TSTP Solution File: KLE037+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE037+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 05:25:48 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   32 (  21 unt;   7 typ;   0 def)
%            Number of atoms       :   31 (  18 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   14 (   8   ~;   4   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   35 (   0 sgn;  20   !;   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,
    leq: ( $i * $i ) > $o ).

tff(decl_27,type,
    star: $i > $i ).

tff(decl_28,type,
    esk1_0: $i ).

fof(goals,conjecture,
    ! [X4] : leq(one,star(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).

fof(star_unfold_right,axiom,
    ! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X4] : leq(one,star(X4)),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_7,plain,
    ! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_8,plain,
    ! [X11] : addition(X11,X11) = X11,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_9,plain,
    ! [X25,X26] :
      ( ( ~ leq(X25,X26)
        | addition(X25,X26) = X26 )
      & ( addition(X25,X26) != X26
        | leq(X25,X26) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

fof(c_0_10,plain,
    ! [X27] : leq(addition(one,multiplication(X27,star(X27))),star(X27)),
    inference(variable_rename,[status(thm)],[star_unfold_right]) ).

fof(c_0_11,plain,
    ! [X5,X6] : addition(X5,X6) = addition(X6,X5),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_12,negated_conjecture,
    ~ leq(one,star(esk1_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_13,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ~ leq(one,star(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_20,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_21,plain,
    addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13]),c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    addition(one,star(esk1_0)) != star(esk1_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    addition(one,star(X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : KLE037+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 10:49:43 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.034000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.037000 s
%------------------------------------------------------------------------------