TSTP Solution File: KLE083+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE083+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 : n031.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 05:25:59 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   41 (  31 unt;  10 typ;   0 def)
%            Number of atoms       :   31 (  30 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   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    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (   0 sgn;  22   !;   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 ).

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

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

fof(goals,conjecture,
    ! [X4] : X4 = multiplication(domain(X4),X4),
    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(domain3,axiom,
    ! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).

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

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_8,plain,
    ! [X11] : addition(X11,zero) = X11,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_9,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X4] : X4 = multiplication(domain(X4),X4),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_11,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_12,plain,
    ! [X28] : multiplication(antidomain(X28),X28) = zero,
    inference(variable_rename,[status(thm)],[domain1]) ).

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

cnf(c_0_14,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_15,plain,
    ! [X31] : addition(antidomain(antidomain(X31)),antidomain(X31)) = one,
    inference(variable_rename,[status(thm)],[domain3]) ).

fof(c_0_16,negated_conjecture,
    esk1_0 != multiplication(domain(esk1_0),esk1_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_17,plain,
    ! [X32] : domain(X32) = antidomain(antidomain(X32)),
    inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_18,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_21,plain,
    addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_22,plain,
    ! [X17] : multiplication(one,X17) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_23,negated_conjecture,
    esk1_0 != multiplication(domain(esk1_0),esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

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

cnf(c_0_25,plain,
    multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_26,plain,
    addition(antidomain(X1),antidomain(antidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_21,c_0_14]) ).

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

cnf(c_0_28,negated_conjecture,
    esk1_0 != multiplication(antidomain(antidomain(esk1_0)),esk1_0),
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    multiplication(antidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE083+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n031.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 12:51:26 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  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
% 0.20/0.60  % Total time : 0.013000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.016000 s
%------------------------------------------------------------------------------