%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET788+1 : TPTP v8.1.0. Released v3.1.0.
% 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 03:37:13 EDT 2022
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 71 ( 16 unt; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 217 ( 83 ~; 88 |; 14 &)
% ( 23 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 63 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ) ).
fof(subgoal_0,plain,
( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
=> equalish(Y,X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_1,plain,
( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(Y,X)
=> equalish(X,Y) ) ),
inference(strip,[],[prove_this]) ).
fof(negate_0_0,plain,
~ ( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
=> equalish(Y,X) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X,Y] :
( ~ equalish(Y,X)
& equalish(X,Y) )
& ! [X,Y] :
( ~ equalish(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ equalish(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ equalish(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ( ~ equalish(X,Y)
| ~ a_member_of(Z,X)
| a_member_of(Z,Y) )
& ( ~ equalish(X,Y)
| ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| equalish(X,Y) )
& ( equalish(X,Y)
| a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z(X,Y),Y) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| equalish(X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [X,Y] :
( ~ equalish(Y,X)
& equalish(X,Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
( ~ equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
& equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ equalish(X,Y)
| ~ a_member_of(Z,X)
| a_member_of(Z,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ equalish(X,Y)
| ~ a_member_of(Z,Y)
| a_member_of(Z,X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( equalish(X,Y)
| a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z(X,Y),Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_11,plain,
~ equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| equalish(X,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
| ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y)
| equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ equalish(X,Y)
| ~ a_member_of(Z,X)
| a_member_of(Z,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ equalish(skolemFOFtoCNF_X,Y)
| ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),Y) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_5,plain,
( ~ equalish(X,Y)
| ~ a_member_of(Z,Y)
| a_member_of(Z,X) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ equalish(X,X_11)
| ~ a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X_11)
| a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X) ),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_11)),bind(Z,$fot(skolemFOFtoCNF_Z(X_11,X_12)))]]) ).
cnf(refute_0_7,plain,
( equalish(X,Y)
| a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z(X,Y),Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( equalish(X_11,X_12)
| a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X_11)
| a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X_12) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_11)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_9,plain,
( ~ equalish(X,X_11)
| equalish(X_11,X_12)
| a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X)
| a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X_12) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(X_11,X_12),X_11) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( ~ equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| equalish(skolemFOFtoCNF_Y,X_15)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,X_15),X_15)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,X_15),skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X)),bind(X_11,$fot(skolemFOFtoCNF_Y)),bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_11,plain,
( equalish(skolemFOFtoCNF_Y,X_15)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,X_15),X_15)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,X_15),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_11:[bind(X_15,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_13,plain,
~ equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ equalish(skolemFOFtoCNF_X,Y)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),Y) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X) )],[refute_0_14,refute_0_4]) ).
cnf(refute_0_16,plain,
( ~ equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_15:[bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_17,plain,
a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
| equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_19,refute_0_13]) ).
fof(negate_1_0,plain,
~ ( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(Y,X)
=> equalish(X,Y) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X,Y] :
( ~ equalish(X,Y)
& equalish(Y,X) )
& ! [X,Y] :
( ~ equalish(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X,Y] :
( ~ equalish(X,Y)
& equalish(Y,X) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X,Y] :
( ~ equalish(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ equalish(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [X,Y,Z] :
( ( ~ equalish(X,Y)
| ~ a_member_of(Z,X)
| a_member_of(Z,Y) )
& ( ~ equalish(X,Y)
| ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(skolemFOFtoCNF_Z_1(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z_1(X,Y),Y)
| equalish(X,Y) )
& ( equalish(X,Y)
| a_member_of(skolemFOFtoCNF_Z_1(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z_1(X,Y),Y) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X,Y,Z] :
( ~ equalish(X,Y)
| ~ a_member_of(Z,X)
| a_member_of(Z,Y) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [X,Y,Z] :
( ~ equalish(X,Y)
| ~ a_member_of(Z,Y)
| a_member_of(Z,X) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_9,plain,
! [X,Y] :
( equalish(X,Y)
| a_member_of(skolemFOFtoCNF_Z_1(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z_1(X,Y),Y) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_10,plain,
~ equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_11,plain,
! [X,Y] :
( ~ a_member_of(skolemFOFtoCNF_Z_1(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z_1(X,Y),Y)
| equalish(X,Y) ),
inference(conjunct,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ equalish(X,Y)
| ~ a_member_of(Z,X)
| a_member_of(Z,Y) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_2,plain,
( ~ equalish(skolemFOFtoCNF_Y_1,Y)
| ~ a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Y) ),
inference(subst,[],[refute_1_1:[bind(X,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_3,plain,
( ~ equalish(X,Y)
| ~ a_member_of(Z,Y)
| a_member_of(Z,X) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_4,plain,
( ~ equalish(X,X_29)
| ~ a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X_29)
| a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X) ),
inference(subst,[],[refute_1_3:[bind(Y,$fot(X_29)),bind(Z,$fot(skolemFOFtoCNF_Z_1(X_29,X_30)))]]) ).
cnf(refute_1_5,plain,
( equalish(X,Y)
| a_member_of(skolemFOFtoCNF_Z_1(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z_1(X,Y),Y) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_6,plain,
( equalish(X_29,X_30)
| a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X_29)
| a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X_30) ),
inference(subst,[],[refute_1_5:[bind(X,$fot(X_29)),bind(Y,$fot(X_30))]]) ).
cnf(refute_1_7,plain,
( ~ equalish(X,X_29)
| equalish(X_29,X_30)
| a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X)
| a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X_30) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z_1(X_29,X_30),X_29) )],[refute_1_6,refute_1_4]) ).
cnf(refute_1_8,plain,
( ~ equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1)
| equalish(skolemFOFtoCNF_X_1,X_33)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,X_33),X_33)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,X_33),skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(skolemFOFtoCNF_Y_1)),bind(X_29,$fot(skolemFOFtoCNF_X_1)),bind(X_30,$fot(X_33))]]) ).
cnf(refute_1_9,plain,
( equalish(skolemFOFtoCNF_X_1,X_33)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,X_33),X_33)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,X_33),skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1) )],[refute_1_0,refute_1_8]) ).
cnf(refute_1_10,plain,
( equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_9:[bind(X_33,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_11,plain,
~ equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_12,plain,
a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ equalish(skolemFOFtoCNF_Y_1,Y)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Y) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1) )],[refute_1_12,refute_1_2]) ).
cnf(refute_1_14,plain,
( ~ equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1)
| a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_1_13:[bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_15,plain,
a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1) )],[refute_1_0,refute_1_14]) ).
cnf(refute_1_16,plain,
( ~ a_member_of(skolemFOFtoCNF_Z_1(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z_1(X,Y),Y)
| equalish(X,Y) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_17,plain,
( ~ a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| ~ a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_16:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_18,plain,
( ~ a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1)
| equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1) )],[refute_1_12,refute_1_17]) ).
cnf(refute_1_19,plain,
~ a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( equalish(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_18,refute_1_11]) ).
cnf(refute_1_20,plain,
$false,
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_1) )],[refute_1_15,refute_1_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET788+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jul 11 06:42:38 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.35
%------------------------------------------------------------------------------