%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 14:07:14 EDT 2023

% Result   : Unsatisfiable 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   16 (  12 unt;   4 typ;   0 def)
%            Number of atoms       :   12 (  11 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    a: $i ).

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

cnf(double_negation,hypothesis,
    negate(negate(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',double_negation) ).

cnf(robbins_axiom,axiom,
    negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).

cnf(prove_huntingtons_axiom,negated_conjecture,
    add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).

cnf(c_0_4,hypothesis,
    negate(negate(X1)) = X1,
    double_negation ).

cnf(c_0_5,axiom,
    negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
    robbins_axiom ).

cnf(c_0_6,negated_conjecture,
    add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
    prove_huntingtons_axiom ).

cnf(c_0_7,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_8,hypothesis,
    add(negate(add(X1,X2)),negate(add(X1,negate(X2)))) = negate(X1),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,hypothesis,
    add(negate(add(X1,X2)),negate(add(X2,negate(X1)))) = negate(X2),
    inference(spm,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_4])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 07:26:24 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.56  % Version  : CSE_E---1.5
% 0.20/0.56  % Problem  : theBenchmark.p
% 0.20/0.56  % Proof found
% 0.20/0.56  % SZS status Theorem for theBenchmark.p
% 0.20/0.56  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.005000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.008000 s
%------------------------------------------------------------------------------