%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN550+1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 09:03:57 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 89 ( 26 unt; 0 def)
% Number of atoms : 243 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 265 ( 111 ~; 91 |; 42 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 136 ( 0 sgn 74 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_of_reachable,axiom,
! [X] : reachable(X,X) ).
fof(transitivity_of_reachable,axiom,
! [X,Y,Z] :
( ( reachable(X,Y)
& reachable(Y,Z) )
=> reachable(X,Z) ) ).
fof(prove_this,conjecture,
( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> p(Y) ) )
<=> ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> ? [Z] :
( reachable(Y,Z)
& ! [W] :
( reachable(Z,W)
=> p(W) ) ) ) ) ) ).
fof(subgoal_0,plain,
( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> p(Y) ) )
=> ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> ? [Z] :
( reachable(Y,Z)
& ! [W] :
( reachable(Z,W)
=> p(W) ) ) ) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_1,plain,
( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> ? [Z] :
( reachable(Y,Z)
& ! [W] :
( reachable(Z,W)
=> p(W) ) ) ) )
=> ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> p(Y) ) ) ),
inference(strip,[],[prove_this]) ).
fof(negate_0_0,plain,
~ ( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> p(Y) ) )
=> ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> ? [Z] :
( reachable(Y,Z)
& ! [W] :
( reachable(Z,W)
=> p(W) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : reachable(X,X),
inference(canonicalize,[],[reflexivity_of_reachable]) ).
fof(normalize_0_1,plain,
! [X] : reachable(X,X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( ~ reachable(X,Y)
| p(Y) ) )
& ! [X] :
( ~ reachable(initial_world,X)
| ? [Y] :
( reachable(X,Y)
& ! [Z] :
( ~ reachable(Y,Z)
| ? [W] :
( ~ p(W)
& reachable(Z,W) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ reachable(initial_world,X)
| ? [Y] :
( reachable(X,Y)
& ! [Z] :
( ~ reachable(Y,Z)
| ? [W] :
( ~ p(W)
& reachable(Z,W) ) ) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ reachable(initial_world,X)
| ? [Y] :
( reachable(X,Y)
& ! [Z] :
( ~ reachable(Y,Z)
| ? [W] :
( ~ p(W)
& reachable(Z,W) ) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Z] :
( ( ~ reachable(initial_world,X)
| reachable(X,skolemFOFtoCNF_Y(X)) )
& ( ~ p(skolemFOFtoCNF_W(Z))
| ~ reachable(initial_world,X)
| ~ reachable(skolemFOFtoCNF_Y(X),Z) )
& ( ~ reachable(initial_world,X)
| ~ reachable(skolemFOFtoCNF_Y(X),Z)
| reachable(Z,skolemFOFtoCNF_W(Z)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Z] :
( ~ p(skolemFOFtoCNF_W(Z))
| ~ reachable(initial_world,X)
| ~ reachable(skolemFOFtoCNF_Y(X),Z) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [X] :
( reachable(initial_world,X)
& ! [Y] :
( ~ reachable(X,Y)
| p(Y) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
( reachable(initial_world,skolemFOFtoCNF_X)
& ! [Y] :
( ~ reachable(skolemFOFtoCNF_X,Y)
| p(Y) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] :
( ~ reachable(skolemFOFtoCNF_X,Y)
| p(Y) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y] :
( ~ reachable(skolemFOFtoCNF_X,Y)
| p(Y) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
reachable(initial_world,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ reachable(initial_world,X)
| reachable(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_13,plain,
! [X,Z] :
( ~ reachable(initial_world,X)
| ~ reachable(skolemFOFtoCNF_Y(X),Z)
| reachable(Z,skolemFOFtoCNF_W(Z)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ reachable(X,Y)
| ~ reachable(Y,Z)
| reachable(X,Z) ),
inference(canonicalize,[],[transitivity_of_reachable]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ reachable(X,Y)
| ~ reachable(Y,Z)
| reachable(X,Z) ),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
reachable(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
reachable(skolemFOFtoCNF_Y(X_3),skolemFOFtoCNF_Y(X_3)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y(X_3)))]]) ).
cnf(refute_0_2,plain,
( ~ p(skolemFOFtoCNF_W(Z))
| ~ reachable(initial_world,X)
| ~ reachable(skolemFOFtoCNF_Y(X),Z) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ p(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(X_3)))
| ~ reachable(initial_world,X_3)
| ~ reachable(skolemFOFtoCNF_Y(X_3),skolemFOFtoCNF_Y(X_3)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_3)),bind(Z,$fot(skolemFOFtoCNF_Y(X_3)))]]) ).
