%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO013-1 : 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 : n026.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 0.18s 0.59s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   57 (  29 unt;  10 typ;   0 def)
%            Number of atoms       :   79 (  12 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   66 (  34   ~;  32   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   5   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   80 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    product: ( $i * $i * $i ) > $o ).

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

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

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

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

tff(decl_30,type,
    y: $i ).

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

cnf(distributivity1,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity1) ).

cnf(multiplicative_identity2,axiom,
    product(X1,multiplicative_identity,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).

cnf(sum_to_multiplicative_identity2,negated_conjecture,
    sum(x,z,multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).

cnf(commutativity_of_multiplication,axiom,
    ( product(X2,X1,X3)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).

cnf(product_to_additive_identity1,negated_conjecture,
    product(x,y,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity1) ).

cnf(sum_to_multiplicative_identity1,negated_conjecture,
    sum(x,y,multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).

cnf(addition_is_well_defined,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).

cnf(product_to_additive_identity2,negated_conjecture,
    product(x,z,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity2) ).

cnf(multiplication_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).

cnf(prove_both_inverse_are_equal,negated_conjecture,
    y != z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).

cnf(c_0_14,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    distributivity1 ).

cnf(c_0_15,axiom,
    product(X1,multiplicative_identity,X1),
    multiplicative_identity2 ).

cnf(c_0_16,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    commutativity_of_addition ).

cnf(c_0_17,negated_conjecture,
    sum(x,z,multiplicative_identity),
    sum_to_multiplicative_identity2 ).

cnf(c_0_18,plain,
    ( sum(X1,X2,X3)
    | ~ product(X3,X4,X2)
    | ~ product(X3,X5,X1)
    | ~ sum(X5,X4,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    sum(z,x,multiplicative_identity),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,axiom,
    ( product(X2,X1,X3)
    | ~ product(X1,X2,X3) ),
    commutativity_of_multiplication ).

cnf(c_0_21,negated_conjecture,
    product(x,y,additive_identity),
    product_to_additive_identity1 ).

cnf(c_0_22,negated_conjecture,
    sum(x,y,multiplicative_identity),
    sum_to_multiplicative_identity1 ).

cnf(c_0_23,negated_conjecture,
    ( sum(X1,X2,X3)
    | ~ product(X3,x,X2)
    | ~ product(X3,z,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    product(y,x,additive_identity),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined ).

cnf(c_0_26,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2 ).

cnf(c_0_27,negated_conjecture,
    sum(y,x,multiplicative_identity),
    inference(spm,[status(thm)],[c_0_16,c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    product(x,z,additive_identity),
    product_to_additive_identity2 ).

cnf(c_0_29,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined ).

cnf(c_0_30,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

cnf(c_0_31,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition ).

cnf(c_0_32,negated_conjecture,
    ( sum(X1,additive_identity,y)
    | ~ product(y,z,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_33,plain,
    ( X1 = X2
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    ( sum(X1,X2,X3)
    | ~ product(X3,x,X2)
    | ~ product(X3,y,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_27]) ).

cnf(c_0_35,negated_conjecture,
    product(z,x,additive_identity),
    inference(spm,[status(thm)],[c_0_20,c_0_28]) ).

cnf(c_0_36,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_37,plain,
    product(X1,X2,multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_20,c_0_30]) ).

cnf(c_0_38,plain,
    ( X1 = add(X2,X3)
    | ~ sum(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_31]) ).

cnf(c_0_39,negated_conjecture,
    sum(multiply(y,z),additive_identity,y),
    inference(spm,[status(thm)],[c_0_32,c_0_30]) ).

cnf(c_0_40,plain,
    add(X1,additive_identity) = X1,
    inference(spm,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_41,negated_conjecture,
    ( sum(X1,additive_identity,z)
    | ~ product(z,y,X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_42,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_43,negated_conjecture,
    multiply(y,z) = y,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    sum(y,additive_identity,z),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_30]),c_0_42]),c_0_43]) ).

cnf(c_0_45,negated_conjecture,
    y != z,
    prove_both_inverse_are_equal ).

cnf(c_0_46,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_40]),c_0_45]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : BOO013-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n026.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   : Sun Aug 27 08:06:49 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.56  start to proof: theBenchmark
% 0.18/0.59  % Version  : CSE_E---1.5
% 0.18/0.59  % Problem  : theBenchmark.p
% 0.18/0.59  % Proof found
% 0.18/0.59  % SZS status Theorem for theBenchmark.p
% 0.18/0.59  % SZS output start Proof
% See solution above
% 0.18/0.60  % Total time : 0.025000 s
% 0.18/0.60  % SZS output end Proof
% 0.18/0.60  % Total time : 0.028000 s
%------------------------------------------------------------------------------