TSTP Solution File: KLE059+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE059+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 02:14:58 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 23 ~; 17 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] :
( addition(domain(X0),domain(X1)) != domain(X1)
& addition(X0,X1) = X1 ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
& addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[domain5]) ).
fof(normalize_0_5,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
introduced(tautology,[refl,[$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_3,plain,
( addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) ),[1,0],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_4,plain,
( addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
| domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( domain(addition(X0,X1)) != addition(domain(X0),domain(X1))
| addition(domain(X0),domain(X1)) = domain(addition(X0,X1)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(domain(addition(X0,X1)))),bind(Y,$fot(addition(domain(X0),domain(X1))))]]) ).
cnf(refute_0_11,plain,
addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(resolve,[$cnf( $equal(domain(addition(X0,X1)),addition(domain(X0),domain(X1))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),
inference(subst,[],[refute_0_11:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_13,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))
| domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)))),bind(Y,$fot(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)))),bind(Z,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_16,plain,
( domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(domain(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_5,refute_0_16]) ).
cnf(refute_0_18,plain,
( addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) != domain(skolemFOFtoCNF_X1)
| domain(skolemFOFtoCNF_X1) != domain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) ),[0],$fot(domain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_19,plain,
( domain(skolemFOFtoCNF_X1) != domain(skolemFOFtoCNF_X1)
| addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)) = domain(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
domain(skolemFOFtoCNF_X1) != domain(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1)),domain(skolemFOFtoCNF_X1)) )],[refute_0_19,refute_0_0]) ).
cnf(refute_0_21,plain,
domain(skolemFOFtoCNF_X1) = domain(skolemFOFtoCNF_X1),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X1),domain(skolemFOFtoCNF_X1)) )],[refute_0_21,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE059+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 08:31:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------