%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET794+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 03:37:16 EDT 2022
% Result : Theorem 0.38s 0.55s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 12 unt; 0 def)
% Number of atoms : 253 ( 24 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 288 ( 111 ~; 119 |; 38 &)
% ( 13 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 157 ( 1 sgn 85 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(total_order,axiom,
! [R,E] :
( total_order(R,E)
<=> ( order(R,E)
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( apply(R,X,Y)
| apply(R,Y,X) ) ) ) ) ).
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(min,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ) ).
fof(thIV6,conjecture,
! [R,E,M] :
( ( total_order(R,E)
& min(M,R,E) )
=> least(M,R,E) ) ).
fof(subgoal_0,plain,
! [R,E,M] :
( ( total_order(R,E)
& min(M,R,E) )
=> least(M,R,E) ),
inference(strip,[],[thIV6]) ).
fof(negate_0_0,plain,
~ ! [R,E,M] :
( ( total_order(R,E)
& min(M,R,E) )
=> least(M,R,E) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_1,plain,
! [E,M,R] :
( ~ lower_bound(M,R,E)
<=> ? [X] :
( ~ apply(R,M,X)
& member(X,E) ) ),
inference(canonicalize,[],[lower_bound]) ).
fof(normalize_0_2,plain,
! [E,M,R] :
( ~ lower_bound(M,R,E)
<=> ? [X] :
( ~ apply(R,M,X)
& member(X,E) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,M,R] :
( ~ least(M,R,E)
<=> ( ~ lower_bound(M,R,E)
| ~ member(M,E) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
! [E,M,R] :
( ~ least(M,R,E)
<=> ( ~ lower_bound(M,R,E)
| ~ member(M,E) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [E,M,R] :
( ~ lower_bound(M,R,E)
| ~ member(M,E)
| least(M,R,E) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_2]) ).
fof(normalize_0_8,plain,
! [E,M,R] :
( ~ apply(R,M,skolemFOFtoCNF_X_5(E,M,R))
| lower_bound(M,R,E) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [E,M,R] :
( lower_bound(M,R,E)
| member(skolemFOFtoCNF_X_5(E,M,R),E) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
? [E,M,R] :
( ~ least(M,R,E)
& min(M,R,E)
& total_order(R,E) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
& min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
& total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [E,M,R] :
( ~ min(M,R,E)
<=> ( ~ member(M,E)
| ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) ) ) ),
inference(canonicalize,[],[min]) ).
fof(normalize_0_14,plain,
! [E,M,R] :
( ~ min(M,R,E)
<=> ( ~ member(M,E)
| ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) ) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [E,M,R,X] :
( ( ~ min(M,R,E)
| member(M,E) )
& ( M != skolemFOFtoCNF_X_7(E,M,R)
| ~ member(M,E)
| min(M,R,E) )
& ( ~ member(M,E)
| apply(R,skolemFOFtoCNF_X_7(E,M,R),M)
| min(M,R,E) )
& ( ~ member(M,E)
| member(skolemFOFtoCNF_X_7(E,M,R),E)
| min(M,R,E) )
& ( ~ apply(R,X,M)
| ~ member(X,E)
| ~ min(M,R,E)
| M = X ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [E,M,R] :
( ~ min(M,R,E)
| member(M,E) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_18,plain,
! [E,R] :
( ~ total_order(R,E)
<=> ( ~ order(R,E)
| ? [X,Y] :
( ~ apply(R,X,Y)
& ~ apply(R,Y,X)
& member(X,E)
& member(Y,E) ) ) ),
inference(canonicalize,[],[total_order]) ).
