TSTP Solution File: KLE089+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE089+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 : 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 05:26:04 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   37 (  23 unt;  11 typ;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   4   ~;   0   |;   1   &)
%                                         (   0 <=>;   1  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   7   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (   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,
    antidomain: $i > $i ).

tff(decl_28,type,
    domain: $i > $i ).

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

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

tff(decl_31,type,
    esk1_0: $i ).

tff(decl_32,type,
    esk2_0: $i ).

fof(goals,conjecture,
    ! [X4,X5] :
      ( multiplication(domain(X4),X5) = zero
     <= addition(domain(X4),antidomain(X5)) = antidomain(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

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

fof(domain1,axiom,
    ! [X4] : multiplication(antidomain(X4),X4) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).

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

fof(domain4,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).

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

fof(c_0_6,negated_conjecture,
    ~ ! [X4,X5] :
        ( addition(domain(X4),antidomain(X5)) = antidomain(X5)
       => multiplication(domain(X4),X5) = zero ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).

fof(c_0_7,plain,
    ! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_8,plain,
    ! [X28] : multiplication(antidomain(X28),X28) = zero,
    inference(variable_rename,[status(thm)],[domain1]) ).

fof(c_0_9,plain,
    ! [X11] : addition(X11,zero) = X11,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_10,negated_conjecture,
    ( addition(domain(esk1_0),antidomain(esk2_0)) = antidomain(esk2_0)
    & multiplication(domain(esk1_0),esk2_0) != zero ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_11,plain,
    ! [X32] : domain(X32) = antidomain(antidomain(X32)),
    inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_12,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

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

cnf(c_0_16,negated_conjecture,
    addition(domain(esk1_0),antidomain(esk2_0)) = antidomain(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

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

cnf(c_0_18,plain,
    multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,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]) ).

cnf(c_0_20,negated_conjecture,
    addition(antidomain(antidomain(esk1_0)),antidomain(esk2_0)) = antidomain(esk2_0),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    multiplication(domain(esk1_0),esk2_0) != zero,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_22,plain,
    multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    addition(antidomain(esk2_0),antidomain(antidomain(esk1_0))) = antidomain(esk2_0),
    inference(rw,[status(thm)],[c_0_20,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    multiplication(antidomain(antidomain(esk1_0)),esk2_0) != zero,
    inference(rw,[status(thm)],[c_0_21,c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13]),c_0_24]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : KLE089+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
% 0.13/0.34  % 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 11:35:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.013000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.016000 s
%------------------------------------------------------------------------------