TSTP Solution File: KLE119+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE119+1 : 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 : n005.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 05:26:27 EDT 2023

% Result   : Theorem 0.16s 0.57s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   56 (  39 unt;  17 typ;   0 def)
%            Number of atoms       :   39 (  38 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  13   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   4 con; 0-2 aty)
%            Number of variables   :   41 (   1 sgn;  26   !;   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,
    c: $i > $i ).

tff(decl_32,type,
    domain_difference: ( $i * $i ) > $i ).

tff(decl_33,type,
    forward_diamond: ( $i * $i ) > $i ).

tff(decl_34,type,
    backward_diamond: ( $i * $i ) > $i ).

tff(decl_35,type,
    forward_box: ( $i * $i ) > $i ).

tff(decl_36,type,
    backward_box: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk1_0: $i ).

tff(decl_38,type,
    esk2_0: $i ).

fof(goals,conjecture,
    ! [X4,X5] : addition(backward_diamond(zero,domain(X4)),domain(X5)) = domain(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(backward_diamond,axiom,
    ! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).

fof(codomain4,axiom,
    ! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain4) ).

fof(domain4,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).

fof(codomain3,axiom,
    ! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).

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

fof(codomain1,axiom,
    ! [X4] : multiplication(X4,coantidomain(X4)) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).

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

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

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

fof(c_0_10,negated_conjecture,
    ~ ! [X4,X5] : addition(backward_diamond(zero,domain(X4)),domain(X5)) = domain(X5),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_11,plain,
    ! [X43,X44] : backward_diamond(X43,X44) = codomain(multiplication(codomain(X44),X43)),
    inference(variable_rename,[status(thm)],[backward_diamond]) ).

fof(c_0_12,plain,
    ! [X37] : codomain(X37) = coantidomain(coantidomain(X37)),
    inference(variable_rename,[status(thm)],[codomain4]) ).

fof(c_0_13,negated_conjecture,
    addition(backward_diamond(zero,domain(esk1_0)),domain(esk2_0)) != domain(esk2_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_14,plain,
    ! [X32] : domain(X32) = antidomain(antidomain(X32)),
    inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_15,plain,
    backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    codomain(X1) = coantidomain(coantidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_17,plain,
    ! [X36] : addition(coantidomain(coantidomain(X36)),coantidomain(X36)) = one,
    inference(variable_rename,[status(thm)],[codomain3]) ).

fof(c_0_18,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_19,plain,
    ! [X33] : multiplication(X33,coantidomain(X33)) = zero,
    inference(variable_rename,[status(thm)],[codomain1]) ).

fof(c_0_20,plain,
    ! [X17] : multiplication(one,X17) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_21,plain,
    ! [X11] : addition(X11,zero) = X11,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_22,negated_conjecture,
    addition(backward_diamond(zero,domain(esk1_0)),domain(esk2_0)) != domain(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,plain,
    domain(X1) = antidomain(antidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_24,plain,
    backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).

fof(c_0_25,plain,
    ! [X24] : multiplication(X24,zero) = zero,
    inference(variable_rename,[status(thm)],[right_annihilation]) ).

cnf(c_0_26,plain,
    addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,plain,
    multiplication(X1,coantidomain(X1)) = zero,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,negated_conjecture,
    addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),zero))),antidomain(antidomain(esk2_0))) != antidomain(antidomain(esk2_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_24]) ).

cnf(c_0_32,plain,
    multiplication(X1,zero) = zero,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_33,plain,
    addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,plain,
    coantidomain(one) = zero,
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(zero))) != antidomain(antidomain(esk2_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_27]),c_0_32]) ).

cnf(c_0_37,plain,
    coantidomain(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : KLE119+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n005.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 29 11:54:08 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.16/0.55  start to proof: theBenchmark
% 0.16/0.57  % Version  : CSE_E---1.5
% 0.16/0.57  % Problem  : theBenchmark.p
% 0.16/0.57  % Proof found
% 0.16/0.57  % SZS status Theorem for theBenchmark.p
% 0.16/0.57  % SZS output start Proof
% See solution above
% 0.16/0.57  % Total time : 0.006000 s
% 0.16/0.57  % SZS output end Proof
% 0.16/0.57  % Total time : 0.009000 s
%------------------------------------------------------------------------------