TSTP Solution File: NUM024-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM024-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n012.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 12:24:10 EDT 2022

% Result   : Unsatisfiable 41.37s 41.56s
% Output   : CNFRefutation 41.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   31 (  16 unt;   0 nHn;  25 RR)
%            Number of literals    :   49 (   0 equ;  20 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   28 (   1 sgn)

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

cnf(less_lemma,axiom,
    ( ~ less(A,B)
    | equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ) ).

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

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

cnf(plus_substitution,axiom,
    ( ~ equalish(add(A,B),add(C,B))
    | equalish(A,C) ) ).

cnf(commutativity_of_plus,axiom,
    equalish(add(A,B),add(B,A)) ).

cnf(impossible_a_is_less_than_itself,hypothesis,
    less(a,a) ).

cnf(prove_a_contradiction,negated_conjecture,
    ~ equalish(successor(A),n0) ).

cnf(refute_0_0,plain,
    ( ~ equalish(n0,successor(predecessor_of_1st_minus_2nd(a,a)))
    | equalish(successor(predecessor_of_1st_minus_2nd(a,a)),n0) ),
    inference(subst,[],[symmetry:[bind(X,$fot(n0)),bind(Y,$fot(successor(predecessor_of_1st_minus_2nd(a,a))))]]) ).

cnf(refute_0_1,plain,
    ( ~ equalish(add(n0,a),add(successor(predecessor_of_1st_minus_2nd(a,a)),a))
    | equalish(n0,successor(predecessor_of_1st_minus_2nd(a,a))) ),
    inference(subst,[],[plus_substitution:[bind(A,$fot(n0)),bind(B,$fot(a)),bind(C,$fot(successor(predecessor_of_1st_minus_2nd(a,a))))]]) ).

cnf(refute_0_2,plain,
    ( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a)
    | equalish(a,add(successor(predecessor_of_1st_minus_2nd(a,a)),a)) ),
    inference(subst,[],[symmetry:[bind(X,$fot(add(successor(predecessor_of_1st_minus_2nd(a,a)),a))),bind(Y,$fot(a))]]) ).

cnf(refute_0_3,plain,
    ( ~ less(a,a)
    | equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a) ),
    inference(subst,[],[less_lemma:[bind(A,$fot(a)),bind(B,$fot(a))]]) ).

cnf(refute_0_4,plain,
    equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a),
    inference(resolve,[$cnf( less(a,a) )],[impossible_a_is_less_than_itself,refute_0_3]) ).

cnf(refute_0_5,plain,
    equalish(a,add(successor(predecessor_of_1st_minus_2nd(a,a)),a)),
    inference(resolve,[$cnf( equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
    ( ~ equalish(X_258,a)
    | ~ equalish(a,add(successor(predecessor_of_1st_minus_2nd(a,a)),a))
    | equalish(X_258,add(successor(predecessor_of_1st_minus_2nd(a,a)),a)) ),
    inference(subst,[],[transitivity:[bind(X,$fot(X_258)),bind(Y,$fot(a)),bind(Z,$fot(add(successor(predecessor_of_1st_minus_2nd(a,a)),a)))]]) ).

cnf(refute_0_7,plain,
    ( ~ equalish(X_258,a)
    | equalish(X_258,add(successor(predecessor_of_1st_minus_2nd(a,a)),a)) ),
    inference(resolve,[$cnf( equalish(a,add(successor(predecessor_of_1st_minus_2nd(a,a)),a)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ equalish(add(n0,a),a)
    | equalish(add(n0,a),add(successor(predecessor_of_1st_minus_2nd(a,a)),a)) ),
    inference(subst,[],[refute_0_7:[bind(X_258,$fot(add(n0,a)))]]) ).

cnf(refute_0_9,plain,
    ( ~ equalish(add(add(n0,X_1129),n0),add(X_1129,n0))
    | equalish(add(n0,X_1129),X_1129) ),
    inference(subst,[],[plus_substitution:[bind(A,$fot(add(n0,X_1129))),bind(B,$fot(n0)),bind(C,$fot(X_1129))]]) ).

cnf(refute_0_10,plain,
    equalish(add(X_259,n0),X_259),
    inference(subst,[],[adding_zero:[bind(A,$fot(X_259))]]) ).

cnf(refute_0_11,plain,
    ( ~ equalish(X_259,X_260)
    | ~ equalish(add(X_259,n0),X_259)
    | equalish(add(X_259,n0),X_260) ),
    inference(subst,[],[transitivity:[bind(X,$fot(add(X_259,n0))),bind(Y,$fot(X_259)),bind(Z,$fot(X_260))]]) ).

cnf(refute_0_12,plain,
    ( ~ equalish(X_259,X_260)
    | equalish(add(X_259,n0),X_260) ),
    inference(resolve,[$cnf( equalish(add(X_259,n0),X_259) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ equalish(add(A,B),add(B,A))
    | equalish(add(add(A,B),n0),add(B,A)) ),
    inference(subst,[],[refute_0_12:[bind(X_259,$fot(add(A,B))),bind(X_260,$fot(add(B,A)))]]) ).

cnf(refute_0_14,plain,
    equalish(add(add(A,B),n0),add(B,A)),
    inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_plus,refute_0_13]) ).

cnf(refute_0_15,plain,
    equalish(add(add(n0,X_1129),n0),add(X_1129,n0)),
    inference(subst,[],[refute_0_14:[bind(A,$fot(n0)),bind(B,$fot(X_1129))]]) ).

cnf(refute_0_16,plain,
    equalish(add(n0,X_1129),X_1129),
    inference(resolve,[$cnf( equalish(add(add(n0,X_1129),n0),add(X_1129,n0)) )],[refute_0_15,refute_0_9]) ).

cnf(refute_0_17,plain,
    equalish(add(n0,a),a),
    inference(subst,[],[refute_0_16:[bind(X_1129,$fot(a))]]) ).

cnf(refute_0_18,plain,
    equalish(add(n0,a),add(successor(predecessor_of_1st_minus_2nd(a,a)),a)),
    inference(resolve,[$cnf( equalish(add(n0,a),a) )],[refute_0_17,refute_0_8]) ).

cnf(refute_0_19,plain,
    equalish(n0,successor(predecessor_of_1st_minus_2nd(a,a))),
    inference(resolve,[$cnf( equalish(add(n0,a),add(successor(predecessor_of_1st_minus_2nd(a,a)),a)) )],[refute_0_18,refute_0_1]) ).

cnf(refute_0_20,plain,
    equalish(successor(predecessor_of_1st_minus_2nd(a,a)),n0),
    inference(resolve,[$cnf( equalish(n0,successor(predecessor_of_1st_minus_2nd(a,a))) )],[refute_0_19,refute_0_0]) ).

cnf(refute_0_21,plain,
    ~ equalish(successor(predecessor_of_1st_minus_2nd(a,a)),n0),
    inference(subst,[],[prove_a_contradiction:[bind(A,$fot(predecessor_of_1st_minus_2nd(a,a)))]]) ).

cnf(refute_0_22,plain,
    $false,
    inference(resolve,[$cnf( equalish(successor(predecessor_of_1st_minus_2nd(a,a)),n0) )],[refute_0_20,refute_0_21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : NUM024-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.04/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n012.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 : Wed Jul  6 08:17:30 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 41.37/41.56  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.37/41.56  
% 41.37/41.56  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.37/41.56  
%------------------------------------------------------------------------------