%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 : Wed Jul 20 20:29:47 EDT 2022

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   9 unt;   0 nHn;  14 RR)
%            Number of literals    :   27 (   0 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   11 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(less_than_successor,axiom,
    less_than(X,successor(X)) ).

cnf(transitivity_of_less_than,axiom,
    ( less_than(X,Z)
    | ~ less_than(X,Y)
    | ~ less_than(Y,Z) ) ).

cnf(x_not_less_than_x,axiom,
    ~ less_than(X,X) ).

cnf(clause_3,negated_conjecture,
    less_than(i,n) ).

cnf(clause_5,negated_conjecture,
    less_than(a(i),a(m)) ).

cnf(clause_6,negated_conjecture,
    ( less_than(X,i)
    | ~ less_than(X,successor(n))
    | ~ less_than(a(X),a(m)) ) ).

cnf(refute_0_0,plain,
    less_than(X_19,successor(X_19)),
    inference(subst,[],[less_than_successor:[bind(X,$fot(X_19))]]) ).

cnf(refute_0_1,plain,
    ( ~ less_than(X_18,X_19)
    | ~ less_than(X_19,successor(X_19))
    | less_than(X_18,successor(X_19)) ),
    inference(subst,[],[transitivity_of_less_than:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(successor(X_19)))]]) ).

cnf(refute_0_2,plain,
    ( ~ less_than(X_18,X_19)
    | less_than(X_18,successor(X_19)) ),
    inference(resolve,[$cnf( less_than(X_19,successor(X_19)) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ less_than(i,n)
    | less_than(i,successor(n)) ),
    inference(subst,[],[refute_0_2:[bind(X_18,$fot(i)),bind(X_19,$fot(n))]]) ).

cnf(refute_0_4,plain,
    less_than(i,successor(n)),
    inference(resolve,[$cnf( less_than(i,n) )],[clause_3,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ less_than(a(i),a(m))
    | ~ less_than(i,successor(n))
    | less_than(i,i) ),
    inference(subst,[],[clause_6:[bind(X,$fot(i))]]) ).

cnf(refute_0_6,plain,
    ( ~ less_than(i,successor(n))
    | less_than(i,i) ),
    inference(resolve,[$cnf( less_than(a(i),a(m)) )],[clause_5,refute_0_5]) ).

cnf(refute_0_7,plain,
    ~ less_than(i,i),
    inference(subst,[],[x_not_less_than_x:[bind(X,$fot(i))]]) ).

cnf(refute_0_8,plain,
    ~ less_than(i,successor(n)),
    inference(resolve,[$cnf( less_than(i,i) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( less_than(i,successor(n)) )],[refute_0_4,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWV006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 19:36:14 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------