TSTP Solution File: SYN067+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 08:59:13 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 126 ( 25 unt; 0 def)
% Number of atoms : 521 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 616 ( 221 ~; 209 |; 161 &)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-1 aty)
% Number of variables : 227 ( 0 sgn 97 !; 102 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel38,conjecture,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) )
& ( ~ big_p(a)
| ~ ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) )
| ? [Z2,W2] :
( big_p(Z2)
& big_r(X1,W2)
& big_r(W2,Z2) ) ) ) ) ).
fof(subgoal_0,plain,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) )
=> ! [X1] :
( ( ~ ~ big_p(a)
& ~ big_p(X1) )
=> ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) ) ),
inference(strip,[],[pel38]) ).
fof(subgoal_1,plain,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) )
=> ! [X1] :
( ( ( ~ big_p(a)
| big_p(X1)
| ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) )
& ~ ~ big_p(a)
& ~ ~ ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) ) )
=> ? [Z2,W2] :
( big_p(Z2)
& big_r(X1,W2)
& big_r(W2,Z2) ) ) ),
inference(strip,[],[pel38]) ).
fof(subgoal_2,plain,
( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) )
& ( ~ big_p(a)
| ~ ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) )
| ? [Z2,W2] :
( big_p(Z2)
& big_r(X1,W2)
& big_r(W2,Z2) ) ) )
=> ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) ) ),
inference(strip,[],[pel38]) ).
fof(negate_0_0,plain,
~ ( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) )
=> ! [X1] :
( ( ~ ~ big_p(a)
& ~ big_p(X1) )
=> ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X1] :
( ~ big_p(X1)
& big_p(a)
& ! [W1,Z1] :
( ~ big_p(Z1)
| ~ big_r(W1,Z1)
| ~ big_r(X1,W1) ) )
& ! [X] :
( ~ big_p(a)
| ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ big_p(a)
| ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X1] :
( ~ big_p(X1)
& big_p(a)
& ! [W1,Z1] :
( ~ big_p(Z1)
| ~ big_r(W1,Z1)
| ~ big_r(X1,W1) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_3,plain,
( ~ big_p(skolemFOFtoCNF_X1)
& big_p(a)
& ! [W1,Z1] :
( ~ big_p(Z1)
| ~ big_r(W1,Z1)
| ~ big_r(skolemFOFtoCNF_X1,W1) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
big_p(a),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ),
inference(simplify,[],[normalize_0_1,normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( big_p(X)
| big_p(skolemFOFtoCNF_Z(X)) )
& ( big_p(X)
| big_r(X,skolemFOFtoCNF_W(X)) )
& ( big_p(X)
| big_r(skolemFOFtoCNF_W(X),skolemFOFtoCNF_Z(X)) )
& ( ~ big_p(Y)
| ~ big_r(X,Y)
| big_p(skolemFOFtoCNF_Z(X)) )
& ( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(X,skolemFOFtoCNF_W(X)) )
& ( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(skolemFOFtoCNF_W(X),skolemFOFtoCNF_Z(X)) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( big_p(X)
| big_p(skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] :
( big_p(X)
| big_r(X,skolemFOFtoCNF_W(X)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
! [X] :
( big_p(X)
| big_r(skolemFOFtoCNF_W(X),skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_11,plain,
! [W1,Z1] :
( ~ big_p(Z1)
| ~ big_r(W1,Z1)
| ~ big_r(skolemFOFtoCNF_X1,W1) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_12,plain,
! [W1,Z1] :
( ~ big_p(Z1)
| ~ big_r(W1,Z1)
| ~ big_r(skolemFOFtoCNF_X1,W1) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ big_p(skolemFOFtoCNF_X1),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( big_p(X)
| big_p(skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
( big_p(skolemFOFtoCNF_X1)
| big_p(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_2,plain,
( big_p(X)
| big_r(X,skolemFOFtoCNF_W(X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( big_p(skolemFOFtoCNF_X1)
| big_r(skolemFOFtoCNF_X1,skolemFOFtoCNF_W(skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_4,plain,
( big_p(X)
| big_r(skolemFOFtoCNF_W(X),skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( ~ big_p(Z1)
| ~ big_r(W1,Z1)
| ~ big_r(skolemFOFtoCNF_X1,W1) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( ~ big_p(skolemFOFtoCNF_Z(X))
| ~ big_r(skolemFOFtoCNF_W(X),skolemFOFtoCNF_Z(X))
| ~ big_r(skolemFOFtoCNF_X1,skolemFOFtoCNF_W(X)) ),
inference(subst,[],[refute_0_5:[bind(W1,$fot(skolemFOFtoCNF_W(X))),bind(Z1,$fot(skolemFOFtoCNF_Z(X)))]]) ).
