%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG007-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 13:48:24 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   26 (  21 unt;   5 typ;   0 def)
%            Number of atoms       :   21 (  20 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 (   2 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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   25 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

cnf(multiply_additive_inverse1,axiom,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).

cnf(boolean_ring,hypothesis,
    multiply(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).

cnf(additive_inverse_additive_inverse,axiom,
    additive_inverse(additive_inverse(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).

cnf(multiply_additive_inverse2,axiom,
    multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).

cnf(left_additive_inverse,axiom,
    add(additive_inverse(X1),X1) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).

cnf(commutative_addition,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).

cnf(prove_inverse,negated_conjecture,
    add(a,a) != additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse) ).

cnf(c_0_7,axiom,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    multiply_additive_inverse1 ).

cnf(c_0_8,hypothesis,
    multiply(X1,X1) = X1,
    boolean_ring ).

cnf(c_0_9,hypothesis,
    multiply(X1,additive_inverse(X1)) = additive_inverse(X1),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,axiom,
    additive_inverse(additive_inverse(X1)) = X1,
    additive_inverse_additive_inverse ).

cnf(c_0_11,axiom,
    multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
    multiply_additive_inverse2 ).

cnf(c_0_12,axiom,
    add(additive_inverse(X1),X1) = additive_identity,
    left_additive_inverse ).

cnf(c_0_13,axiom,
    add(X1,X2) = add(X2,X1),
    commutative_addition ).

cnf(c_0_14,hypothesis,
    multiply(additive_inverse(X1),X1) = X1,
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,plain,
    multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
    inference(rw,[status(thm)],[c_0_11,c_0_7]) ).

cnf(c_0_16,plain,
    add(X1,additive_inverse(X1)) = additive_identity,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,hypothesis,
    additive_inverse(X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_9]) ).

cnf(c_0_18,negated_conjecture,
    add(a,a) != additive_identity,
    prove_inverse ).

cnf(c_0_19,plain,
    add(X1,X1) = additive_identity,
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : RNG007-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n023.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 01:45:11 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.004000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------