fof(normalize_0_19,plain,
! [E,R] :
( ~ total_order(R,E)
<=> ( ~ order(R,E)
| ? [X,Y] :
( ~ apply(R,X,Y)
& ~ apply(R,Y,X)
& member(X,E)
& member(Y,E) ) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [E,R,X,Y] :
( ( ~ total_order(R,E)
| order(R,E) )
& ( ~ apply(R,skolemFOFtoCNF_X_3(E,R),skolemFOFtoCNF_Y_2(E,R))
| ~ order(R,E)
| total_order(R,E) )
& ( ~ apply(R,skolemFOFtoCNF_Y_2(E,R),skolemFOFtoCNF_X_3(E,R))
| ~ order(R,E)
| total_order(R,E) )
& ( ~ order(R,E)
| member(skolemFOFtoCNF_X_3(E,R),E)
| total_order(R,E) )
& ( ~ order(R,E)
| member(skolemFOFtoCNF_Y_2(E,R),E)
| total_order(R,E) )
& ( ~ member(X,E)
| ~ member(Y,E)
| ~ total_order(R,E)
| apply(R,X,Y)
| apply(R,Y,X) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [E,R,X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ total_order(R,E)
| apply(R,X,Y)
| apply(R,Y,X) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [E,M,R,X] :
( ~ apply(R,X,M)
| ~ member(X,E)
| ~ min(M,R,E)
| M = X ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_23,plain,
~ least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ lower_bound(M,R,E)
| ~ member(M,E)
| least(M,R,E) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| least(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,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_2,plain,
( ~ apply(R,M,skolemFOFtoCNF_X_5(E,M,R))
| lower_bound(M,R,E) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R))
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_2:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_4,plain,
( lower_bound(M,R,E)
| member(skolemFOFtoCNF_X_5(E,M,R),E) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( lower_bound(M,R,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R),skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_4:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_6,plain,
min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( ~ min(M,R,E)
| member(M,E) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_8,plain,
( ~ min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_7:[bind(E,$fot(skolemFOFtoCNF_E)),bind(M,$fot(skolemFOFtoCNF_M_2)),bind(R,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_9,plain,
member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E),
inference(resolve,[$cnf( min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_11,plain,
( ~ member(X,E)
| ~ member(Y,E)
| ~ total_order(R,E)
| apply(R,X,Y)
| apply(R,Y,X) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_12,plain,
( ~ member(X_398,skolemFOFtoCNF_E)
| ~ member(X_399,skolemFOFtoCNF_E)
| ~ total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_398,X_399)
| apply(skolemFOFtoCNF_R,X_399,X_398) ),
inference(subst,[],[refute_0_11:[bind(E,$fot(skolemFOFtoCNF_E)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_399)),bind(Y,$fot(X_398))]]) ).
cnf(refute_0_13,plain,
( ~ member(X_398,skolemFOFtoCNF_E)
| ~ member(X_399,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_398,X_399)
| apply(skolemFOFtoCNF_R,X_399,X_398) ),
inference(resolve,[$cnf( total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ member(X_401,skolemFOFtoCNF_E)
| ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_401,skolemFOFtoCNF_M_2)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,X_401) ),
inference(subst,[],[refute_0_13:[bind(X_398,$fot(skolemFOFtoCNF_M_2)),bind(X_399,$fot(X_401))]]) ).
cnf(refute_0_15,plain,
( ~ member(X_401,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_401,skolemFOFtoCNF_M_2)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,X_401) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R),skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R))
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R),skolemFOFtoCNF_M_2) ),
inference(subst,[],[refute_0_15:[bind(X_401,$fot(skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R)))]]) ).
cnf(refute_0_17,plain,
( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R))
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R),skolemFOFtoCNF_M_2)
| lower_bound(M,R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,M,R),skolemFOFtoCNF_E) )],[refute_0_5,refute_0_16]) ).
cnf(refute_0_18,plain,
( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504))
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504),skolemFOFtoCNF_M_2)
| lower_bound(X_503,X_504,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_17:[bind(M,$fot(X_503)),bind(R,$fot(X_504))]]) ).
cnf(refute_0_19,plain,
( lower_bound(M,R,X_185)
| member(skolemFOFtoCNF_X_5(X_185,M,R),X_185) ),
inference(subst,[],[refute_0_4:[bind(E,$fot(X_185))]]) ).