cnf(refute_0_7,plain,
( ~ big_p(skolemFOFtoCNF_Z(X))
| ~ big_r(skolemFOFtoCNF_X1,skolemFOFtoCNF_W(X))
| big_p(X) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_W(X),skolemFOFtoCNF_Z(X)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ big_p(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1))
| ~ big_r(skolemFOFtoCNF_X1,skolemFOFtoCNF_W(skolemFOFtoCNF_X1))
| big_p(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_9,plain,
( ~ big_p(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1))
| big_p(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X1,skolemFOFtoCNF_W(skolemFOFtoCNF_X1)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
~ big_p(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
~ big_p(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X1) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
big_p(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1)) )],[refute_0_1,refute_0_11]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X1) )],[refute_0_12,refute_0_10]) ).
fof(negate_1_0,plain,
~ ( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) )
=> ! [X1] :
( ( ( ~ big_p(a)
| big_p(X1)
| ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) )
& ~ ~ big_p(a)
& ~ ~ ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) ) )
=> ? [Z2,W2] :
( big_p(Z2)
& big_r(X1,W2)
& big_r(W2,Z2) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X1] :
( big_p(a)
& ( ~ big_p(a)
| big_p(X1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(X1,W1) ) )
& ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) )
& ! [W2,Z2] :
( ~ big_p(Z2)
| ~ big_r(W2,Z2)
| ~ big_r(X1,W2) ) )
& ! [X] :
( ~ big_p(a)
| ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X1] :
( big_p(a)
& ( ~ big_p(a)
| big_p(X1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(X1,W1) ) )
& ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) )
& ! [W2,Z2] :
( ~ big_p(Z2)
| ~ big_r(W2,Z2)
| ~ big_r(X1,W2) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( big_p(a)
& ( ~ big_p(a)
| big_p(skolemFOFtoCNF_X1_1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(skolemFOFtoCNF_X1_1,W1) ) )
& ? [Y1] :
( big_p(Y1)
& big_r(skolemFOFtoCNF_X1_1,Y1) )
& ! [W2,Z2] :
( ~ big_p(Z2)
| ~ big_r(W2,Z2)
| ~ big_r(skolemFOFtoCNF_X1_1,W2) ) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [W2,Z2] :
( ~ big_p(Z2)
| ~ big_r(W2,Z2)
| ~ big_r(skolemFOFtoCNF_X1_1,W2) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [W2,Z2] :
( ~ big_p(Z2)
| ~ big_r(W2,Z2)
| ~ big_r(skolemFOFtoCNF_X1_1,W2) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [Y1] :
( big_p(Y1)
& big_r(skolemFOFtoCNF_X1_1,Y1) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_6,plain,
( big_p(skolemFOFtoCNF_Y1)
& big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [X] :
( ~ big_p(a)
| ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_9,plain,
big_p(a),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_10,plain,
! [X] :
( ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ),
inference(simplify,[],[normalize_1_8,normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X] :
( ( big_p(X)
& ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) ) )
| ? [W,Z] :
( big_p(Z)
& big_r(W,Z)
& big_r(X,W) ) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [X,Y] :
( ( big_p(X)
| big_p(skolemFOFtoCNF_Z_1(X)) )
& ( big_p(X)
| big_r(X,skolemFOFtoCNF_W_1(X)) )
& ( big_p(X)
| big_r(skolemFOFtoCNF_W_1(X),skolemFOFtoCNF_Z_1(X)) )
& ( ~ big_p(Y)
| ~ big_r(X,Y)
| big_p(skolemFOFtoCNF_Z_1(X)) )
& ( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(X,skolemFOFtoCNF_W_1(X)) )
& ( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(skolemFOFtoCNF_W_1(X),skolemFOFtoCNF_Z_1(X)) ) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X,Y] :
( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(skolemFOFtoCNF_W_1(X),skolemFOFtoCNF_Z_1(X)) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
big_p(skolemFOFtoCNF_Y1),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_15,plain,
! [X,Y] :
( ~ big_p(Y)
| ~ big_r(X,Y)
| big_p(skolemFOFtoCNF_Z_1(X)) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_16,plain,
! [X,Y] :
( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(X,skolemFOFtoCNF_W_1(X)) ),
inference(conjunct,[],[normalize_1_12]) ).