cnf(refute_0_4,plain,
( ~ p(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(X_3)))
| ~ reachable(initial_world,X_3) ),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_Y(X_3),skolemFOFtoCNF_Y(X_3)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ p(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))
| ~ reachable(initial_world,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_4:[bind(X_3,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_6,plain,
( ~ reachable(skolemFOFtoCNF_X,Y)
| p(Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))
| p(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_6:[bind(Y,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_8,plain,
reachable(initial_world,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ reachable(initial_world,X)
| reachable(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ reachable(initial_world,skolemFOFtoCNF_X)
| reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_11,plain,
reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( reachable(initial_world,skolemFOFtoCNF_X) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
reachable(skolemFOFtoCNF_Y(X_6),skolemFOFtoCNF_Y(X_6)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y(X_6)))]]) ).
cnf(refute_0_13,plain,
( ~ reachable(initial_world,X)
| ~ reachable(skolemFOFtoCNF_Y(X),Z)
| reachable(Z,skolemFOFtoCNF_W(Z)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( ~ reachable(initial_world,X_6)
| ~ reachable(skolemFOFtoCNF_Y(X_6),skolemFOFtoCNF_Y(X_6))
| reachable(skolemFOFtoCNF_Y(X_6),skolemFOFtoCNF_W(skolemFOFtoCNF_Y(X_6))) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_6)),bind(Z,$fot(skolemFOFtoCNF_Y(X_6)))]]) ).
cnf(refute_0_15,plain,
( ~ reachable(initial_world,X_6)
| reachable(skolemFOFtoCNF_Y(X_6),skolemFOFtoCNF_W(skolemFOFtoCNF_Y(X_6))) ),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_Y(X_6),skolemFOFtoCNF_Y(X_6)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ reachable(initial_world,skolemFOFtoCNF_X)
| reachable(skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_15:[bind(X_6,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_17,plain,
reachable(skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( reachable(initial_world,skolemFOFtoCNF_X) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ reachable(X,Y)
| ~ reachable(Y,Z)
| reachable(X,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_19,plain,
( ~ reachable(X_9,skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| ~ reachable(skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))
| reachable(X_9,skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_9)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),bind(Z,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_20,plain,
( ~ reachable(X_9,skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| reachable(X_9,skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) ),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_20:[bind(X_9,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_22,plain,
reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) )],[refute_0_11,refute_0_21]) ).
cnf(refute_0_23,plain,
p(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_X,skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) )],[refute_0_22,refute_0_7]) ).
cnf(refute_0_24,plain,
~ reachable(initial_world,skolemFOFtoCNF_X),
inference(resolve,[$cnf( p(skolemFOFtoCNF_W(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) )],[refute_0_23,refute_0_5]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( reachable(initial_world,skolemFOFtoCNF_X) )],[refute_0_8,refute_0_24]) ).
fof(negate_1_0,plain,
~ ( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> ? [Z] :
( reachable(Y,Z)
& ! [W] :
( reachable(Z,W)
=> p(W) ) ) ) )
=> ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( reachable(X,Y)
=> p(Y) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X] :
( reachable(initial_world,X)
& ! [Y] :
( ~ reachable(X,Y)
| ? [Z] :
( reachable(Y,Z)
& ! [W] :
( ~ reachable(Z,W)
| p(W) ) ) ) )
& ! [X] :
( ~ reachable(initial_world,X)
| ? [Y] :
( ~ p(Y)
& reachable(X,Y) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X] :
( reachable(initial_world,X)
& ! [Y] :
( ~ reachable(X,Y)
| ? [Z] :
( reachable(Y,Z)
& ! [W] :
( ~ reachable(Z,W)
| p(W) ) ) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( reachable(initial_world,skolemFOFtoCNF_X_1)
& ! [Y] :
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| ? [Z] :
( reachable(Y,Z)
& ! [W] :
( ~ reachable(Z,W)
| p(W) ) ) ) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [Y] :
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| ? [Z] :
( reachable(Y,Z)
& ! [W] :
( ~ reachable(Z,W)
| p(W) ) ) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [Y] :
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| ? [Z] :
( reachable(Y,Z)
& ! [W] :
( ~ reachable(Z,W)
| p(W) ) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [W,Y] :
( ( ~ reachable(skolemFOFtoCNF_X_1,Y)
| reachable(Y,skolemFOFtoCNF_Z(Y)) )
& ( ~ reachable(skolemFOFtoCNF_X_1,Y)
| ~ reachable(skolemFOFtoCNF_Z(Y),W)
| p(W) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [W,Y] :
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| ~ reachable(skolemFOFtoCNF_Z(Y),W)
| p(W) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X] :
( ~ reachable(initial_world,X)
| ? [Y] :
( ~ p(Y)
& reachable(X,Y) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_8,plain,
! [X] :
( ~ reachable(initial_world,X)
| ? [Y] :
( ~ p(Y)
& reachable(X,Y) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X] :
( ( ~ p(skolemFOFtoCNF_Y_1(X))
| ~ reachable(initial_world,X) )
& ( ~ reachable(initial_world,X)
| reachable(X,skolemFOFtoCNF_Y_1(X)) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [X] :
( ~ reachable(initial_world,X)
| reachable(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
reachable(initial_world,skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_12,plain,
! [X] : reachable(X,X),
inference(canonicalize,[],[reflexivity_of_reachable]) ).
