TSTP Solution File: LAT225-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT225-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 06:00:06 EDT 2023

% Result   : Unsatisfiable 166.41s 166.59s
% Output   : CNFRefutation 166.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   73 (  59 unt;   7 typ;   0 def)
%            Number of atoms       :   77 (  76 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   25 (  14   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   96 (  13 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    meet: ( $i * $i ) > $i ).

tff(decl_23,type,
    join: ( $i * $i ) > $i ).

tff(decl_24,type,
    complement: $i > $i ).

tff(decl_25,type,
    one: $i ).

tff(decl_26,type,
    zero: $i ).

tff(decl_27,type,
    b: $i ).

tff(decl_28,type,
    a: $i ).

cnf(equation_H10,axiom,
    meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H10) ).

cnf(commutativity_of_join,axiom,
    join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).

cnf(absorption1,axiom,
    meet(X1,join(X1,X2)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).

cnf(complement_join,axiom,
    join(X1,complement(X1)) = one,
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).

cnf(absorption2,axiom,
    join(X1,meet(X1,X2)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).

cnf(commutativity_of_meet,axiom,
    meet(X1,X2) = meet(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).

cnf(prove_distributivity_hypothesis,hypothesis,
    meet(b,a) = a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).

cnf(associativity_of_join,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).

cnf(idempotence_of_join,axiom,
    join(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).

cnf(meet_join_complement,axiom,
    ( complement(X1) = X2
    | meet(X1,X2) != zero
    | join(X1,X2) != one ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).

cnf(associativity_of_meet,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).

cnf(complement_meet,axiom,
    meet(X1,complement(X1)) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).

cnf(prove_distributivity,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).

cnf(c_0_13,axiom,
    meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))),
    equation_H10 ).

cnf(c_0_14,axiom,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

cnf(c_0_15,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption1 ).

cnf(c_0_16,axiom,
    join(X1,complement(X1)) = one,
    complement_join ).

cnf(c_0_17,axiom,
    join(X1,meet(X1,X2)) = X1,
    absorption2 ).

cnf(c_0_18,axiom,
    meet(X1,X2) = meet(X2,X1),
    commutativity_of_meet ).

cnf(c_0_19,hypothesis,
    meet(b,a) = a,
    prove_distributivity_hypothesis ).

cnf(c_0_20,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    associativity_of_join ).

cnf(c_0_21,axiom,
    join(X1,X1) = X1,
    idempotence_of_join ).

cnf(c_0_22,plain,
    meet(X1,join(X2,meet(X3,join(meet(X2,X3),X1)))) = meet(X1,join(X2,meet(X1,X3))),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_23,plain,
    meet(X1,one) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_24,plain,
    join(X1,meet(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,hypothesis,
    meet(a,b) = a,
    inference(rw,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_26,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    meet(complement(meet(X1,X2)),join(X1,meet(X2,complement(meet(X1,X2))))) = meet(join(X1,X2),complement(meet(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23]),c_0_18]),c_0_18]) ).

cnf(c_0_28,hypothesis,
    join(a,b) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]) ).

cnf(c_0_29,plain,
    join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_20]) ).

cnf(c_0_30,plain,
    join(X1,one) = one,
    inference(spm,[status(thm)],[c_0_26,c_0_16]) ).

cnf(c_0_31,axiom,
    ( complement(X1) = X2
    | meet(X1,X2) != zero
    | join(X1,X2) != one ),
    meet_join_complement ).

cnf(c_0_32,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    associativity_of_meet ).

cnf(c_0_33,axiom,
    meet(X1,complement(X1)) = zero,
    complement_meet ).

cnf(c_0_34,hypothesis,
    meet(complement(a),join(a,meet(b,complement(a)))) = meet(b,complement(a)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).

cnf(c_0_35,plain,
    join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
    inference(spm,[status(thm)],[c_0_29,c_0_24]) ).

cnf(c_0_36,plain,
    meet(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_37,plain,
    join(X1,join(complement(X1),X2)) = join(one,X2),
    inference(spm,[status(thm)],[c_0_20,c_0_16]) ).

cnf(c_0_38,plain,
    join(one,X1) = one,
    inference(spm,[status(thm)],[c_0_14,c_0_30]) ).

cnf(c_0_39,plain,
    join(X1,join(X2,X1)) = join(X2,X1),
    inference(spm,[status(thm)],[c_0_26,c_0_14]) ).

cnf(c_0_40,plain,
    ( complement(X1) = X2
    | meet(X2,X1) != zero
    | join(X1,X2) != one ),
    inference(spm,[status(thm)],[c_0_31,c_0_18]) ).

