%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE025+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 : n022.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 05:25:43 EDT 2023

% Result   : Theorem 0.48s 0.65s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   46 (  23 unt;  12 typ;   0 def)
%            Number of atoms       :   67 (  42 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   52 (  19   ~;  15   |;  11   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   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    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   52 (   0 sgn;  34   !;   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 ).

tff(decl_33,type,
    esk4_0: $i ).

fof(goals,conjecture,
    ! [X4,X5,X6] :
      ( ( test(X5)
        & test(X6) )
     => ( multiplication(multiplication(X5,X4),c(X6)) = zero
       => multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

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

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

fof(c_0_8,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( ( test(X5)
          & test(X6) )
       => ( multiplication(multiplication(X5,X4),c(X6)) = zero
         => multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6) ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_9,negated_conjecture,
    ( test(esk3_0)
    & test(esk4_0)
    & multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) = zero
    & multiplication(esk3_0,esk2_0) != multiplication(multiplication(esk3_0,esk2_0),esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_10,plain,
    ! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_11,plain,
    ! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_12,negated_conjecture,
    multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) = zero,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X12] : addition(X12,zero) = X12,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_15,plain,
    ! [X35,X36] :
      ( ( c(X35) != X36
        | complement(X35,X36)
        | ~ test(X35) )
      & ( ~ complement(X35,X36)
        | c(X35) = X36
        | ~ test(X35) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).

cnf(c_0_16,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) = zero,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

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

fof(c_0_19,plain,
    ! [X33,X34] :
      ( ( multiplication(X33,X34) = zero
        | ~ complement(X34,X33) )
      & ( multiplication(X34,X33) = zero
        | ~ complement(X34,X33) )
      & ( addition(X33,X34) = one
        | ~ complement(X34,X33) )
      & ( multiplication(X33,X34) != zero
        | multiplication(X34,X33) != zero
        | addition(X33,X34) != one
        | complement(X34,X33) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).

cnf(c_0_20,plain,
    ( complement(X1,X2)
    | c(X1) != X2
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_21,plain,
    ! [X7,X8] : addition(X7,X8) = addition(X8,X7),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

cnf(c_0_22,negated_conjecture,
    multiplication(esk3_0,addition(X1,multiplication(esk2_0,c(esk4_0)))) = multiplication(esk3_0,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_23,plain,
    ( addition(X1,X2) = one
    | ~ complement(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,plain,
    ( complement(X1,c(X1))
    | ~ test(X1) ),
    inference(er,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_26,plain,
    ! [X17] : multiplication(X17,one) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_27,negated_conjecture,
    multiplication(esk3_0,esk2_0) != multiplication(multiplication(esk3_0,esk2_0),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_28,negated_conjecture,
    multiplication(esk3_0,multiplication(esk2_0,addition(X1,c(esk4_0)))) = multiplication(esk3_0,multiplication(esk2_0,X1)),
    inference(spm,[status(thm)],[c_0_22,c_0_16]) ).

cnf(c_0_29,plain,
    ( addition(X1,c(X1)) = one
    | ~ test(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_30,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    test(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_32,negated_conjecture,
    multiplication(esk3_0,multiplication(esk2_0,esk4_0)) != multiplication(esk3_0,esk2_0),
    inference(rw,[status(thm)],[c_0_27,c_0_13]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KLE025+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n022.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 12:16:08 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.48/0.65  % Version  : CSE_E---1.5
% 0.48/0.65  % Problem  : theBenchmark.p
% 0.48/0.65  % Proof found
% 0.48/0.65  % SZS status Theorem for theBenchmark.p
% 0.48/0.65  % SZS output start Proof
% See solution above
% 0.48/0.66  % Total time : 0.068000 s
% 0.48/0.66  % SZS output end Proof
% 0.48/0.66  % Total time : 0.071000 s
%------------------------------------------------------------------------------