TSTP Solution File: SYN077+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN077+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 : Thu Jul 21 08:59:22 EDT 2022
% Result : Theorem 1.99s 2.14s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of formulae : 73 ( 9 unt; 0 def)
% Number of atoms : 203 ( 17 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 234 ( 104 ~; 99 |; 17 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 44 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel54_1,axiom,
! [Y] :
? [Z] :
! [X] :
( big_f(X,Z)
<=> X = Y ) ).
fof(pel54,conjecture,
~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( big_f(Y,U)
& ~ ? [Z] :
( big_f(Z,U)
& big_f(Z,Y) ) ) ) ) ).
fof(subgoal_0,plain,
! [W] :
~ ! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( big_f(Y,U)
& ~ ? [Z] :
( big_f(Z,U)
& big_f(Z,Y) ) ) ) ),
inference(strip,[],[pel54]) ).
fof(negate_0_0,plain,
~ ! [W] :
~ ! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( big_f(Y,U)
& ~ ? [Z] :
( big_f(Z,U)
& big_f(Z,Y) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Y] :
? [Z] :
! [X] :
( X != Y
<=> ~ big_f(X,Z) ),
inference(canonicalize,[],[pel54_1]) ).
fof(normalize_0_1,plain,
! [Y] :
? [Z] :
! [X] :
( X != Y
<=> ~ big_f(X,Z) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y,X] :
( X != Y
<=> ~ big_f(X,skolemFOFtoCNF_Z(Y)) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( X != Y
<=> ~ big_f(X,skolemFOFtoCNF_Z(Y)) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ( X != Y
| big_f(X,skolemFOFtoCNF_Z(Y)) )
& ( ~ big_f(X,skolemFOFtoCNF_Z(Y))
| X = Y ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( X != Y
| big_f(X,skolemFOFtoCNF_Z(Y)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [W] :
! [X] :
( ~ big_f(X,W)
<=> ? [U] :
( big_f(X,U)
& ! [Y] :
( ~ big_f(Y,U)
| ? [Z] :
( big_f(Z,U)
& big_f(Z,Y) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ big_f(X,skolemFOFtoCNF_W)
<=> ? [U] :
( big_f(X,U)
& ! [Y] :
( ~ big_f(Y,U)
| ? [Z] :
( big_f(Z,U)
& big_f(Z,Y) ) ) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ big_f(X,skolemFOFtoCNF_W)
<=> ? [U] :
( big_f(X,U)
& ! [Y] :
( ~ big_f(Y,U)
| ? [Z] :
( big_f(Z,U)
& big_f(Z,Y) ) ) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [U,X,Y,Z] :
( ( big_f(X,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W) )
& ( ~ big_f(X,U)
| ~ big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(U),U) )
& ( ~ big_f(Y,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X,Y),Y) )
& ( ~ big_f(Y,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X,Y),skolemFOFtoCNF_U(X)) )
& ( ~ big_f(X,U)
| ~ big_f(X,skolemFOFtoCNF_W)
| ~ big_f(Z,U)
| ~ big_f(Z,skolemFOFtoCNF_Y(U)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [U,X,Z] :
( ~ big_f(X,U)
| ~ big_f(X,skolemFOFtoCNF_W)
| ~ big_f(Z,U)
| ~ big_f(Z,skolemFOFtoCNF_Y(U)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [U,X] :
( ~ big_f(X,U)
| ~ big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(U),U) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_12,plain,
! [X] :
( big_f(X,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ big_f(Y,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X,Y),Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ big_f(Y,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X,Y),skolemFOFtoCNF_U(X)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ big_f(X,skolemFOFtoCNF_Z(Y))
| X = Y ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
( X != Y
| big_f(X,skolemFOFtoCNF_Z(Y)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( Y != Y
| big_f(Y,skolemFOFtoCNF_Z(Y)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(Y))]]) ).
cnf(refute_0_2,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_3,plain,
big_f(Y,skolemFOFtoCNF_Z(Y)),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),
inference(subst,[],[refute_0_3:[bind(Y,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_5,plain,
( ~ big_f(X,U)
| ~ big_f(X,skolemFOFtoCNF_W)
| ~ big_f(Z,U)
| ~ big_f(Z,skolemFOFtoCNF_Y(U)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)))
| ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
| ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W)
| ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_5:[bind(U,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))),bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))))]]) ).
cnf(refute_0_7,plain,
big_f(X_6,skolemFOFtoCNF_Z(X_6)),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_6))]]) ).
