%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD015-3 : 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 : n013.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 22:27:18 EDT 2023

% Result   : Unsatisfiable 0.19s 0.65s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   43 (  17 unt;  12 typ;   0 def)
%            Number of atoms       :   55 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   50 (  26   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    additive_identity: $i ).

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

tff(decl_25,type,
    additive_inverse: $i > $i ).

tff(decl_26,type,
    product: ( $i * $i * $i ) > $o ).

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

tff(decl_28,type,
    multiplicative_inverse: $i > $i ).

tff(decl_29,type,
    add: ( $i * $i ) > $i ).

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

tff(decl_31,type,
    less_or_equal: ( $i * $i ) > $o ).

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

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

cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).

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

cnf(associativity_addition_2,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).

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

cnf(commutativity_addition,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).

cnf(sum_3,negated_conjecture,
    sum(additive_identity,additive_inverse(a),additive_inverse(b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).

cnf(associativity_addition_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).

cnf(not_sum_4,negated_conjecture,
    ~ sum(additive_identity,a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).

cnf(c_0_9,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_10,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_11,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    associativity_addition_2 ).

cnf(c_0_12,hypothesis,
    sum(additive_identity,a,a),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_14,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_15,hypothesis,
    ( sum(X1,a,X2)
    | ~ sum(X3,a,X2)
    | ~ sum(X3,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,hypothesis,
    sum(additive_inverse(a),a,additive_identity),
    inference(spm,[status(thm)],[c_0_13,c_0_10]) ).

cnf(c_0_17,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_18,negated_conjecture,
    sum(additive_identity,additive_inverse(a),additive_inverse(b)),
    sum_3 ).

cnf(c_0_19,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_20,hypothesis,
    sum(additive_identity,b,b),
    inference(spm,[status(thm)],[c_0_9,c_0_14]) ).

cnf(c_0_21,hypothesis,
    ( sum(X1,a,additive_identity)
    | ~ sum(additive_inverse(a),additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    sum(additive_inverse(a),additive_identity,additive_inverse(b)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,hypothesis,
    ( sum(X1,X2,b)
    | ~ sum(X3,b,X2)
    | ~ sum(X1,X3,additive_identity) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,hypothesis,
    sum(additive_inverse(b),b,additive_identity),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_25,negated_conjecture,
    sum(additive_inverse(b),a,additive_identity),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,hypothesis,
    ( sum(X1,additive_identity,b)
    | ~ sum(X1,additive_inverse(b),additive_identity) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    sum(a,additive_inverse(b),additive_identity),
    inference(spm,[status(thm)],[c_0_17,c_0_25]) ).

cnf(c_0_28,hypothesis,
    sum(a,additive_identity,b),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    ~ sum(additive_identity,a,b),
    not_sum_4 ).

cnf(c_0_30,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : FLD015-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun Aug 27 23:28:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.64  % Version  : CSE_E---1.5
% 0.19/0.65  % Problem  : theBenchmark.p
% 0.19/0.65  % Proof found
% 0.19/0.65  % SZS status Theorem for theBenchmark.p
% 0.19/0.65  % SZS output start Proof
% See solution above
% 0.19/0.65  % Total time : 0.066000 s
% 0.19/0.65  % SZS output end Proof
% 0.19/0.65  % Total time : 0.069000 s
%------------------------------------------------------------------------------