TSTP Solution File: KLE038+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE038+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 : n011.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 0.22s 0.62s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   51 (  40 unt;   7 typ;   0 def)
%            Number of atoms       :   50 (  37 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   :   71 (   0 sgn;  36   !;   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(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).

fof(star_unfold_right,axiom,
    ! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).

fof(left_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).

fof(goals,conjecture,
    ! [X4] : leq(X4,star(X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).

fof(c_0_10,plain,
    ! [X5,X6] : addition(X5,X6) = addition(X6,X5),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_11,plain,
    ! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

cnf(c_0_12,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X11] : addition(X11,X11) = X11,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_15,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_16,plain,
    ! [X27] : leq(addition(one,multiplication(X27,star(X27))),star(X27)),
    inference(variable_rename,[status(thm)],[star_unfold_right]) ).

cnf(c_0_17,plain,
    addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_21,plain,
    ! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_22,plain,
    ! [X16] : multiplication(one,X16) = X16,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_23,negated_conjecture,
    ~ ! [X4] : leq(X4,star(X4)),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_24,plain,
    ! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

fof(c_0_25,plain,
    ! [X15] : multiplication(X15,one) = X15,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_26,plain,
    addition(X1,addition(X2,X1)) = addition(X2,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_27,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_19,c_0_20]),c_0_13]),c_0_12]) ).

cnf(c_0_28,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_13,c_0_18]) ).

cnf(c_0_29,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_31,negated_conjecture,
    ~ leq(esk1_0,star(esk1_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).

cnf(c_0_32,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_34,plain,
    addition(star(X1),multiplication(X1,star(X1))) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_13]),c_0_12]),c_0_28]) ).

cnf(c_0_35,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_12]) ).

cnf(c_0_36,negated_conjecture,
    ~ leq(esk1_0,star(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_37,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_38,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_12]) ).

cnf(c_0_39,plain,
    multiplication(addition(X1,one),star(X1)) = star(X1),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    addition(one,star(X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_28,c_0_27]) ).

cnf(c_0_41,negated_conjecture,
    addition(esk1_0,star(esk1_0)) != star(esk1_0),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_42,plain,
    addition(X1,star(X1)) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_13]),c_0_40]),c_0_12]),c_0_40]),c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KLE038+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n011.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Aug 29 11:20:26 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.57  start to proof: theBenchmark
% 0.22/0.62  % Version  : CSE_E---1.5
% 0.22/0.62  % Problem  : theBenchmark.p
% 0.22/0.62  % Proof found
% 0.22/0.62  % SZS status Theorem for theBenchmark.p
% 0.22/0.62  % SZS output start Proof
% See solution above
% 0.22/0.63  % Total time : 0.045000 s
% 0.22/0.63  % SZS output end Proof
% 0.22/0.63  % Total time : 0.048000 s
%------------------------------------------------------------------------------