TSTP Solution File: KLE053+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE053+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 02:14:56 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 27 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 21 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 36 ( 0 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(goals,conjecture,
! [X0] : domain(domain(X0)) = domain(X0) ).
fof(subgoal_0,plain,
! [X0] : domain(domain(X0)) = domain(X0),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : domain(domain(X0)) = domain(X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : domain(domain(X0)) != domain(X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
domain(domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[domain2]) ).
fof(normalize_0_3,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_5,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
domain(domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
domain(multiplication(one,X_31)) = domain(multiplication(one,domain(X_31))),
inference(subst,[],[refute_0_1:[bind(X0,$fot(one)),bind(X1,$fot(X_31))]]) ).
cnf(refute_0_3,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
multiplication(one,domain(X_31)) = domain(X_31),
inference(subst,[],[refute_0_3:[bind(A,$fot(domain(X_31)))]]) ).
cnf(refute_0_5,plain,
( domain(multiplication(one,X_31)) != domain(multiplication(one,domain(X_31)))
| multiplication(one,domain(X_31)) != domain(X_31)
| domain(multiplication(one,X_31)) = domain(domain(X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,domain(X_31)))) ),[1,0],$fot(domain(X_31))]]) ).
cnf(refute_0_6,plain,
( domain(multiplication(one,X_31)) != domain(multiplication(one,domain(X_31)))
| domain(multiplication(one,X_31)) = domain(domain(X_31)) ),
inference(resolve,[$cnf( $equal(multiplication(one,domain(X_31)),domain(X_31)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
domain(multiplication(one,X_31)) = domain(domain(X_31)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,domain(X_31)))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
multiplication(one,X_31) = X_31,
inference(subst,[],[refute_0_3:[bind(A,$fot(X_31))]]) ).
cnf(refute_0_9,plain,
domain(multiplication(one,X_31)) = domain(multiplication(one,X_31)),
introduced(tautology,[refl,[$fot(domain(multiplication(one,X_31)))]]) ).
cnf(refute_0_10,plain,
( domain(multiplication(one,X_31)) != domain(multiplication(one,X_31))
| multiplication(one,X_31) != X_31
| domain(multiplication(one,X_31)) = domain(X_31) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,X_31))) ),[1,0],$fot(X_31)]]) ).
cnf(refute_0_11,plain,
( multiplication(one,X_31) != X_31
| domain(multiplication(one,X_31)) = domain(X_31) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(multiplication(one,X_31))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
domain(multiplication(one,X_31)) = domain(X_31),
inference(resolve,[$cnf( $equal(multiplication(one,X_31),X_31) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( domain(multiplication(one,X_31)) != domain(X_31)
| domain(multiplication(one,X_31)) != domain(domain(X_31))
| domain(X_31) = domain(domain(X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(domain(multiplication(one,X_31)),domain(domain(X_31))) ),[0],$fot(domain(X_31))]]) ).
cnf(refute_0_14,plain,
( domain(multiplication(one,X_31)) != domain(domain(X_31))
| domain(X_31) = domain(domain(X_31)) ),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(X_31)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
domain(X_31) = domain(domain(X_31)),
inference(resolve,[$cnf( $equal(domain(multiplication(one,X_31)),domain(domain(X_31))) )],[refute_0_7,refute_0_14]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( domain(X_31) != domain(domain(X_31))
| domain(domain(X_31)) = domain(X_31) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(domain(X_31))),bind(Y,$fot(domain(domain(X_31))))]]) ).
cnf(refute_0_20,plain,
domain(domain(X_31)) = domain(X_31),
inference(resolve,[$cnf( $equal(domain(X_31),domain(domain(X_31))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
domain(domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_20:[bind(X_31,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_22,plain,
( domain(domain(skolemFOFtoCNF_X0)) != domain(skolemFOFtoCNF_X0)
| domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| domain(domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) ),[0],$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_23,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| domain(domain(skolemFOFtoCNF_X0)) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(domain(domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(domain(domain(skolemFOFtoCNF_X0)),domain(skolemFOFtoCNF_X0)) )],[refute_0_23,refute_0_0]) ).
cnf(refute_0_25,plain,
domain(skolemFOFtoCNF_X0) = domain(skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) )],[refute_0_25,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE053+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 12:05:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.41
%------------------------------------------------------------------------------