ~ member(M,E)
| max(M,R,E) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [E,M,R] :
( ~ max(M,R,E)
& greatest(M,R,E)
& order(R,E) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
& greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
& order(skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [E,M,R] :
( ~ greatest(M,R,E)
<=> ( ~ member(M,E)
| ? [X] :
( ~ apply(R,X,M)
& member(X,E) ) ) ),
inference(canonicalize,[],[greatest]) ).
fof(normalize_0_8,plain,
! [E,M,R] :
( ~ upper_bound(M,R,E)
<=> ? [X] :
( ~ apply(R,X,M)
& member(X,E) ) ),
inference(canonicalize,[],[upper_bound]) ).
fof(normalize_0_9,plain,
! [E,M,R] :
( ~ upper_bound(M,R,E)
<=> ? [X] :
( ~ apply(R,X,M)
& member(X,E) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [E,M,R] :
( ~ greatest(M,R,E)
<=> ( ~ member(M,E)
| ~ upper_bound(M,R,E) ) ),
inference(simplify,[],[normalize_0_7,normalize_0_9]) ).
fof(normalize_0_11,plain,
! [E,M,R] :
( ~ greatest(M,R,E)
<=> ( ~ member(M,E)
| ~ upper_bound(M,R,E) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [E,M,R] :
( ( ~ greatest(M,R,E)
| member(M,E) )
& ( ~ greatest(M,R,E)
| upper_bound(M,R,E) )
& ( ~ member(M,E)
| ~ upper_bound(M,R,E)
| greatest(M,R,E) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [E,M,R] :
( ~ greatest(M,R,E)
| member(M,E) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [E,M,R] :
( ~ member(M,E)
| max(M,R,E)
| member(skolemFOFtoCNF_X_6(E,M,R),E) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_15,plain,
! [E,M,R] :
( ~ member(M,E)
| apply(R,M,skolemFOFtoCNF_X_6(E,M,R))
| max(M,R,E) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_16,plain,
! [E,M,R] :
( ~ greatest(M,R,E)
| upper_bound(M,R,E) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_17,plain,
! [E,M,R,X] :
( ( ~ apply(R,skolemFOFtoCNF_X_4(E,M,R),M)
| upper_bound(M,R,E) )
& ( member(skolemFOFtoCNF_X_4(E,M,R),E)
| upper_bound(M,R,E) )
& ( ~ member(X,E)
| ~ upper_bound(M,R,E)
| apply(R,X,M) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_18,plain,
! [E,M,R,X] :
( ~ member(X,E)
| ~ upper_bound(M,R,E)
| apply(R,X,M) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
order(skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_20,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_21,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_20]) ).
fof(normalize_0_22,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_23,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_21,normalize_0_22]) ).
fof(normalize_0_24,plain,
! [E,R,X] :
( ~ definitionFOFtoCNF_1(E,R,X)
<=> ( ~ apply(R,X,X)
& member(X,E) ) ),
inference(canonicalize,[],[definition_1]) ).
fof(normalize_0_25,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_23,normalize_0_24]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [E,R,X,Y] :
( ~ order(R,E)
| definitionFOFtoCNF_0(E,R,X,Y) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,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_22]) ).
fof(normalize_0_29,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_28]) ).
fof(normalize_0_30,plain,
~ max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( M != skolemFOFtoCNF_X_6(E,M,R)
| ~ member(M,E)
| max(M,R,E) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_M_2 != skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_0:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_2,plain,
greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ greatest(M,R,E)
| member(M,E) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_4,plain,
( ~ greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_3:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_5,plain,
member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E),
inference(resolve,[$cnf( greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(M,E)
| max(M,R,E)
| member(skolemFOFtoCNF_X_6(E,M,R),E) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| max(skolemFOFtoCNF_M_2,X_124,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(X_124))]]) ).
cnf(refute_0_8,plain,
( max(skolemFOFtoCNF_M_2,X_124,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_8:[bind(X_124,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_10,plain,
( ~ member(M,E)
| apply(R,M,skolemFOFtoCNF_X_6(E,M,R))
| max(M,R,E) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| apply(X_145,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_145))
| max(skolemFOFtoCNF_M_2,X_145,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_10:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(X_145))]]) ).
