TSTP Solution File: LCL636+1.001 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL636+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 12:53:27 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 387 ( 0 equ)
% Maximal formula atoms : 69 ( 18 avg)
% Number of connectives : 652 ( 286 ~; 203 |; 161 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 82 ( 0 sgn 66 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
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) ) ) )
& ( ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ p2(Y)
& ~ p102(Y)
& p101(Y) ) )
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
& ~ p102(Y)
& p101(Y) ) ) )
| ~ ( ~ p101(X)
& p100(X) ) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y)
| ~ p101(Y) )
| p2(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ p101(Y) )
| ~ p2(X) ) )
| ~ p101(X) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y)
| ~ p100(Y) )
| p1(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ p100(Y) )
| ~ p1(X) ) )
| ~ p100(X) )
& ( p101(X)
| ~ p102(X) )
& ( p100(X)
| ~ p101(X) )
& ~ 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) ) ) )
& ( ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ p2(Y)
& ~ p102(Y)
& p101(Y) ) )
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
& ~ p102(Y)
& p101(Y) ) ) )
| ~ ( ~ p101(X)
& p100(X) ) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y)
| ~ p101(Y) )
| p2(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ p101(Y) )
| ~ p2(X) ) )
| ~ p101(X) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y)
| ~ p100(Y) )
| p1(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ p100(Y) )
| ~ p1(X) ) )
| ~ p100(X) )
& ( p101(X)
| ~ p102(X) )
& ( p100(X)
| ~ p101(X) )
& ~ 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) ) ) )
& ( ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ p2(Y)
& ~ p102(Y)
& p101(Y) ) )
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
& ~ p102(Y)
& p101(Y) ) ) )
| ~ ( ~ p101(X)
& p100(X) ) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y)
| ~ p101(Y) )
| p2(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ p101(Y) )
| ~ p2(X) ) )
| ~ p101(X) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y)
| ~ p100(Y) )
| p1(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ p100(Y) )
| ~ p1(X) ) )
| ~ p100(X) )
& ( p101(X)
| ~ p102(X) )
& ( p100(X)
| ~ p101(X) )
& ~ p101(X) )
=> ~ p100(X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ p101(X)
& p100(X)
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| ~ r1(X,Y)
| p1(Y) ) )
& ( p1(X)
| ! [Y] :
( ~ p1(Y)
| ~ p100(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p101(X)
| p100(X) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ r1(X,Y)
| p2(Y) ) )
& ( p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| p101(X)
| ( ? [Y] :
( ~ p102(Y)
& ~ p2(Y)
& p101(Y)
& r1(X,Y) )
& ? [Y] :
( ~ p102(Y)
& p101(Y)
& p2(Y)
& r1(X,Y) ) ) )
& ! [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)
& ( ~ p100(skolemFOFtoCNF_X)
| ( ( ~ p1(skolemFOFtoCNF_X)
| ! [Y] :
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p1(Y) ) )
& ( p1(skolemFOFtoCNF_X)
| ! [Y] :
( ~ p1(Y)
| ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ) ) ) )
& ( ~ p101(skolemFOFtoCNF_X)
| p100(skolemFOFtoCNF_X) )
& ( ~ p101(skolemFOFtoCNF_X)
| ( ( ~ p2(skolemFOFtoCNF_X)
| ! [Y] :
( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ) )
& ( p2(skolemFOFtoCNF_X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ) ) ) )
& ( ~ p102(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X) )
& ( ~ p100(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| ( ? [Y] :
( ~ p102(Y)
& ~ p2(Y)
& p101(Y)
& r1(skolemFOFtoCNF_X,Y) )
& ? [Y] :
( ~ p102(Y)
& p101(Y)
& p2(Y)
& r1(skolemFOFtoCNF_X,Y) ) ) )
& ! [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,
( ~ p100(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| ( ? [Y] :
( ~ p102(Y)
& ~ p2(Y)
& p101(Y)
& r1(skolemFOFtoCNF_X,Y) )
& ? [Y] :
( ~ p102(Y)
& p101(Y)
& p2(Y)
& r1(skolemFOFtoCNF_X,Y) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
p100(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
~ p101(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
( ? [Y] :
( ~ p102(Y)
& ~ p2(Y)
& p101(Y)
& r1(skolemFOFtoCNF_X,Y) )
& ? [Y] :
( ~ p102(Y)
& p101(Y)
& p2(Y)
& r1(skolemFOFtoCNF_X,Y) ) ),
inference(simplify,[],[normalize_0_2,normalize_0_3,normalize_0_4]) ).
fof(normalize_0_6,plain,
? [Y] :
( ~ p102(Y)
& ~ p2(Y)
& p101(Y)
& r1(skolemFOFtoCNF_X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ p102(skolemFOFtoCNF_Y)
& ~ p2(skolemFOFtoCNF_Y)
& p101(skolemFOFtoCNF_Y)
& r1(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ p2(skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
( ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_2,plain,
( ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| p2(skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_1:[bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_3,plain,
p2(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
~ p2(skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( p2(skolemFOFtoCNF_Y) )],[refute_0_3,refute_0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL636+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 5 00:10:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------