%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE007+4 : 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 : n021.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 05:25:32 EDT 2023

% Result   : Theorem 0.41s 0.62s
% Output   : CNFRefutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   42 (  17 unt;  11 typ;   0 def)
%            Number of atoms       :   69 (  29 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   60 (  22   ~;  19   |;  13   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   2 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   :   36 (   0 sgn;  24   !;   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/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

fof(goals,conjecture,
    ! [X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => ( leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
        & leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).

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

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

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

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

fof(c_0_7,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_8,negated_conjecture,
    ~ ! [X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => ( leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
          & leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_9,plain,
    ( complement(X1,X2)
    | c(X1) != X2
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,negated_conjecture,
    ( test(esk3_0)
    & test(esk2_0)
    & ( ~ leq(one,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))))
      | ~ leq(addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))),one) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_11,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_12,plain,
    ( complement(X1,c(X1))
    | ~ test(X1) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    test(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

cnf(c_0_15,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,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_17,plain,
    ! [X12] : addition(X12,X12) = X12,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

cnf(c_0_18,plain,
    ( addition(X1,X2) = one
    | ~ complement(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    complement(esk2_0,c(esk2_0)),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

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

fof(c_0_21,plain,
    ! [X17] : multiplication(one,X17) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_22,negated_conjecture,
    complement(esk3_0,c(esk3_0)),
    inference(spm,[status(thm)],[c_0_12,c_0_15]) ).

cnf(c_0_23,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ leq(one,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))))
    | ~ leq(addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk2_0,c(esk2_0)),c(esk3_0))),one) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    addition(esk2_0,c(esk2_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_27,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    addition(esk3_0,c(esk3_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_20]) ).

cnf(c_0_29,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_25,c_0_26]),c_0_27]),c_0_27]),c_0_28]),c_0_29]),c_0_27]),c_0_27]),c_0_28]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : KLE007+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n021.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 12:00:14 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.41/0.60  start to proof: theBenchmark
% 0.41/0.62  % Version  : CSE_E---1.5
% 0.41/0.62  % Problem  : theBenchmark.p
% 0.41/0.62  % Proof found
% 0.41/0.62  % SZS status Theorem for theBenchmark.p
% 0.41/0.62  % SZS output start Proof
% See solution above
% 0.41/0.63  % Total time : 0.011000 s
% 0.41/0.63  % SZS output end Proof
% 0.41/0.63  % Total time : 0.014000 s
%------------------------------------------------------------------------------