%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE022+4 : 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 : n018.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 05:25:42 EDT 2023

% Result   : Theorem 0.19s 0.62s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   43 (  18 unt;  11 typ;   0 def)
%            Number of atoms       :   67 (  32 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   57 (  22   ~;  19   |;  10   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   46 (   0 sgn;  30   !;   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,
    test: $i > $o ).

tff(decl_28,type,
    complement: ( $i * $i ) > $o ).

tff(decl_29,type,
    c: $i > $i ).

tff(decl_30,type,
    esk1_1: $i > $i ).

tff(decl_31,type,
    esk2_0: $i ).

tff(decl_32,type,
    esk3_0: $i ).

fof(test_3,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).

fof(goals,conjecture,
    ! [X4,X5] :
      ( test(X5)
     => ( leq(X4,addition(multiplication(X4,X5),multiplication(X4,c(X5))))
        & leq(addition(multiplication(X4,X5),multiplication(X4,c(X5))),X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(test_2,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

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/KLE001+0.ax',right_distributivity) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(c_0_8,plain,
    ! [X34,X35] :
      ( ( c(X34) != X35
        | complement(X34,X35)
        | ~ test(X34) )
      & ( ~ complement(X34,X35)
        | c(X34) = X35
        | ~ test(X34) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X4,X5] :
        ( test(X5)
       => ( leq(X4,addition(multiplication(X4,X5),multiplication(X4,c(X5))))
          & leq(addition(multiplication(X4,X5),multiplication(X4,c(X5))),X4) ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_10,plain,
    ( complement(X1,X2)
    | c(X1) != X2
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,negated_conjecture,
    ( test(esk3_0)
    & ( ~ leq(esk2_0,addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))))
      | ~ leq(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),esk2_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_12,plain,
    ! [X32,X33] :
      ( ( multiplication(X32,X33) = zero
        | ~ complement(X33,X32) )
      & ( multiplication(X33,X32) = zero
        | ~ complement(X33,X32) )
      & ( addition(X32,X33) = one
        | ~ complement(X33,X32) )
      & ( multiplication(X32,X33) != zero
        | multiplication(X33,X32) != zero
        | addition(X32,X33) != one
        | complement(X33,X32) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).

cnf(c_0_13,plain,
    ( complement(X1,c(X1))
    | ~ test(X1) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_16,plain,
    ! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_17,plain,
    ( addition(X1,X2) = one
    | ~ complement(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,negated_conjecture,
    complement(esk3_0,c(esk3_0)),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

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

fof(c_0_20,plain,
    ! [X16] : multiplication(X16,one) = X16,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

fof(c_0_21,plain,
    ! [X26,X27] :
      ( ( ~ leq(X26,X27)
        | addition(X26,X27) = X27 )
      & ( addition(X26,X27) != X27
        | leq(X26,X27) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

fof(c_0_22,plain,
    ! [X12] : addition(X12,X12) = X12,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

cnf(c_0_23,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    addition(esk3_0,c(esk3_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_25,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ leq(esk2_0,addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))))
    | ~ leq(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_29,negated_conjecture,
    addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_30,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_29]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n018.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 12:08:18 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.62  % Version  : CSE_E---1.5
% 0.19/0.62  % Problem  : theBenchmark.p
% 0.19/0.62  % Proof found
% 0.19/0.62  % SZS status Theorem for theBenchmark.p
% 0.19/0.62  % SZS output start Proof
% See solution above
% 0.19/0.62  % Total time : 0.044000 s
% 0.19/0.62  % SZS output end Proof
% 0.19/0.62  % Total time : 0.047000 s
%------------------------------------------------------------------------------