cnf(refute_1_0,plain,
( ~ big_p(Z2)
| ~ big_r(W2,Z2)
| ~ big_r(skolemFOFtoCNF_X1_1,W2) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
( ~ big_p(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1))
| ~ big_r(skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1))
| ~ big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_0:[bind(W2,$fot(skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1))),bind(Z2,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_1_2,plain,
big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(skolemFOFtoCNF_W_1(X),skolemFOFtoCNF_Z_1(X)) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_4,plain,
( ~ big_p(skolemFOFtoCNF_Y1)
| ~ big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1)
| big_r(skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_3:[bind(X,$fot(skolemFOFtoCNF_X1_1)),bind(Y,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_1_5,plain,
( ~ big_p(skolemFOFtoCNF_Y1)
| big_r(skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1) )],[refute_1_2,refute_1_4]) ).
cnf(refute_1_6,plain,
big_p(skolemFOFtoCNF_Y1),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_7,plain,
big_r(skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y1) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
( ~ big_p(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1))
| ~ big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)) )],[refute_1_7,refute_1_1]) ).
cnf(refute_1_9,plain,
( ~ big_p(Y)
| ~ big_r(X,Y)
| big_p(skolemFOFtoCNF_Z_1(X)) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_10,plain,
( ~ big_p(skolemFOFtoCNF_Y1)
| ~ big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1)
| big_p(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_X1_1)),bind(Y,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_1_11,plain,
( ~ big_p(skolemFOFtoCNF_Y1)
| big_p(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1) )],[refute_1_2,refute_1_10]) ).
cnf(refute_1_12,plain,
big_p(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y1) )],[refute_1_6,refute_1_11]) ).
cnf(refute_1_13,plain,
~ big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_X1_1)) )],[refute_1_12,refute_1_8]) ).
cnf(refute_1_14,plain,
( ~ big_p(Y)
| ~ big_r(X,Y)
| big_r(X,skolemFOFtoCNF_W_1(X)) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_15,plain,
( ~ big_p(skolemFOFtoCNF_Y1)
| ~ big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1)
| big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_1_14:[bind(X,$fot(skolemFOFtoCNF_X1_1)),bind(Y,$fot(skolemFOFtoCNF_Y1))]]) ).
cnf(refute_1_16,plain,
( ~ big_p(skolemFOFtoCNF_Y1)
| big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_Y1) )],[refute_1_2,refute_1_15]) ).
cnf(refute_1_17,plain,
big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y1) )],[refute_1_6,refute_1_16]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_W_1(skolemFOFtoCNF_X1_1)) )],[refute_1_17,refute_1_13]) ).
fof(negate_2_0,plain,
~ ( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| ? [Z1,W1] :
( big_p(Z1)
& big_r(X1,W1)
& big_r(W1,Z1) ) )
& ( ~ big_p(a)
| ~ ? [Y1] :
( big_p(Y1)
& big_r(X1,Y1) )
| ? [Z2,W2] :
( big_p(Z2)
& big_r(X1,W2)
& big_r(W2,Z2) ) ) )
=> ! [X] :
( ( big_p(a)
& ( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) )
=> ? [Z,W] :
( big_p(Z)
& big_r(X,W)
& big_r(W,Z) ) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [X] :
( big_p(a)
& ( ~ big_p(X)
| ? [Y] :
( big_p(Y)
& big_r(X,Y) ) )
& ! [W,Z] :
( ~ big_p(Z)
| ~ big_r(W,Z)
| ~ big_r(X,W) ) )
& ! [X1] :
( ~ big_p(a)
| big_p(X1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(X1,W1) ) )
& ! [X1] :
( ~ big_p(a)
| ? [W2,Z2] :
( big_p(Z2)
& big_r(W2,Z2)
& big_r(X1,W2) )
| ! [Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1) ) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
? [X] :
( big_p(a)
& ( ~ big_p(X)
| ? [Y] :
( big_p(Y)
& big_r(X,Y) ) )
& ! [W,Z] :
( ~ big_p(Z)
| ~ big_r(W,Z)
| ~ big_r(X,W) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
( big_p(a)
& ( ~ big_p(skolemFOFtoCNF_X)
| ? [Y] :
( big_p(Y)
& big_r(skolemFOFtoCNF_X,Y) ) )
& ! [W,Z] :
( ~ big_p(Z)
| ~ big_r(W,Z)
| ~ big_r(skolemFOFtoCNF_X,W) ) ),
inference(skolemize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [W,Z] :
( ~ big_p(Z)
| ~ big_r(W,Z)
| ~ big_r(skolemFOFtoCNF_X,W) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [W,Z] :
( ~ big_p(Z)
| ~ big_r(W,Z)
| ~ big_r(skolemFOFtoCNF_X,W) ),
inference(specialize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
( ~ big_p(skolemFOFtoCNF_X)
| ? [Y] :
( big_p(Y)
& big_r(skolemFOFtoCNF_X,Y) ) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_6,plain,
( ( ~ big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_Y) )
& ( ~ big_p(skolemFOFtoCNF_X)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ) ),
inference(clausify,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(conjunct,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [X1] :
( ~ big_p(a)
| big_p(X1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(X1,W1) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_9,plain,
big_p(a),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_10,plain,
! [X1] :
( big_p(X1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(X1,W1) ) ),
inference(simplify,[],[normalize_2_8,normalize_2_9]) ).