cnf(refute_0_12,plain,
( apply(X_145,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_145))
| max(skolemFOFtoCNF_M_2,X_145,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R))
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_12:[bind(X_145,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_14,plain,
( ~ greatest(M,R,E)
| upper_bound(M,R,E) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
( ~ greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| upper_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_14:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_16,plain,
upper_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(resolve,[$cnf( greatest(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(X,E)
| ~ upper_bound(M,R,E)
| apply(R,X,M) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_18,plain,
( ~ member(X_150,skolemFOFtoCNF_E)
| ~ upper_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_150,skolemFOFtoCNF_M_2) ),
inference(subst,[],[refute_0_17:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_150))]]) ).
cnf(refute_0_19,plain,
( ~ member(X_150,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_150,skolemFOFtoCNF_M_2) ),
inference(resolve,[$cnf( upper_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_M_2) ),
inference(subst,[],[refute_0_19:[bind(X_150,$fot(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124)))]]) ).
cnf(refute_0_21,plain,
( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_M_2)
| max(skolemFOFtoCNF_M_2,X_124,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E) )],[refute_0_8,refute_0_20]) ).
cnf(refute_0_22,plain,
order(skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_23,plain,
( ~ order(R,E)
| definitionFOFtoCNF_0(E,R,X,Y) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_24,plain,
( ~ order(skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_57,X_58) ),
inference(subst,[],[refute_0_23:[bind(E,$fot(skolemFOFtoCNF_E)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_57)),bind(Y,$fot(X_58))]]) ).
cnf(refute_0_25,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_57,X_58),
inference(resolve,[$cnf( order(skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_648,X_649),
inference(subst,[],[refute_0_25:[bind(X_57,$fot(X_648)),bind(X_58,$fot(X_649))]]) ).
cnf(refute_0_27,plain,
( ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| ~ definitionFOFtoCNF_0(E,R,X,Y)
| ~ member(X,E)
| ~ member(Y,E)
| X = Y ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_28,plain,
( ~ apply(skolemFOFtoCNF_R,X_648,X_649)
| ~ apply(skolemFOFtoCNF_R,X_649,X_648)
| ~ definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_648,X_649)
| ~ member(X_648,skolemFOFtoCNF_E)
| ~ member(X_649,skolemFOFtoCNF_E)
| X_648 = X_649 ),
inference(subst,[],[refute_0_27:[bind(E,$fot(skolemFOFtoCNF_E)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_648)),bind(Y,$fot(X_649))]]) ).
cnf(refute_0_29,plain,
( ~ apply(skolemFOFtoCNF_R,X_648,X_649)
| ~ apply(skolemFOFtoCNF_R,X_649,X_648)
| ~ member(X_648,skolemFOFtoCNF_E)
| ~ member(X_649,skolemFOFtoCNF_E)
| X_648 = X_649 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_E,skolemFOFtoCNF_R,X_648,X_649) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124))
| ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_M_2)
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124) = skolemFOFtoCNF_M_2 ),
inference(subst,[],[refute_0_29:[bind(X_648,$fot(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124))),bind(X_649,$fot(skolemFOFtoCNF_M_2))]]) ).
cnf(refute_0_31,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124))
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124) = skolemFOFtoCNF_M_2
| max(skolemFOFtoCNF_M_2,X_124,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_M_2) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124))
| ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124),skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,X_124) = skolemFOFtoCNF_M_2
| max(skolemFOFtoCNF_M_2,X_124,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_5,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R))
| ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_32:[bind(X_124,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_34,plain,
( ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) )],[refute_0_13,refute_0_33]) ).
cnf(refute_0_35,plain,
~ max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_36,plain,
( ~ member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_E)
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2 ),
inference(resolve,[$cnf( max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_E) )],[refute_0_9,refute_0_36]) ).
cnf(refute_0_38,plain,
skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2,
inference(resolve,[$cnf( max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_37,refute_0_35]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_M_2 != skolemFOFtoCNF_M_2
| skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) != skolemFOFtoCNF_M_2
| skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) ),[1],$fot(skolemFOFtoCNF_M_2)]]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_M_2 != skolemFOFtoCNF_M_2
| skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_M_2) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_M_2 != skolemFOFtoCNF_M_2
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_6(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) )],[refute_0_40,refute_0_1]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_M_2 = skolemFOFtoCNF_M_2,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_M_2)]]) ).
cnf(refute_0_43,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_5,refute_0_43]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( max(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_44,refute_0_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 10 11:56:20 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.49/0.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.66
% 0.49/0.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.49/0.67
%------------------------------------------------------------------------------