fof(normalize_1_13,plain,
! [X] : reachable(X,X),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [Y] :
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| reachable(Y,skolemFOFtoCNF_Z(Y)) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_15,plain,
! [X,Y,Z] :
( ~ reachable(X,Y)
| ~ reachable(Y,Z)
| reachable(X,Z) ),
inference(canonicalize,[],[transitivity_of_reachable]) ).
fof(normalize_1_16,plain,
! [X,Y,Z] :
( ~ reachable(X,Y)
| ~ reachable(Y,Z)
| reachable(X,Z) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [X] :
( ~ p(skolemFOFtoCNF_Y_1(X))
| ~ reachable(initial_world,X) ),
inference(conjunct,[],[normalize_1_9]) ).
cnf(refute_1_0,plain,
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| ~ reachable(skolemFOFtoCNF_Z(Y),W)
| p(W) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_1,plain,
( ~ reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1)
| ~ reachable(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)))
| p(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))) ),
inference(subst,[],[refute_1_0:[bind(W,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)))),bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_2,plain,
( ~ reachable(initial_world,X)
| reachable(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_3,plain,
( ~ reachable(initial_world,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))
| reachable(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_4,plain,
reachable(initial_world,skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_5,plain,
reachable(X,X),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_6,plain,
reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_7,plain,
( ~ reachable(skolemFOFtoCNF_X_1,Y)
| reachable(Y,skolemFOFtoCNF_Z(Y)) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_8,plain,
( ~ reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1)
| reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_7:[bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_9,plain,
reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) )],[refute_1_6,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ reachable(X,Y)
| ~ reachable(Y,Z)
| reachable(X,Z) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_11,plain,
( ~ reachable(X_24,skolemFOFtoCNF_X_1)
| ~ reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))
| reachable(X_24,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_10:[bind(X,$fot(X_24)),bind(Y,$fot(skolemFOFtoCNF_X_1)),bind(Z,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_12,plain,
( ~ reachable(X_24,skolemFOFtoCNF_X_1)
| reachable(X_24,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) ),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) )],[refute_1_9,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ reachable(initial_world,skolemFOFtoCNF_X_1)
| reachable(initial_world,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_12:[bind(X_24,$fot(initial_world))]]) ).
cnf(refute_1_14,plain,
reachable(initial_world,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)),
inference(resolve,[$cnf( reachable(initial_world,skolemFOFtoCNF_X_1) )],[refute_1_4,refute_1_13]) ).
cnf(refute_1_15,plain,
reachable(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))),
inference(resolve,[$cnf( reachable(initial_world,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) )],[refute_1_14,refute_1_3]) ).
cnf(refute_1_16,plain,
( ~ reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1)
| p(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))) ),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))) )],[refute_1_15,refute_1_1]) ).
cnf(refute_1_17,plain,
p(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))),
inference(resolve,[$cnf( reachable(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) )],[refute_1_6,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ p(skolemFOFtoCNF_Y_1(X))
| ~ reachable(initial_world,X) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_19,plain,
( ~ p(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)))
| ~ reachable(initial_world,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_18:[bind(X,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_20,plain,
~ p(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))),
inference(resolve,[$cnf( reachable(initial_world,skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1)) )],[refute_1_14,refute_1_19]) ).
cnf(refute_1_21,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_Z(skolemFOFtoCNF_X_1))) )],[refute_1_17,refute_1_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN550+1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 03:48:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------