fof(normalize_2_11,plain,
! [X1] :
( big_p(X1)
| ? [W1,Z1] :
( big_p(Z1)
& big_r(W1,Z1)
& big_r(X1,W1) ) ),
inference(specialize,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [X1] :
( ( big_p(X1)
| big_p(skolemFOFtoCNF_Z1_1(X1)) )
& ( big_p(X1)
| big_r(X1,skolemFOFtoCNF_W1_1(X1)) )
& ( big_p(X1)
| big_r(skolemFOFtoCNF_W1_1(X1),skolemFOFtoCNF_Z1_1(X1)) ) ),
inference(clausify,[],[normalize_2_11]) ).
fof(normalize_2_13,plain,
! [X1] :
( big_p(X1)
| big_p(skolemFOFtoCNF_Z1_1(X1)) ),
inference(conjunct,[],[normalize_2_12]) ).
fof(normalize_2_14,plain,
! [X1] :
( big_p(X1)
| big_r(X1,skolemFOFtoCNF_W1_1(X1)) ),
inference(conjunct,[],[normalize_2_12]) ).
fof(normalize_2_15,plain,
! [X1] :
( big_p(X1)
| big_r(skolemFOFtoCNF_W1_1(X1),skolemFOFtoCNF_Z1_1(X1)) ),
inference(conjunct,[],[normalize_2_12]) ).
fof(normalize_2_16,plain,
! [X1] :
( ~ big_p(a)
| ? [W2,Z2] :
( big_p(Z2)
& big_r(W2,Z2)
& big_r(X1,W2) )
| ! [Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_17,plain,
! [X1] :
( ? [W2,Z2] :
( big_p(Z2)
& big_r(W2,Z2)
& big_r(X1,W2) )
| ! [Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1) ) ),
inference(simplify,[],[normalize_2_16,normalize_2_9]) ).
fof(normalize_2_18,plain,
! [X1] :
( ? [W2,Z2] :
( big_p(Z2)
& big_r(W2,Z2)
& big_r(X1,W2) )
| ! [Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1) ) ),
inference(specialize,[],[normalize_2_17]) ).
fof(normalize_2_19,plain,
! [X1,Y1] :
( ( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_p(skolemFOFtoCNF_Z2(X1)) )
& ( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_r(X1,skolemFOFtoCNF_W2(X1)) )
& ( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_r(skolemFOFtoCNF_W2(X1),skolemFOFtoCNF_Z2(X1)) ) ),
inference(clausify,[],[normalize_2_18]) ).
fof(normalize_2_20,plain,
! [X1,Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_r(skolemFOFtoCNF_W2(X1),skolemFOFtoCNF_Z2(X1)) ),
inference(conjunct,[],[normalize_2_19]) ).
fof(normalize_2_21,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_Y) ),
inference(conjunct,[],[normalize_2_6]) ).
fof(normalize_2_22,plain,
! [X1,Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_p(skolemFOFtoCNF_Z2(X1)) ),
inference(conjunct,[],[normalize_2_19]) ).
fof(normalize_2_23,plain,
! [X1,Y1] :
( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_r(X1,skolemFOFtoCNF_W2(X1)) ),
inference(conjunct,[],[normalize_2_19]) ).
cnf(refute_2_0,plain,
( ~ big_p(Z)
| ~ big_r(W,Z)
| ~ big_r(skolemFOFtoCNF_X,W) ),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_1,plain,
( ~ big_p(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X))
| ~ big_r(skolemFOFtoCNF_W2(skolemFOFtoCNF_X),skolemFOFtoCNF_Z2(skolemFOFtoCNF_X))
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_2_0:[bind(W,$fot(skolemFOFtoCNF_W2(skolemFOFtoCNF_X))),bind(Z,$fot(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)))]]) ).
