%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 18:05:53 EDT 2023

% Result   : Unsatisfiable 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :   11 (  10 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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   17 (   4 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,
    n1: $i ).

tff(decl_26,type,
    n0: $i ).

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

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

cnf(add_multiply,axiom,
    add(multiply(X1,X2),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply) ).

cnf(multiply_add,axiom,
    multiply(add(X1,X2),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).

cnf(multiply_add_property,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).

cnf(prove_commutativity_of_multiply,negated_conjecture,
    multiply(b,a) != multiply(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity_of_multiply) ).

cnf(c_0_4,axiom,
    add(multiply(X1,X2),X2) = X2,
    add_multiply ).

cnf(c_0_5,axiom,
    multiply(add(X1,X2),X2) = X2,
    multiply_add ).

cnf(c_0_6,plain,
    add(X1,X1) = X1,
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
    multiply_add_property ).

cnf(c_0_8,negated_conjecture,
    multiply(b,a) != multiply(a,b),
    prove_commutativity_of_multiply ).

cnf(c_0_9,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun Aug 27 08:51:53 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.59  % Total time : 0.007000 s
% 0.21/0.59  % SZS output end Proof
% 0.21/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------