cnf(refute_0_8,plain,
( ~ big_f(X,U)
| ~ big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(U),U) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ big_f(X_6,skolemFOFtoCNF_W)
| ~ big_f(X_6,skolemFOFtoCNF_Z(X_6))
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(X_6)),skolemFOFtoCNF_Z(X_6)) ),
inference(subst,[],[refute_0_8:[bind(U,$fot(skolemFOFtoCNF_Z(X_6))),bind(X,$fot(X_6))]]) ).
cnf(refute_0_10,plain,
( ~ big_f(X_6,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(X_6)),skolemFOFtoCNF_Z(X_6)) ),
inference(resolve,[$cnf( big_f(X_6,skolemFOFtoCNF_Z(X_6)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_10:[bind(X_6,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_12,plain,
( big_f(X,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
( big_f(X_10,skolemFOFtoCNF_U(X_10))
| big_f(X_10,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_14,plain,
( ~ big_f(Y,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X,Y),Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ big_f(X_10,skolemFOFtoCNF_U(X_10))
| big_f(X_10,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X_10,X_10),X_10) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_10)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_16,plain,
( big_f(X_10,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X_10,X_10),X_10) ),
inference(resolve,[$cnf( big_f(X_10,skolemFOFtoCNF_U(X_10)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_16:[bind(X_10,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_18,plain,
( big_f(X_14,skolemFOFtoCNF_U(X_14))
| big_f(X_14,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_19,plain,
( ~ big_f(Y,skolemFOFtoCNF_U(X))
| big_f(X,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X,Y),skolemFOFtoCNF_U(X)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( ~ big_f(X_14,skolemFOFtoCNF_U(X_14))
| big_f(X_14,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X_14,X_14),skolemFOFtoCNF_U(X_14)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_14)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
( big_f(X_14,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(X_14,X_14),skolemFOFtoCNF_U(X_14)) ),
inference(resolve,[$cnf( big_f(X_14,skolemFOFtoCNF_U(X_14)) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_21:[bind(X_14,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_23,plain,
( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))))]]) ).
cnf(refute_0_24,plain,
( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),U)
| ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(U),U) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_25,plain,
( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),U)
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(U),U) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_25:[bind(U,$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_27,plain,
( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))))]]) ).
cnf(refute_0_30,plain,
( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ big_f(X_49,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| ~ big_f(X_49,skolemFOFtoCNF_W)
| ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) ),
inference(subst,[],[refute_0_5:[bind(U,$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),bind(X,$fot(X_49)),bind(Z,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)))))]]) ).
cnf(refute_0_32,plain,
( ~ big_f(X_49,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| ~ big_f(X_49,skolemFOFtoCNF_W)
| ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ big_f(X_113,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| ~ big_f(X_113,skolemFOFtoCNF_W)
| ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_32:[bind(X_49,$fot(X_113))]]) ).
cnf(refute_0_34,plain,
( ~ big_f(X_113,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| ~ big_f(X_113,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
| ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_34:[bind(X_113,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_36,plain,
( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_22,refute_0_35]) ).
cnf(refute_0_37,plain,
big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_17,refute_0_36]) ).
cnf(refute_0_38,plain,
big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_11]) ).
cnf(refute_0_39,plain,
( ~ big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)))
| ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
| ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) )],[refute_0_38,refute_0_6]) ).
cnf(refute_0_40,plain,
( ~ big_f(X,skolemFOFtoCNF_Z(Y))
| X = Y ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_41,plain,
( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
| skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) = skolemFOFtoCNF_W ),
inference(subst,[],[refute_0_40:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)))),bind(Y,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) = skolemFOFtoCNF_W,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) != skolemFOFtoCNF_W
| ~ big_f(Z,skolemFOFtoCNF_W)
| big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) ),
introduced(tautology,[equality,[$cnf( ~ big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) ),[1],$fot(skolemFOFtoCNF_W)]]) ).
cnf(refute_0_44,plain,
( ~ big_f(Z,skolemFOFtoCNF_W)
| big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ big_f(Z,skolemFOFtoCNF_W)
| ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
| ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) )],[refute_0_44,refute_0_39]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) != skolemFOFtoCNF_W
| ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
introduced(tautology,[equality,[$cnf( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),[0],$fot(skolemFOFtoCNF_W)]]) ).
cnf(refute_0_47,plain,
( ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) )],[refute_0_42,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ big_f(Z,skolemFOFtoCNF_W)
| ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
| ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) )],[refute_0_47,refute_0_45]) ).
cnf(refute_0_49,plain,
( ~ big_f(Z,skolemFOFtoCNF_W)
| ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
| ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_49:[bind(Z,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_51,plain,
~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) )],[refute_0_4,refute_0_50]) ).
cnf(refute_0_52,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN077+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 12 04:27:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.99/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.99/2.14
% 1.99/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.99/2.15
%------------------------------------------------------------------------------