cnf(refute_2_2,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_3,plain,
( big_p(X1)
| big_p(skolemFOFtoCNF_Z1_1(X1)) ),
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_4,plain,
( big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_Z1_1(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_2_3:[bind(X1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_5,plain,
( big_p(X1)
| big_r(X1,skolemFOFtoCNF_W1_1(X1)) ),
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_6,plain,
( big_p(skolemFOFtoCNF_X)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W1_1(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_2_5:[bind(X1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_7,plain,
( big_p(X1)
| big_r(skolemFOFtoCNF_W1_1(X1),skolemFOFtoCNF_Z1_1(X1)) ),
inference(canonicalize,[],[normalize_2_15]) ).
cnf(refute_2_8,plain,
( ~ big_p(skolemFOFtoCNF_Z1_1(X1))
| ~ big_r(skolemFOFtoCNF_W1_1(X1),skolemFOFtoCNF_Z1_1(X1))
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W1_1(X1)) ),
inference(subst,[],[refute_2_0:[bind(W,$fot(skolemFOFtoCNF_W1_1(X1))),bind(Z,$fot(skolemFOFtoCNF_Z1_1(X1)))]]) ).
cnf(refute_2_9,plain,
( ~ big_p(skolemFOFtoCNF_Z1_1(X1))
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W1_1(X1))
| big_p(X1) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_W1_1(X1),skolemFOFtoCNF_Z1_1(X1)) )],[refute_2_7,refute_2_8]) ).
cnf(refute_2_10,plain,
( ~ big_p(skolemFOFtoCNF_Z1_1(skolemFOFtoCNF_X))
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W1_1(skolemFOFtoCNF_X))
| big_p(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_2_9:[bind(X1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_11,plain,
( ~ big_p(skolemFOFtoCNF_Z1_1(skolemFOFtoCNF_X))
| big_p(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W1_1(skolemFOFtoCNF_X)) )],[refute_2_6,refute_2_10]) ).
cnf(refute_2_12,plain,
big_p(skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Z1_1(skolemFOFtoCNF_X)) )],[refute_2_4,refute_2_11]) ).
cnf(refute_2_13,plain,
big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_2_12,refute_2_2]) ).
cnf(refute_2_14,plain,
( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_r(skolemFOFtoCNF_W2(X1),skolemFOFtoCNF_Z2(X1)) ),
inference(canonicalize,[],[normalize_2_20]) ).
cnf(refute_2_15,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| big_r(skolemFOFtoCNF_W2(skolemFOFtoCNF_X),skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_2_14:[bind(X1,$fot(skolemFOFtoCNF_X)),bind(Y1,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_2_16,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| big_r(skolemFOFtoCNF_W2(skolemFOFtoCNF_X),skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_2_13,refute_2_15]) ).
cnf(refute_2_17,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_Y) ),
inference(canonicalize,[],[normalize_2_21]) ).
cnf(refute_2_18,plain,
big_p(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_2_12,refute_2_17]) ).
cnf(refute_2_19,plain,
big_r(skolemFOFtoCNF_W2(skolemFOFtoCNF_X),skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y) )],[refute_2_18,refute_2_16]) ).
cnf(refute_2_20,plain,
( ~ big_p(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X))
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_W2(skolemFOFtoCNF_X),skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)) )],[refute_2_19,refute_2_1]) ).
cnf(refute_2_21,plain,
( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_p(skolemFOFtoCNF_Z2(X1)) ),
inference(canonicalize,[],[normalize_2_22]) ).
cnf(refute_2_22,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| big_p(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_2_21:[bind(X1,$fot(skolemFOFtoCNF_X)),bind(Y1,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_2_23,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| big_p(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_2_13,refute_2_22]) ).
cnf(refute_2_24,plain,
big_p(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y) )],[refute_2_18,refute_2_23]) ).
cnf(refute_2_25,plain,
~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Z2(skolemFOFtoCNF_X)) )],[refute_2_24,refute_2_20]) ).
cnf(refute_2_26,plain,
( ~ big_p(Y1)
| ~ big_r(X1,Y1)
| big_r(X1,skolemFOFtoCNF_W2(X1)) ),
inference(canonicalize,[],[normalize_2_23]) ).
cnf(refute_2_27,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| ~ big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_2_26:[bind(X1,$fot(skolemFOFtoCNF_X)),bind(Y1,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_2_28,plain,
( ~ big_p(skolemFOFtoCNF_Y)
| big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_2_13,refute_2_27]) ).
cnf(refute_2_29,plain,
big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y) )],[refute_2_18,refute_2_28]) ).
cnf(refute_2_30,plain,
$false,
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X,skolemFOFtoCNF_W2(skolemFOFtoCNF_X)) )],[refute_2_29,refute_2_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 15:10:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------