TSTP Solution File: LAT005-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT005-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n018.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 05:59:05 EDT 2023

% Result   : Unsatisfiable 0.91s 0.94s
% Output   : CNFRefutation 0.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   77 (  62 unt;   9 typ;   0 def)
%            Number of atoms       :   74 (  65 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (  11   ~;   6   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  114 (  14 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,
    n0: $i ).

tff(decl_25,type,
    n1: $i ).

tff(decl_26,type,
    complement: ( $i * $i ) > $o ).

tff(decl_27,type,
    r1: $i ).

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

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

tff(decl_30,type,
    r2: $i ).

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

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

cnf(modular,axiom,
    ( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
    | meet(X1,X2) != X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',modular) ).

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

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

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(complement_join,axiom,
    ( join(X1,X2) = n1
    | ~ complement(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_join) ).

cnf(complement_of_a_meet_b,hypothesis,
    complement(r2,meet(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).

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(x_meet_1,axiom,
    meet(X1,n1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_meet_1) ).

cnf(complement_meet,axiom,
    ( meet(X1,X2) = n0
    | ~ complement(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_meet) ).

cnf(complement_of_a_join_b,hypothesis,
    complement(r1,join(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).

cnf(x_meet_0,axiom,
    meet(X1,n0) = n0,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_meet_0) ).

cnf(prove_lemma,negated_conjecture,
    r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).

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

cnf(x_join_0,axiom,
    join(X1,n0) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_join_0) ).

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

cnf(c_0_17,axiom,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

cnf(c_0_18,axiom,
    ( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
    | meet(X1,X2) != X1 ),
    modular ).

cnf(c_0_19,plain,
    meet(X1,join(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,axiom,
    meet(X1,X2) = meet(X2,X1),
    commutativity_of_meet ).

cnf(c_0_21,plain,
    join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,plain,
    join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_16]) ).

cnf(c_0_23,axiom,
    join(X1,meet(X1,X2)) = X1,
    absorption2 ).

cnf(c_0_24,axiom,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    associativity_of_meet ).

cnf(c_0_25,plain,
    meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X2,join(X3,X1))),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X1,X3))),
    inference(spm,[status(thm)],[c_0_20,c_0_22]) ).

cnf(c_0_27,plain,
    meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_21,c_0_20]) ).

cnf(c_0_28,plain,
    join(X1,meet(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_23,c_0_20]) ).

cnf(c_0_29,plain,
    meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_16,c_0_24]) ).

cnf(c_0_30,plain,
    meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X3,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_20]) ).

cnf(c_0_31,axiom,
    ( join(X1,X2) = n1
    | ~ complement(X1,X2) ),
    complement_join ).

cnf(c_0_32,hypothesis,
    complement(r2,meet(a,b)),
    complement_of_a_meet_b ).

cnf(c_0_33,plain,
    join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X1,X3))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_27]) ).

cnf(c_0_34,plain,
    join(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X2,join(meet(X1,X2),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_17]) ).

cnf(c_0_35,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    associativity_of_join ).

cnf(c_0_36,plain,
    meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,X3)),
    inference(spm,[status(thm)],[c_0_30,c_0_20]) ).

cnf(c_0_37,hypothesis,
    join(meet(a,b),r2) = n1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]) ).

cnf(c_0_38,axiom,
    meet(X1,n1) = X1,
    x_meet_1 ).

cnf(c_0_39,axiom,
    ( meet(X1,X2) = n0
    | ~ complement(X1,X2) ),
    complement_meet ).

cnf(c_0_40,hypothesis,
    complement(r1,join(a,b)),
    complement_of_a_join_b ).

cnf(c_0_41,axiom,
    meet(X1,n0) = n0,
    x_meet_0 ).

cnf(c_0_42,plain,
    meet(X1,join(meet(X2,X1),X3)) = join(meet(X2,X1),meet(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_34]) ).

cnf(c_0_43,plain,
    join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
    inference(spm,[status(thm)],[c_0_35,c_0_28]) ).

cnf(c_0_44,hypothesis,
    join(meet(a,b),meet(a,r2)) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
    prove_lemma ).

cnf(c_0_46,plain,
    meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
    inference(spm,[status(thm)],[c_0_24,c_0_16]) ).

cnf(c_0_47,hypothesis,
    meet(r1,join(a,b)) = n0,
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,plain,
    meet(n0,X1) = n0,
    inference(spm,[status(thm)],[c_0_41,c_0_20]) ).

cnf(c_0_49,plain,
    meet(X1,join(X2,meet(X3,X1))) = join(meet(X3,X1),meet(X1,X2)),
    inference(spm,[status(thm)],[c_0_42,c_0_17]) ).

cnf(c_0_50,hypothesis,
    join(b,meet(a,r2)) = join(a,b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17]) ).

cnf(c_0_51,axiom,
    meet(X1,X1) = X1,
    idempotence_of_meet ).

cnf(c_0_52,negated_conjecture,
    meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))) != r1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_20]),c_0_20]),c_0_20]) ).

cnf(c_0_53,plain,
    meet(join(X1,X2),join(X3,X2)) = join(X2,meet(X1,join(X3,X2))),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_54,plain,
    meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_46,c_0_20]) ).

cnf(c_0_55,hypothesis,
    meet(r1,meet(join(a,b),X1)) = n0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_47]),c_0_48]) ).

cnf(c_0_56,hypothesis,
    meet(join(a,b),r2) = join(meet(a,r2),meet(b,r2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_20]),c_0_20]) ).

cnf(c_0_57,plain,
    meet(X1,meet(X1,X2)) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_24,c_0_51]) ).

cnf(c_0_58,negated_conjecture,
    join(r1,meet(a,meet(r2,join(r1,meet(b,r2))))) != r1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_26]),c_0_24]) ).

cnf(c_0_59,plain,
    meet(X1,join(X2,meet(X3,X1))) = join(meet(X3,X1),meet(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_28]),c_0_20]) ).

cnf(c_0_60,plain,
    meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,X3)),
    inference(spm,[status(thm)],[c_0_54,c_0_25]) ).

cnf(c_0_61,hypothesis,
    meet(r1,join(meet(a,r2),meet(b,r2))) = n0,
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,axiom,
    join(X1,n0) = X1,
    x_join_0 ).

cnf(c_0_63,plain,
    meet(X1,meet(X2,X1)) = meet(X2,X1),
    inference(spm,[status(thm)],[c_0_57,c_0_20]) ).

cnf(c_0_64,hypothesis,
    meet(a,meet(b,r2)) = n0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_20]),c_0_24]) ).

cnf(c_0_65,negated_conjecture,
    join(r1,meet(a,join(meet(r1,r2),meet(b,r2)))) != r1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_17]) ).

cnf(c_0_66,hypothesis,
    meet(a,join(meet(r1,r2),meet(b,r2))) = n0,
    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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_24]),c_0_63]),c_0_64]),c_0_24]),c_0_42]),c_0_20]),c_0_17]) ).

cnf(c_0_67,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_62])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT005-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n018.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 09:18:27 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.91/0.94  % Version  : CSE_E---1.5
% 0.91/0.94  % Problem  : theBenchmark.p
% 0.91/0.94  % Proof found
% 0.91/0.94  % SZS status Theorem for theBenchmark.p
% 0.91/0.94  % SZS output start Proof
% See solution above
% 0.91/0.95  % Total time : 0.387000 s
% 0.91/0.95  % SZS output end Proof
% 0.91/0.95  % Total time : 0.390000 s
%------------------------------------------------------------------------------