TSTP Solution File: LAT235-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT235-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 06:00:09 EDT 2023

% Result   : Unsatisfiable 0.17s 0.75s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   56 (  46 unt;   7 typ;   0 def)
%            Number of atoms       :   54 (  53 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   8   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Maximal term depth    :    7 (   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   :   72 (  11 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(absorption2,axiom,
    join(X1,meet(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).

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

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

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

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

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

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

cnf(equation_H34,axiom,
    meet(X1,join(X2,meet(X3,X4))) = meet(X1,join(X2,meet(X3,join(X2,meet(X4,join(X2,X3)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H34) ).

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

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

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

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

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

cnf(c_0_13,axiom,
    join(X1,meet(X1,X2)) = X1,
    absorption2 ).

cnf(c_0_14,axiom,
    meet(X1,X2) = meet(X2,X1),
    commutativity_of_meet ).

cnf(c_0_15,hypothesis,
    meet(b,a) = a,
    prove_distributivity_hypothesis ).

cnf(c_0_16,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption1 ).

cnf(c_0_17,axiom,
    join(X1,complement(X1)) = one,
    complement_join ).

cnf(c_0_18,plain,
    join(X1,meet(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,hypothesis,
    meet(a,b) = a,
    inference(rw,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_20,plain,
    meet(X1,one) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    associativity_of_join ).

cnf(c_0_22,hypothesis,
    join(b,a) = b,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,axiom,
    join(X1,X1) = X1,
    idempotence_of_join ).

cnf(c_0_24,plain,
    meet(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_20,c_0_14]) ).

cnf(c_0_25,hypothesis,
    join(b,join(a,X1)) = join(b,X1),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_21,c_0_23]) ).

cnf(c_0_27,plain,
    join(one,X1) = one,
    inference(spm,[status(thm)],[c_0_16,c_0_24]) ).

cnf(c_0_28,axiom,
    meet(X1,join(X2,meet(X3,X4))) = meet(X1,join(X2,meet(X3,join(X2,meet(X4,join(X2,X3)))))),
    equation_H34 ).

cnf(c_0_29,hypothesis,
    join(b,complement(a)) = join(b,one),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_30,plain,
    join(X1,one) = one,
    inference(spm,[status(thm)],[c_0_26,c_0_17]) ).

cnf(c_0_31,plain,
    join(X1,join(X2,X1)) = join(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_21]) ).

cnf(c_0_32,plain,
    join(X1,join(complement(X1),X2)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_27]) ).

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

cnf(c_0_34,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    associativity_of_meet ).

cnf(c_0_35,plain,
    join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))) = join(X1,meet(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_28]),c_0_24]) ).

cnf(c_0_36,hypothesis,
    join(b,complement(a)) = one,
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_37,plain,
    join(complement(X1),join(X2,X1)) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]),c_0_21]) ).

cnf(c_0_38,axiom,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

cnf(c_0_39,axiom,
    ( complement(X1) = X2
    | meet(X1,X2) != zero
    | join(X1,X2) != one ),
    meet_join_complement ).

cnf(c_0_40,plain,
    meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,hypothesis,
    join(b,meet(complement(a),join(b,X1))) = join(b,meet(complement(a),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_20]) ).

cnf(c_0_42,plain,
    join(X1,complement(meet(X1,X2))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_13]),c_0_38]) ).

cnf(c_0_43,plain,
    ( meet(X1,complement(meet(X2,X1))) = complement(X2)
    | join(X2,meet(X1,complement(meet(X2,X1)))) != one ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_44,hypothesis,
    join(b,meet(complement(a),complement(meet(b,X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]),c_0_29]),c_0_30]) ).

cnf(c_0_45,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    prove_distributivity ).

cnf(c_0_46,hypothesis,
    meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_47,negated_conjecture,
    join(complement(a),complement(b)) != complement(a),
    inference(rw,[status(thm)],[c_0_45,c_0_38]) ).

cnf(c_0_48,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_46]),c_0_47]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT235-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32  % Computer : n004.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Thu Aug 24 06:22:08 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.17/0.60  start to proof: theBenchmark
% 0.17/0.75  % Version  : CSE_E---1.5
% 0.17/0.75  % Problem  : theBenchmark.p
% 0.17/0.75  % Proof found
% 0.17/0.75  % SZS status Theorem for theBenchmark.p
% 0.17/0.75  % SZS output start Proof
% See solution above
% 0.17/0.76  % Total time : 0.146000 s
% 0.17/0.76  % SZS output end Proof
% 0.17/0.76  % Total time : 0.148000 s
%------------------------------------------------------------------------------