TSTP Solution File: LAT019-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT019-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 05:59:13 EDT 2023

% Result   : Unsatisfiable 0.19s 0.66s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   49 (  44 unt;   5 typ;   0 def)
%            Number of atoms       :   44 (  43 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (   0 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,
    a: $i ).

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

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

cnf(quasi_lattice2,axiom,
    meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).

cnf(commutativity_of_meet,axiom,
    meet(X1,X2) = meet(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).

cnf(associativity_of_meet,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).

cnf(idempotence_of_meet,axiom,
    meet(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).

cnf(distributivity_law,hypothesis,
    meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_law) ).

cnf(commutativity_of_join,axiom,
    join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).

cnf(associativity_of_join,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',associativity_of_join) ).

cnf(idempotence_of_join,axiom,
    join(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).

cnf(prove_distributivity_law_dual,negated_conjecture,
    join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_law_dual) ).

cnf(c_0_9,axiom,
    meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
    quasi_lattice2 ).

cnf(c_0_10,axiom,
    meet(X1,X2) = meet(X2,X1),
    commutativity_of_meet ).

cnf(c_0_11,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    associativity_of_meet ).

cnf(c_0_12,axiom,
    meet(X1,X1) = X1,
    idempotence_of_meet ).

cnf(c_0_13,plain,
    meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
    distributivity_law ).

cnf(c_0_15,plain,
    meet(X1,meet(X1,X2)) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,axiom,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

cnf(c_0_17,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    associativity_of_join ).

cnf(c_0_18,axiom,
    join(X1,X1) = X1,
    idempotence_of_join ).

cnf(c_0_19,plain,
    meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
    inference(spm,[status(thm)],[c_0_13,c_0_10]) ).

cnf(c_0_20,hypothesis,
    meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).

cnf(c_0_21,hypothesis,
    meet(X1,join(X2,X1)) = join(X1,meet(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_16]) ).

cnf(c_0_22,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_17]) ).

cnf(c_0_24,hypothesis,
    join(X1,join(X2,meet(X2,X1))) = join(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_12]),c_0_10]),c_0_21]) ).

cnf(c_0_25,plain,
    meet(join(X1,X2),join(meet(X2,X3),X1)) = join(meet(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_13,c_0_16]) ).

cnf(c_0_26,hypothesis,
    meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).

cnf(c_0_27,plain,
    meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_22]),c_0_20]) ).

cnf(c_0_28,hypothesis,
    join(X1,join(X2,meet(X1,X2))) = join(X2,X1),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    meet(join(X1,X2),join(X3,X1)) = join(X1,meet(join(X1,X2),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_26]),c_0_16]) ).

cnf(c_0_30,hypothesis,
    meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,plain,
    join(X1,meet(join(X2,X1),X3)) = join(X1,meet(join(X1,X3),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_29]),c_0_30]) ).

cnf(c_0_32,plain,
    meet(join(X1,join(X2,X3)),join(X1,join(X2,meet(X3,X4)))) = join(X1,join(X2,meet(X3,X4))),
    inference(spm,[status(thm)],[c_0_13,c_0_13]) ).

cnf(c_0_33,plain,
    join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X1,X3))),
    inference(spm,[status(thm)],[c_0_31,c_0_10]) ).

cnf(c_0_34,plain,
    join(X1,meet(join(X1,join(X2,X3)),join(X2,meet(X3,X4)))) = join(X1,join(X2,meet(X3,X4))),
    inference(rw,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_35,plain,
    join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,join(X1,X3))),
    inference(spm,[status(thm)],[c_0_33,c_0_16]) ).

cnf(c_0_36,hypothesis,
    meet(join(X1,X2),join(X3,join(X1,meet(X2,X4)))) = join(X1,join(meet(join(X1,X2),X3),meet(X2,X4))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_23]) ).

cnf(c_0_37,negated_conjecture,
    join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
    prove_distributivity_law_dual ).

cnf(c_0_38,plain,
    join(X1,join(X2,join(meet(join(X2,X3),X1),meet(X3,X4)))) = join(X1,join(X2,meet(X3,X4))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_39,hypothesis,
    meet(X1,join(X1,X2)) = join(X1,meet(X1,X2)),
    inference(spm,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_40,hypothesis,
    join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X1,X3)),
    inference(spm,[status(thm)],[c_0_14,c_0_10]) ).

cnf(c_0_41,negated_conjecture,
    join(a,meet(c,join(a,b))) != join(a,meet(b,c)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_27]),c_0_10]) ).

cnf(c_0_42,plain,
    join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
    inference(rw,[status(thm)],[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_22,c_0_38]),c_0_22]),c_0_10]),c_0_39]),c_0_17]),c_0_40]),c_0_22]) ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT019-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n029.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   : Thu Aug 24 09:48:38 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.66  % Version  : CSE_E---1.5
% 0.19/0.66  % Problem  : theBenchmark.p
% 0.19/0.66  % Proof found
% 0.19/0.66  % SZS status Theorem for theBenchmark.p
% 0.19/0.66  % SZS output start Proof
% See solution above
% 0.19/0.67  % Total time : 0.082000 s
% 0.19/0.67  % SZS output end Proof
% 0.19/0.67  % Total time : 0.085000 s
%------------------------------------------------------------------------------