cnf(c_0_41,plain,
    meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_32]) ).

cnf(c_0_42,plain,
    meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
    inference(spm,[status(thm)],[c_0_33,c_0_32]) ).

cnf(c_0_43,hypothesis,
    meet(complement(meet(b,complement(a))),join(complement(a),meet(join(a,meet(b,complement(a))),complement(meet(b,complement(a)))))) = complement(meet(b,complement(a))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_34]),c_0_35]),c_0_16]),c_0_36]) ).

cnf(c_0_44,plain,
    join(X1,join(complement(X1),X2)) = one,
    inference(rw,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_45,plain,
    join(X1,join(X2,join(X3,X1))) = join(X2,join(X3,X1)),
    inference(spm,[status(thm)],[c_0_39,c_0_20]) ).

cnf(c_0_46,plain,
    ( complement(meet(X1,X2)) = X3
    | meet(X2,meet(X3,X1)) != zero
    | join(meet(X1,X2),X3) != one ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,hypothesis,
    meet(complement(a),meet(join(a,meet(b,complement(a))),complement(meet(b,complement(a))))) = zero,
    inference(spm,[status(thm)],[c_0_42,c_0_34]) ).

cnf(c_0_48,hypothesis,
    meet(complement(a),join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a))))))) = complement(a),
    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_13,c_0_43]),c_0_20]),c_0_16]),c_0_30]),c_0_23]),c_0_20]) ).

cnf(c_0_49,plain,
    join(X1,join(X2,join(X3,complement(X1)))) = one,
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_50,hypothesis,
    ( complement(meet(complement(a),complement(meet(b,complement(a))))) = join(a,meet(b,complement(a)))
    | join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a)))))) != one ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_18]),c_0_18]),c_0_14]),c_0_20]) ).

cnf(c_0_51,hypothesis,
    join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a)))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_48]),c_0_20]),c_0_20]),c_0_49]) ).

cnf(c_0_52,plain,
    complement(complement(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_14]),c_0_16])]) ).

cnf(c_0_53,hypothesis,
    complement(meet(complement(a),complement(meet(b,complement(a))))) = join(a,meet(b,complement(a))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).

cnf(c_0_54,plain,
    join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
    inference(spm,[status(thm)],[c_0_20,c_0_17]) ).

cnf(c_0_55,plain,
    ( complement(meet(X1,complement(meet(X2,X1)))) = X2
    | join(X2,meet(X1,complement(meet(X2,X1)))) != one ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_14]) ).

cnf(c_0_56,hypothesis,
    meet(complement(a),complement(meet(b,complement(a)))) = complement(join(a,meet(b,complement(a)))),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_57,plain,
    join(X1,join(X2,join(meet(X1,X3),X4))) = join(X2,join(X1,X4)),
    inference(spm,[status(thm)],[c_0_29,c_0_54]) ).

cnf(c_0_58,hypothesis,
    join(a,join(b,X1)) = join(b,X1),
    inference(spm,[status(thm)],[c_0_20,c_0_28]) ).

cnf(c_0_59,hypothesis,
    ( join(a,meet(b,complement(a))) = b
    | join(b,complement(join(a,meet(b,complement(a))))) != one ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52]) ).

cnf(c_0_60,hypothesis,
    join(b,complement(join(a,meet(b,complement(a))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_51]),c_0_30]),c_0_58]),c_0_56]) ).

cnf(c_0_61,hypothesis,
    join(a,meet(b,complement(a))) = b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).

cnf(c_0_62,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    prove_distributivity ).

cnf(c_0_63,hypothesis,
    meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
    inference(rw,[status(thm)],[c_0_56,c_0_61]) ).

cnf(c_0_64,negated_conjecture,
    join(complement(a),complement(b)) != complement(a),
    inference(rw,[status(thm)],[c_0_62,c_0_14]) ).

cnf(c_0_65,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_63]),c_0_64]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : LAT225-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.16  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.37  % Computer : n025.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Thu Aug 24 06:26:06 EDT 2023
% 0.16/0.38  % CPUTime  : 
% 0.23/0.60  start to proof: theBenchmark
% 166.41/166.59  % Version  : CSE_E---1.5
% 166.41/166.59  % Problem  : theBenchmark.p
% 166.41/166.59  % Proof found
% 166.41/166.59  % SZS status Theorem for theBenchmark.p
% 166.41/166.59  % SZS output start Proof
% See solution above
% 166.41/166.59  % Total time : 165.786000 s
% 166.41/166.59  % SZS output end Proof
% 166.41/166.59  % Total time : 165.798000 s
%------------------------------------------------------------------------------