%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG038-2 : 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 : n032.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 13:48:39 EDT 2023

% Result   : Unsatisfiable 0.13s 0.45s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   28 (  10 unt;  10 typ;   0 def)
%            Number of atoms       :   30 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  14   ~;  12   |;   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  :   15 (   7   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   31 (   4 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

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

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

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

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

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

cnf(addition_is_well_defined,axiom,
    ( equalish(X3,X4)
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).

cnf(multiplication_is_well_defined,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).

cnf(multiplicative_identity1,axiom,
    product(additive_identity,X1,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).

cnf(some_property,hypothesis,
    ( product(X1,h(X1,X2),X2)
    | ~ equalish(X1,additive_identity) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',some_property) ).

cnf(a_not_additive_identity,negated_conjecture,
    ~ equalish(a,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_additive_identity) ).

cnf(c_0_6,axiom,
    ( equalish(X3,X4)
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined ).

cnf(c_0_7,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2 ).

cnf(c_0_8,plain,
    ( equalish(X1,X2)
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined ).

cnf(c_0_10,axiom,
    product(additive_identity,X1,additive_identity),
    multiplicative_identity1 ).

cnf(c_0_11,hypothesis,
    ( product(X1,h(X1,X2),X2)
    | ~ equalish(X1,additive_identity) ),
    some_property ).

cnf(c_0_12,plain,
    equalish(X1,X1),
    inference(spm,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_13,plain,
    ( equalish(X1,additive_identity)
    | ~ product(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    product(additive_identity,h(additive_identity,X1),X1),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    ~ equalish(a,additive_identity),
    a_not_additive_identity ).

cnf(c_0_16,hypothesis,
    equalish(X1,additive_identity),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : RNG038-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Sun Aug 27 02:55:44 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 0.13/0.43  start to proof: theBenchmark
% 0.13/0.45  % Version  : CSE_E---1.5
% 0.13/0.45  % Problem  : theBenchmark.p
% 0.13/0.45  % Proof found
% 0.13/0.45  % SZS status Theorem for theBenchmark.p
% 0.13/0.45  % SZS output start Proof
% See solution above
% 0.13/0.45  % Total time : 0.010000 s
% 0.13/0.45  % SZS output end Proof
% 0.13/0.45  % Total time : 0.012000 s
%------------------------------------------------------------------------------