TSTP Solution File: KLE001+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 02:14:29 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 45 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 9 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 22 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] :
( ? [X1] : leq(X0,X1)
& ? [X2] : ~ leq(addition(X0,X2),addition(X0,X2)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [X1] : leq(skolemFOFtoCNF_X0,X1)
& ? [X2] : ~ leq(addition(skolemFOFtoCNF_X0,X2),addition(skolemFOFtoCNF_X0,X2)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X2] : ~ leq(addition(skolemFOFtoCNF_X0,X2),addition(skolemFOFtoCNF_X0,X2)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ leq(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_5,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_9,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
~ leq(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( addition(X_26,X_26) != X_26
| leq(X_26,X_26) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_26)),bind(B,$fot(X_26))]]) ).
cnf(refute_0_3,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
addition(X_26,X_26) = X_26,
inference(subst,[],[refute_0_3:[bind(A,$fot(X_26))]]) ).
cnf(refute_0_5,plain,
( X_26 != X_26
| addition(X_26,X_26) != X_26
| addition(X_26,X_26) = X_26 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_26,X_26),X_26) ),[0,0],$fot(X_26)]]) ).
cnf(refute_0_6,plain,
( X_26 != X_26
| addition(X_26,X_26) = X_26 ),
inference(resolve,[$cnf( $equal(addition(X_26,X_26),X_26) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( X_26 != X_26
| leq(X_26,X_26) ),
inference(resolve,[$cnf( $equal(addition(X_26,X_26),X_26) )],[refute_0_6,refute_0_2]) ).
cnf(refute_0_8,plain,
X_26 = X_26,
introduced(tautology,[refl,[$fot(X_26)]]) ).
cnf(refute_0_9,plain,
leq(X_26,X_26),
inference(resolve,[$cnf( $equal(X_26,X_26) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
leq(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_9:[bind(X_26,$fot(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( leq(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2),addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)) )],[refute_0_10,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.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 : Thu Jun 16 14:43:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------