%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO013-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 18:05:48 EDT 2023

% Result   : Unsatisfiable 0.21s 0.55s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   30 (  22 unt;   8 typ;   0 def)
%            Number of atoms       :   22 (  21 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    inverse: $i > $i ).

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

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

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

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

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

cnf(distributivity1,axiom,
    add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).

cnf(c_and_multiplicative_identity,hypothesis,
    add(a,c) = multiplicative_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_and_multiplicative_identity) ).

cnf(multiplicative_id2,axiom,
    multiply(multiplicative_identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).

cnf(b_and_multiplicative_identity,hypothesis,
    add(a,b) = multiplicative_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_and_multiplicative_identity) ).

cnf(b_a_additive_identity,hypothesis,
    multiply(a,b) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_additive_identity) ).

cnf(additive_id1,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).

cnf(c_a_additive_identity,hypothesis,
    multiply(a,c) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_a_additive_identity) ).

cnf(prove_b_is_a,negated_conjecture,
    b != c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_a) ).

cnf(c_0_9,axiom,
    add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
    distributivity1 ).

cnf(c_0_10,hypothesis,
    add(a,c) = multiplicative_identity,
    c_and_multiplicative_identity ).

cnf(c_0_11,axiom,
    multiply(multiplicative_identity,X1) = X1,
    multiplicative_id2 ).

cnf(c_0_12,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_13,hypothesis,
    add(a,b) = multiplicative_identity,
    b_and_multiplicative_identity ).

cnf(c_0_14,hypothesis,
    add(c,multiply(a,X1)) = add(X1,c),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]) ).

cnf(c_0_15,hypothesis,
    multiply(a,b) = additive_identity,
    b_a_additive_identity ).

cnf(c_0_16,axiom,
    add(X1,additive_identity) = X1,
    additive_id1 ).

cnf(c_0_17,hypothesis,
    add(b,multiply(a,X1)) = add(X1,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_13]),c_0_11]),c_0_12]) ).

cnf(c_0_18,hypothesis,
    multiply(a,c) = additive_identity,
    c_a_additive_identity ).

cnf(c_0_19,hypothesis,
    add(b,c) = c,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    b != c,
    prove_b_is_a ).

cnf(c_0_21,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]),c_0_12]),c_0_19]),c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : BOO013-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34  % Computer : n008.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.34  % DateTime   : Sun Aug 27 07:44:17 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.21/0.53  start to proof: theBenchmark
% 0.21/0.54  % Version  : CSE_E---1.5
% 0.21/0.54  % Problem  : theBenchmark.p
% 0.21/0.55  % Proof found
% 0.21/0.55  % SZS status Theorem for theBenchmark.p
% 0.21/0.55  % SZS output start Proof
% See solution above
% 0.21/0.55  % Total time : 0.007000 s
% 0.21/0.55  % SZS output end Proof
% 0.21/0.55  % Total time : 0.009000 s
%------------------------------------------------------------------------------