%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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  : 300s
% DateTime : Thu Aug 31 21:36:06 EDT 2023

% Result   : Unsatisfiable 0.18s 0.57s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   31 (  13 unt;   9 typ;   0 def)
%            Number of atoms       :   37 (   3 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   33 (  18   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   4   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-1 aty)
%            Number of variables   :   20 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    successor: $i > $i ).

tff(decl_23,type,
    predecessor: $i > $i ).

tff(decl_24,type,
    less_than: ( $i * $i ) > $o ).

tff(decl_25,type,
    n: $i ).

tff(decl_26,type,
    k: $i ).

tff(decl_27,type,
    i: $i ).

tff(decl_28,type,
    m: $i ).

tff(decl_29,type,
    one: $i ).

tff(decl_30,type,
    a: $i > $i ).

cnf(anti_symmetry_of_less_than,axiom,
    ( ~ less_than(X1,X2)
    | ~ less_than(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',anti_symmetry_of_less_than) ).

cnf(clause_5,negated_conjecture,
    less_than(i,m),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).

cnf(clause_11,negated_conjecture,
    ( less_than(X1,i)
    | ~ less_than(X1,successor(n))
    | ~ less_than(a(X1),a(k)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).

cnf(clause_8,negated_conjecture,
    less_than(a(m),a(k)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).

cnf(transitivity_of_less_than,axiom,
    ( less_than(X1,X2)
    | ~ less_than(X1,X3)
    | ~ less_than(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',transitivity_of_less_than) ).

cnf(less_than_successor,axiom,
    less_than(X1,successor(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',less_than_successor) ).

cnf(all_related,axiom,
    ( less_than(X1,X2)
    | less_than(X2,X1)
    | X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',all_related) ).

cnf(clause_4,negated_conjecture,
    ~ less_than(n,m),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).

cnf(c_0_8,axiom,
    ( ~ less_than(X1,X2)
    | ~ less_than(X2,X1) ),
    anti_symmetry_of_less_than ).

cnf(c_0_9,negated_conjecture,
    less_than(i,m),
    clause_5 ).

cnf(c_0_10,negated_conjecture,
    ( less_than(X1,i)
    | ~ less_than(X1,successor(n))
    | ~ less_than(a(X1),a(k)) ),
    clause_11 ).

cnf(c_0_11,negated_conjecture,
    less_than(a(m),a(k)),
    clause_8 ).

cnf(c_0_12,negated_conjecture,
    ~ less_than(m,i),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,axiom,
    ( less_than(X1,X2)
    | ~ less_than(X1,X3)
    | ~ less_than(X3,X2) ),
    transitivity_of_less_than ).

cnf(c_0_14,axiom,
    less_than(X1,successor(X1)),
    less_than_successor ).

cnf(c_0_15,negated_conjecture,
    ~ less_than(m,successor(n)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

cnf(c_0_16,plain,
    ( less_than(X1,successor(X2))
    | ~ less_than(X1,X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    ~ less_than(m,n),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_18,axiom,
    ( less_than(X1,X2)
    | less_than(X2,X1)
    | X1 = X2 ),
    all_related ).

cnf(c_0_19,negated_conjecture,
    ~ less_than(n,m),
    clause_4 ).

cnf(c_0_20,negated_conjecture,
    m = n,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_20]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWV007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n028.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    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 06:54:55 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.57  % Version  : CSE_E---1.5
% 0.18/0.57  % Problem  : theBenchmark.p
% 0.18/0.57  % Proof found
% 0.18/0.57  % SZS status Theorem for theBenchmark.p
% 0.18/0.57  % SZS output start Proof
% See solution above
% 0.18/0.57  % Total time : 0.010000 s
% 0.18/0.57  % SZS output end Proof
% 0.18/0.57  % Total time : 0.013000 s
%------------------------------------------------------------------------------