%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG023-7 : 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 : n004.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 13:48:31 EDT 2023

% Result   : Unsatisfiable 0.17s 0.59s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   24 (  16 unt;   8 typ;   0 def)
%            Number of atoms       :   16 (  15 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   24 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    additive_identity: $i ).

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

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

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

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

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

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

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

cnf(prove_left_alternative,negated_conjecture,
    associator(x,x,y) != additive_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_alternative) ).

cnf(associator,axiom,
    associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).

cnf(inverse_product2,axiom,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).

cnf(left_alternative,axiom,
    multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_alternative) ).

cnf(distribute1,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).

cnf(right_additive_inverse,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).

cnf(right_multiplicative_zero,axiom,
    multiply(X1,additive_identity) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).

cnf(c_0_7,negated_conjecture,
    associator(x,x,y) != additive_identity,
    prove_left_alternative ).

cnf(c_0_8,axiom,
    associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
    associator ).

cnf(c_0_9,negated_conjecture,
    add(multiply(multiply(x,x),y),additive_inverse(multiply(x,multiply(x,y)))) != additive_identity,
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,axiom,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    inverse_product2 ).

cnf(c_0_11,axiom,
    multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
    left_alternative ).

cnf(c_0_12,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distribute1 ).

cnf(c_0_13,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    right_additive_inverse ).

cnf(c_0_14,axiom,
    multiply(X1,additive_identity) = additive_identity,
    right_multiplicative_zero ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_11]),c_0_12]),c_0_12]),c_0_13]),c_0_14]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG023-7 : 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 : n004.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 03:05:52 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.17/0.57  start to proof: theBenchmark
% 0.17/0.59  % Version  : CSE_E---1.5
% 0.17/0.59  % Problem  : theBenchmark.p
% 0.17/0.59  % Proof found
% 0.17/0.59  % SZS status Theorem for theBenchmark.p
% 0.17/0.59  % SZS output start Proof
% See solution above
% 0.17/0.59  % Total time : 0.003000 s
% 0.17/0.59  % SZS output end Proof
% 0.17/0.59  % Total time : 0.005000 s
%------------------------------------------------------------------------------