TSTP Solution File: LAT241-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT241-1 : 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 : n032.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 06:00:11 EDT 2023

% Result   : Unsatisfiable 0.13s 0.67s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   54 (  45 unt;   7 typ;   0 def)
%            Number of atoms       :   51 (  50 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   11 (   7   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Maximal term depth    :    5 (   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   :   64 (   8 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/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(complement_meet,axiom,
    meet(X1,complement(X1)) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).

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

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

cnf(equation_H51,axiom,
    meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,X4)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H51) ).

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

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

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

cnf(c_0_17,hypothesis,
    meet(a,b) = a,
    inference(rw,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_18,axiom,
    meet(X1,complement(X1)) = zero,
    complement_meet ).

cnf(c_0_19,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    associativity_of_join ).

cnf(c_0_20,hypothesis,
    join(b,a) = b,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

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

cnf(c_0_22,plain,
    join(X1,zero) = X1,
    inference(spm,[status(thm)],[c_0_13,c_0_18]) ).

cnf(c_0_23,axiom,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

cnf(c_0_24,hypothesis,
    join(b,join(a,X1)) = join(b,X1),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,axiom,
    join(X1,complement(X1)) = one,
    complement_join ).

cnf(c_0_26,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_21]) ).

cnf(c_0_27,axiom,
    meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,X4)))),
    equation_H51 ).

cnf(c_0_28,plain,
    join(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,hypothesis,
    join(b,complement(a)) = join(b,one),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_30,plain,
    join(X1,one) = one,
    inference(spm,[status(thm)],[c_0_26,c_0_25]) ).

cnf(c_0_31,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption1 ).

cnf(c_0_32,plain,
    meet(X1,join(X2,meet(complement(X1),join(X1,X3)))) = meet(X1,join(X2,meet(complement(X1),X3))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_28]) ).

cnf(c_0_33,hypothesis,
    join(b,complement(a)) = one,
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,plain,
    meet(X1,one) = X1,
    inference(spm,[status(thm)],[c_0_31,c_0_25]) ).

cnf(c_0_35,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    associativity_of_meet ).

cnf(c_0_36,hypothesis,
    meet(b,join(X1,meet(complement(a),complement(b)))) = meet(b,join(X1,complement(b))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_14]) ).

cnf(c_0_37,plain,
    meet(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_34,c_0_14]) ).

cnf(c_0_38,hypothesis,
    meet(a,meet(b,X1)) = meet(a,X1),
    inference(spm,[status(thm)],[c_0_35,c_0_17]) ).

cnf(c_0_39,hypothesis,
    meet(b,join(complement(a),complement(b))) = meet(b,complement(a)),
    inference(spm,[status(thm)],[c_0_36,c_0_13]) ).

cnf(c_0_40,plain,
    join(one,X1) = one,
    inference(spm,[status(thm)],[c_0_31,c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    prove_distributivity ).

cnf(c_0_42,axiom,
    ( complement(X1) = X2
    | meet(X1,X2) != zero
    | join(X1,X2) != one ),
    meet_join_complement ).

cnf(c_0_43,hypothesis,
    meet(a,join(complement(a),complement(b))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_38]),c_0_18]) ).

cnf(c_0_44,plain,
    join(X1,join(complement(X1),X2)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_25]),c_0_40]) ).

cnf(c_0_45,negated_conjecture,
    join(complement(a),complement(b)) != complement(a),
    inference(rw,[status(thm)],[c_0_41,c_0_23]) ).

cnf(c_0_46,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]),c_0_45]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : LAT241-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.09  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit   : 300
% 0.08/0.27  % WCLimit    : 300
% 0.08/0.27  % DateTime   : Thu Aug 24 05:14:41 EDT 2023
% 0.08/0.27  % CPUTime  : 
% 0.13/0.45  start to proof: theBenchmark
% 0.13/0.67  % Version  : CSE_E---1.5
% 0.13/0.67  % Problem  : theBenchmark.p
% 0.13/0.67  % Proof found
% 0.13/0.67  % SZS status Theorem for theBenchmark.p
% 0.13/0.67  % SZS output start Proof
% See solution above
% 0.13/0.68  % Total time : 0.212000 s
% 0.13/0.68  % SZS output end Proof
% 0.13/0.68  % Total time : 0.214000 s
%------------------------------------------------------------------------------