TSTP Solution File: LAT241-10 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 06:00:10 EDT 2023

% Result   : Unsatisfiable 78.10s 78.09s
% Output   : CNFRefutation 78.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   60 (  52 unt;   8 typ;   0 def)
%            Number of atoms       :   52 (  51 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    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    9 (   4   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-4 aty)
%            Number of variables   :   80 (  15 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    join: ( $i * $i ) > $i ).

tff(decl_25,type,
    complement: $i > $i ).

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

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

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

tff(decl_29,type,
    a: $i ).

cnf(absorption2,axiom,
    join(X1,meet(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).

cnf(commutativity_of_meet,axiom,
    meet(X1,X2) = meet(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).

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

cnf(commutativity_of_join,axiom,
    join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).

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

cnf(absorption1,axiom,
    meet(X1,join(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).

cnf(complement_join,axiom,
    join(X1,complement(X1)) = one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).

cnf(complement_meet,axiom,
    meet(X1,complement(X1)) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).

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/sandbox/benchmark/theBenchmark.p',equation_H51) ).

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

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

cnf(meet_join_complement,axiom,
    ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).

cnf(ifeq_axiom,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

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,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

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

cnf(c_0_20,hypothesis,
    join(a,b) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_21,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption1 ).

cnf(c_0_22,hypothesis,
    join(a,join(b,X1)) = join(b,X1),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,axiom,
    join(X1,complement(X1)) = one,
    complement_join ).

cnf(c_0_24,axiom,
    meet(X1,complement(X1)) = zero,
    complement_meet ).

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

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

cnf(c_0_27,plain,
    join(X1,zero) = X1,
    inference(spm,[status(thm)],[c_0_13,c_0_24]) ).

cnf(c_0_28,hypothesis,
    join(b,join(X1,a)) = join(b,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_25]),c_0_19]) ).

cnf(c_0_29,plain,
    meet(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_14,c_0_26]) ).

cnf(c_0_30,plain,
    meet(X1,join(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_21,c_0_18]) ).

cnf(c_0_31,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_32,plain,
    join(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_27]) ).

cnf(c_0_33,hypothesis,
    join(b,join(a,X1)) = join(b,X1),
    inference(spm,[status(thm)],[c_0_28,c_0_18]) ).

cnf(c_0_34,plain,
    join(X1,one) = one,
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

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

cnf(c_0_36,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_31,c_0_24]),c_0_32]) ).

cnf(c_0_37,hypothesis,
    join(b,complement(a)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_34]) ).

cnf(c_0_38,plain,
    meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_21,c_0_35]) ).

cnf(c_0_39,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_36,c_0_37]),c_0_26]),c_0_14]) ).

cnf(c_0_40,plain,
    meet(X1,meet(complement(X1),X2)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24]),c_0_32]) ).

cnf(c_0_41,hypothesis,
    meet(a,meet(b,X1)) = meet(a,X1),
    inference(spm,[status(thm)],[c_0_35,c_0_17]) ).

cnf(c_0_42,hypothesis,
    meet(b,join(complement(a),complement(b))) = meet(b,complement(a)),
    inference(spm,[status(thm)],[c_0_39,c_0_13]) ).

cnf(c_0_43,plain,
    meet(X1,meet(X2,complement(X1))) = zero,
    inference(spm,[status(thm)],[c_0_40,c_0_14]) ).

cnf(c_0_44,plain,
    join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_13,c_0_19]) ).

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

cnf(c_0_46,axiom,
    ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
    meet_join_complement ).

cnf(c_0_47,hypothesis,
    meet(a,join(complement(a),complement(b))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_48,plain,
    join(X1,join(complement(X1),X2)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_23]),c_0_29]) ).

cnf(c_0_49,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom ).

cnf(c_0_50,negated_conjecture,
    join(complement(a),complement(b)) != complement(a),
    inference(rw,[status(thm)],[c_0_45,c_0_18]) ).

cnf(c_0_51,hypothesis,
    $false,
    inference(sr,[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_48]),c_0_49]),c_0_49]),c_0_50]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n023.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 05:24:57 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.44/0.61  start to proof: theBenchmark
% 78.10/78.09  % Version  : CSE_E---1.5
% 78.10/78.09  % Problem  : theBenchmark.p
% 78.10/78.09  % Proof found
% 78.10/78.09  % SZS status Theorem for theBenchmark.p
% 78.10/78.09  % SZS output start Proof
% See solution above
% 78.10/78.10  % Total time : 77.479000 s
% 78.10/78.10  % SZS output end Proof
% 78.10/78.10  % Total time : 77.485000 s
%------------------------------------------------------------------------------