TSTP Solution File: KLE138+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 02:15:29 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 31 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ).
fof(goals,conjecture,
strong_iteration(zero) = one ).
fof(subgoal_0,plain,
strong_iteration(zero) = one,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
strong_iteration(zero) != one,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[infty_unfold1]) ).
fof(normalize_0_1,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_3,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_5,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_7,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
strong_iteration(zero) != one,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_6,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(multiplication(A,strong_iteration(A)),one) = addition(one,multiplication(A,strong_iteration(A))),
inference(subst,[],[refute_0_6:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_8,plain,
( addition(multiplication(A,strong_iteration(A)),one) != addition(one,multiplication(A,strong_iteration(A)))
| strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) ),[1],$fot(addition(one,multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_9,plain,
( strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,strong_iteration(A)),one),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
strong_iteration(zero) = addition(one,multiplication(zero,strong_iteration(zero))),
inference(subst,[],[refute_0_10:[bind(A,$fot(zero))]]) ).
cnf(refute_0_12,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
multiplication(zero,strong_iteration(zero)) = zero,
inference(subst,[],[refute_0_12:[bind(A,$fot(strong_iteration(zero)))]]) ).
cnf(refute_0_14,plain,
( multiplication(zero,strong_iteration(zero)) != zero
| strong_iteration(zero) != addition(one,multiplication(zero,strong_iteration(zero)))
| strong_iteration(zero) = addition(one,zero) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(zero),addition(one,multiplication(zero,strong_iteration(zero)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_15,plain,
( strong_iteration(zero) != addition(one,multiplication(zero,strong_iteration(zero)))
| strong_iteration(zero) = addition(one,zero) ),
inference(resolve,[$cnf( $equal(multiplication(zero,strong_iteration(zero)),zero) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
strong_iteration(zero) = addition(one,zero),
inference(resolve,[$cnf( $equal(strong_iteration(zero),addition(one,multiplication(zero,strong_iteration(zero)))) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_18,plain,
addition(one,zero) = one,
inference(subst,[],[refute_0_17:[bind(A,$fot(one))]]) ).
cnf(refute_0_19,plain,
( addition(one,zero) != one
| strong_iteration(zero) != addition(one,zero)
| strong_iteration(zero) = one ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(zero),addition(one,zero)) ),[1],$fot(one)]]) ).
cnf(refute_0_20,plain,
( strong_iteration(zero) != addition(one,zero)
| strong_iteration(zero) = one ),
inference(resolve,[$cnf( $equal(addition(one,zero),one) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
strong_iteration(zero) = one,
inference(resolve,[$cnf( $equal(strong_iteration(zero),addition(one,zero)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
strong_iteration(zero) != one,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(strong_iteration(zero),one) )],[refute_0_21,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 12:51:34 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.39
% 0.21/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.39
%------------------------------------------------------------------------------