%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE138+1 : TPTP v8.1.2. Released v4.0.0.
% 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 05:26:31 EDT 2023

% Result   : Theorem 0.15s 0.55s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   24 (  17 unt;   7 typ;   0 def)
%            Number of atoms       :   17 (  16 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (   1 sgn;  10   !;   0   ?;   0   :)

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

tff(decl_23,type,
    zero: $i ).

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

tff(decl_25,type,
    one: $i ).

tff(decl_26,type,
    star: $i > $i ).

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

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

fof(infty_unfold1,axiom,
    ! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

fof(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

fof(goals,conjecture,
    strong_iteration(zero) = one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(c_0_5,plain,
    ! [X31] : strong_iteration(X31) = addition(multiplication(X31,strong_iteration(X31)),one),
    inference(variable_rename,[status(thm)],[infty_unfold1]) ).

fof(c_0_6,plain,
    ! [X4,X5] : addition(X4,X5) = addition(X5,X4),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

cnf(c_0_7,plain,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X22] : multiplication(zero,X22) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

fof(c_0_10,plain,
    ! [X9] : addition(X9,zero) = X9,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_11,negated_conjecture,
    strong_iteration(zero) != one,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).

cnf(c_0_12,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    strong_iteration(zero) != one,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : KLE138+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.34  % Computer : n032.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit   : 300
% 0.10/0.34  % WCLimit    : 300
% 0.10/0.34  % DateTime   : Tue Aug 29 11:58:16 EDT 2023
% 0.10/0.34  % CPUTime  : 
% 0.15/0.54  start to proof: theBenchmark
% 0.15/0.55  % Version  : CSE_E---1.5
% 0.15/0.55  % Problem  : theBenchmark.p
% 0.15/0.55  % Proof found
% 0.15/0.55  % SZS status Theorem for theBenchmark.p
% 0.15/0.55  % SZS output start Proof
% See solution above
% 0.15/0.55  % Total time : 0.004000 s
% 0.15/0.55  % SZS output end Proof
% 0.15/0.55  % Total time : 0.006000 s
%------------------------------------------------------------------------------