%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD017-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 : Wed Aug 30 22:27:19 EDT 2023

% Result   : Unsatisfiable 0.22s 0.65s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   32 (  11 unt;  13 typ;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   28 (  15   ~;  13   |;   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  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   19 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    equalish: ( $i * $i ) > $o ).

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

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

tff(decl_26,type,
    additive_inverse: $i > $i ).

tff(decl_27,type,
    multiply: ( $i * $i ) > $i ).

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

tff(decl_29,type,
    multiplicative_inverse: $i > $i ).

tff(decl_30,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(decl_31,type,
    a: $i ).

tff(decl_32,type,
    b: $i ).

tff(decl_33,type,
    c: $i ).

tff(decl_34,type,
    x: $i ).

cnf(compatibility_of_equality_and_addition,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).

cnf(a_equals_x_5,negated_conjecture,
    equalish(a,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_x_5) ).

cnf(transitivity_of_equality,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).

cnf(symmetry_of_equality,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).

cnf(add_equals_c_6,negated_conjecture,
    equalish(add(a,b),c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_c_6) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).

cnf(add_not_equal_to_c_7,negated_conjecture,
    ~ equalish(add(x,b),c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_not_equal_to_c_7) ).

cnf(c_0_7,axiom,
    ( equalish(add(X1,X2),add(X3,X2))
    | ~ defined(X2)
    | ~ equalish(X1,X3) ),
    compatibility_of_equality_and_addition ).

cnf(c_0_8,negated_conjecture,
    equalish(a,x),
    a_equals_x_5 ).

cnf(c_0_9,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X1,X3)
    | ~ equalish(X3,X2) ),
    transitivity_of_equality ).

cnf(c_0_10,negated_conjecture,
    ( equalish(add(a,X1),add(x,X1))
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,axiom,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    symmetry_of_equality ).

cnf(c_0_12,negated_conjecture,
    equalish(add(a,b),c),
    add_equals_c_6 ).

cnf(c_0_13,negated_conjecture,
    ( equalish(X1,add(x,X2))
    | ~ defined(X2)
    | ~ equalish(X1,add(a,X2)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    equalish(c,add(a,b)),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_16,negated_conjecture,
    equalish(c,add(x,b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_17,negated_conjecture,
    ~ equalish(add(x,b),c),
    add_not_equal_to_c_7 ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_16]),c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15  % Problem    : FLD017-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n003.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 23:52:25 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.59  start to proof: theBenchmark
% 0.22/0.65  % Version  : CSE_E---1.5
% 0.22/0.65  % Problem  : theBenchmark.p
% 0.22/0.65  % Proof found
% 0.22/0.65  % SZS status Theorem for theBenchmark.p
% 0.22/0.65  % SZS output start Proof
% See solution above
% 0.22/0.65  % Total time : 0.040000 s
% 0.22/0.65  % SZS output end Proof
% 0.22/0.65  % Total time : 0.043000 s
%------------------------------------------------------------------------------