TSTP Solution File: NUM020-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 : Mon Jul 18 12:24:09 EDT 2022

% Result   : Unsatisfiable 52.11s 52.27s
% Output   : CNFRefutation 52.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   24 (  14 unt;   0 nHn;  13 RR)
%            Number of literals    :   36 (   0 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   30 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(adding_zero,axiom,
    equalish(add(A,n0),A) ).

cnf(addition,axiom,
    equalish(add(A,successor(B)),successor(add(A,B))) ).

cnf(successor_substitution,axiom,
    ( ~ equalish(A,B)
    | equalish(successor(A),successor(B)) ) ).

cnf(symmetry,axiom,
    ( ~ equalish(X,Y)
    | equalish(Y,X) ) ).

cnf(transitivity,axiom,
    ( ~ equalish(X,Y)
    | ~ equalish(Y,Z)
    | equalish(X,Z) ) ).

cnf(deny_addition_lemma,negated_conjecture,
    ~ equalish(add(a,successor(n0)),successor(a)) ).

cnf(refute_0_0,plain,
    ( ~ equalish(successor(X_877),add(X_877,successor(n0)))
    | equalish(add(X_877,successor(n0)),successor(X_877)) ),
    inference(subst,[],[symmetry:[bind(X,$fot(successor(X_877))),bind(Y,$fot(add(X_877,successor(n0))))]]) ).

cnf(refute_0_1,plain,
    ( ~ equalish(add(A,successor(B)),successor(add(A,B)))
    | equalish(successor(add(A,B)),add(A,successor(B))) ),
    inference(subst,[],[symmetry:[bind(X,$fot(add(A,successor(B)))),bind(Y,$fot(successor(add(A,B))))]]) ).

cnf(refute_0_2,plain,
    equalish(successor(add(A,B)),add(A,successor(B))),
    inference(resolve,[$cnf( equalish(add(A,successor(B)),successor(add(A,B))) )],[addition,refute_0_1]) ).

cnf(refute_0_3,plain,
    equalish(successor(add(X_875,n0)),add(X_875,successor(n0))),
    inference(subst,[],[refute_0_2:[bind(A,$fot(X_875)),bind(B,$fot(n0))]]) ).

cnf(refute_0_4,plain,
    equalish(add(X_9,n0),X_9),
    inference(subst,[],[adding_zero:[bind(A,$fot(X_9))]]) ).

cnf(refute_0_5,plain,
    ( ~ equalish(add(X_9,n0),X_9)
    | equalish(X_9,add(X_9,n0)) ),
    inference(subst,[],[symmetry:[bind(X,$fot(add(X_9,n0))),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_6,plain,
    equalish(X_9,add(X_9,n0)),
    inference(resolve,[$cnf( equalish(add(X_9,n0),X_9) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    equalish(X_16,add(X_16,n0)),
    inference(subst,[],[refute_0_6:[bind(X_9,$fot(X_16))]]) ).

cnf(refute_0_8,plain,
    ( ~ equalish(X_16,add(X_16,n0))
    | equalish(successor(X_16),successor(add(X_16,n0))) ),
    inference(subst,[],[successor_substitution:[bind(A,$fot(X_16)),bind(B,$fot(add(X_16,n0)))]]) ).

cnf(refute_0_9,plain,
    equalish(successor(X_16),successor(add(X_16,n0))),
    inference(resolve,[$cnf( equalish(X_16,add(X_16,n0)) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ equalish(successor(X_16),successor(add(X_16,n0)))
    | ~ equalish(successor(add(X_16,n0)),X_74)
    | equalish(successor(X_16),X_74) ),
    inference(subst,[],[transitivity:[bind(X,$fot(successor(X_16))),bind(Y,$fot(successor(add(X_16,n0)))),bind(Z,$fot(X_74))]]) ).

cnf(refute_0_11,plain,
    ( ~ equalish(successor(add(X_16,n0)),X_74)
    | equalish(successor(X_16),X_74) ),
    inference(resolve,[$cnf( equalish(successor(X_16),successor(add(X_16,n0))) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ equalish(successor(add(X_875,n0)),add(X_875,successor(n0)))
    | equalish(successor(X_875),add(X_875,successor(n0))) ),
    inference(subst,[],[refute_0_11:[bind(X_16,$fot(X_875)),bind(X_74,$fot(add(X_875,successor(n0))))]]) ).

cnf(refute_0_13,plain,
    equalish(successor(X_875),add(X_875,successor(n0))),
    inference(resolve,[$cnf( equalish(successor(add(X_875,n0)),add(X_875,successor(n0))) )],[refute_0_3,refute_0_12]) ).

cnf(refute_0_14,plain,
    equalish(successor(X_877),add(X_877,successor(n0))),
    inference(subst,[],[refute_0_13:[bind(X_875,$fot(X_877))]]) ).

cnf(refute_0_15,plain,
    equalish(add(X_877,successor(n0)),successor(X_877)),
    inference(resolve,[$cnf( equalish(successor(X_877),add(X_877,successor(n0))) )],[refute_0_14,refute_0_0]) ).

cnf(refute_0_16,plain,
    equalish(add(a,successor(n0)),successor(a)),
    inference(subst,[],[refute_0_15:[bind(X_877,$fot(a))]]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( equalish(add(a,successor(n0)),successor(a)) )],[refute_0_16,deny_addition_lemma]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.08/0.15  % Command  : metis --show proof --show saturation %s
% 0.15/0.37  % Computer : n013.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Thu Jul  7 21:31:44 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 52.11/52.27  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.11/52.27  
% 52.11/52.27  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.11/52.27  
%------------------------------------------------------------------------------