TSTP Solution File: LCL656+1.001 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL656+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 : Sun Jul 17 12:53:59 EDT 2022
% Result : Theorem 0.17s 0.33s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 368 ( 0 equ)
% Maximal formula atoms : 62 ( 10 avg)
% Number of connectives : 591 ( 258 ~; 218 |; 113 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 71 ( 0 sgn 57 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).
fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
| ~ ( ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X)
& p100(X) ) ) ).
fof(subgoal_0,plain,
! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X) )
=> ~ p100(X) ),
inference(strip,[],[main]) ).
fof(negate_0_0,plain,
~ ! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X) )
=> ~ p100(X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ p101(X)
& p100(X)
& ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ p101(skolemFOFtoCNF_X)
& p100(skolemFOFtoCNF_X)
& ! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : r1(X,X),
inference(canonicalize,[],[reflexivity]) ).
fof(normalize_0_5,plain,
! [X] : r1(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p100(Y) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ p102(skolemFOFtoCNF_X_1(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ p102(skolemFOFtoCNF_X_2(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ p2(skolemFOFtoCNF_X_2(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p101(skolemFOFtoCNF_X_1(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p101(skolemFOFtoCNF_X_2(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p2(skolemFOFtoCNF_X_1(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_1(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_2(Y)) )
& ( ~ p1(X)
| ~ p100(X)
| ~ p100(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p1(Y) )
& ( ~ p1(Y)
| ~ p100(X)
| ~ p100(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p1(X) )
& ( ~ p101(X)
| ~ p101(Y)
| ~ p2(X)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) )
& ( ~ p101(X)
| ~ p101(Y)
| ~ p2(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p2(X) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] :
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_2(Y)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
p100(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
~ p101(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
! [Y] :
( ~ p100(Y)
| ~ p2(skolemFOFtoCNF_X_2(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_2(skolemFOFtoCNF_X))
| p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_2,plain,
r1(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_4,plain,
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_2(Y)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_4:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_6,plain,
( ~ p100(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
p100(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( p101(skolemFOFtoCNF_X)
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( p100(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
~ p101(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
( ~ p100(Y)
| ~ p2(skolemFOFtoCNF_X_2(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X))
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_12:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_14,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X))
| p101(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_3,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X))
| p101(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( p100(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_14]) ).
cnf(refute_0_16,plain,
~ p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_15,refute_0_9]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( p2(skolemFOFtoCNF_X_2(skolemFOFtoCNF_X)) )],[refute_0_11,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL656+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sun Jul 3 07:22:37 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.17/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.33
% 0.17/0.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.34
%------------------------------------------------------------------------------