cnf(refute_0_20,plain,
( ~ apply(R,X,M)
| ~ member(X,E)
| ~ min(M,R,E)
| M = X ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_21,plain,
( ~ apply(X_187,skolemFOFtoCNF_X_5(X_185,M,R),X_186)
| ~ member(skolemFOFtoCNF_X_5(X_185,M,R),X_185)
| ~ min(X_186,X_187,X_185)
| X_186 = skolemFOFtoCNF_X_5(X_185,M,R) ),
inference(subst,[],[refute_0_20:[bind(E,$fot(X_185)),bind(M,$fot(X_186)),bind(R,$fot(X_187)),bind(X,$fot(skolemFOFtoCNF_X_5(X_185,M,R)))]]) ).
cnf(refute_0_22,plain,
( ~ apply(X_187,skolemFOFtoCNF_X_5(X_185,M,R),X_186)
| ~ min(X_186,X_187,X_185)
| X_186 = skolemFOFtoCNF_X_5(X_185,M,R)
| lower_bound(M,R,X_185) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_5(X_185,M,R),X_185) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504),skolemFOFtoCNF_M_2)
| ~ min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504)
| lower_bound(X_503,X_504,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_22:[bind(M,$fot(X_503)),bind(R,$fot(X_504)),bind(X_185,$fot(skolemFOFtoCNF_E)),bind(X_186,$fot(skolemFOFtoCNF_M_2)),bind(X_187,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_24,plain,
( ~ min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504))
| lower_bound(X_503,X_504,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504),skolemFOFtoCNF_M_2) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,X_503,X_504))
| lower_bound(X_503,X_504,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( min(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_6,refute_0_24]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R))
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_25:[bind(X_503,$fot(skolemFOFtoCNF_M_2)),bind(X_504,$fot(skolemFOFtoCNF_R))]]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_M_2 = skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_29,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_30,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_M_2 != skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)
| skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(skolemFOFtoCNF_M_2)),bind(Y0,$fot(skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)))]]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) = skolemFOFtoCNF_M_2
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R) != skolemFOFtoCNF_M_2
| ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) ),
introduced(tautology,[equality,[$cnf( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) ),[2],$fot(skolemFOFtoCNF_M_2)]]) ).
cnf(refute_0_34,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R))
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R),skolemFOFtoCNF_M_2) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2)
| lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_X_5(skolemFOFtoCNF_E,skolemFOFtoCNF_M_2,skolemFOFtoCNF_R)) )],[refute_0_34,refute_0_3]) ).
cnf(refute_0_36,plain,
( ~ member(X_89,skolemFOFtoCNF_E)
| ~ total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_89,X_89) ),
inference(subst,[],[refute_0_11:[bind(E,$fot(skolemFOFtoCNF_E)),bind(R,$fot(skolemFOFtoCNF_R)),bind(X,$fot(X_89)),bind(Y,$fot(X_89))]]) ).
cnf(refute_0_37,plain,
( ~ member(X_89,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,X_89,X_89) ),
inference(resolve,[$cnf( total_order(skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_10,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2) ),
inference(subst,[],[refute_0_37:[bind(X_89,$fot(skolemFOFtoCNF_M_2))]]) ).
cnf(refute_0_39,plain,
apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_9,refute_0_38]) ).
cnf(refute_0_40,plain,
lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(resolve,[$cnf( apply(skolemFOFtoCNF_R,skolemFOFtoCNF_M_2,skolemFOFtoCNF_M_2) )],[refute_0_39,refute_0_35]) ).
cnf(refute_0_41,plain,
( ~ member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E)
| least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( lower_bound(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_40,refute_0_1]) ).
cnf(refute_0_42,plain,
least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(resolve,[$cnf( member(skolemFOFtoCNF_M_2,skolemFOFtoCNF_E) )],[refute_0_9,refute_0_41]) ).
cnf(refute_0_43,plain,
~ least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( least(skolemFOFtoCNF_M_2,skolemFOFtoCNF_R,skolemFOFtoCNF_E) )],[refute_0_42,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET794+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 11:02:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.55
% 0.38/0.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.40/0.55
%------------------------------------------------------------------------------