TSTP Solution File: LAT005-5 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT005-5 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 05:59:06 EDT 2023

% Result   : Unsatisfiable 1.14s 1.25s
% Output   : CNFRefutation 1.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  113 (  60 unt;  16 typ;   0 def)
%            Number of atoms       :  163 (  17 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  134 (  68   ~;  66   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   4   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;  12 con; 0-2 aty)
%            Number of variables   :  146 (   8 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    n1: $i ).

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

tff(decl_24,type,
    n0: $i ).

tff(decl_25,type,
    meet: ( $i * $i * $i ) > $o ).

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

tff(decl_27,type,
    join_of: ( $i * $i ) > $i ).

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

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

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

tff(decl_31,type,
    r2: $i ).

tff(decl_32,type,
    e: $i ).

tff(decl_33,type,
    c2: $i ).

tff(decl_34,type,
    r1: $i ).

tff(decl_35,type,
    d: $i ).

tff(decl_36,type,
    a2: $i ).

tff(decl_37,type,
    b2: $i ).

cnf(commutativity_of_meet,axiom,
    ( meet(X2,X1,X3)
    | ~ meet(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',commutativity_of_meet) ).

cnf(meet_r2_and_a,negated_conjecture,
    meet(r2,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_a) ).

cnf(associativity_of_join2,axiom,
    ( join(X1,X5,X6)
    | ~ join(X1,X2,X3)
    | ~ join(X2,X4,X5)
    | ~ join(X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',associativity_of_join2) ).

cnf(join_a_and_b,negated_conjecture,
    join(a,b,c2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_a_and_b) ).

cnf(absorbtion1,axiom,
    ( join(X1,X3,X1)
    | ~ meet(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',absorbtion1) ).

cnf(commutativity_of_join,axiom,
    ( join(X2,X1,X3)
    | ~ join(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',commutativity_of_join) ).

cnf(join_r1_and_d,negated_conjecture,
    join(r1,d,b2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_d) ).

cnf(meet_r2_and_b,negated_conjecture,
    meet(r2,b,e),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_b) ).

cnf(modularity1,axiom,
    ( join(X1,X5,X6)
    | ~ meet(X1,X2,X1)
    | ~ join(X1,X3,X4)
    | ~ meet(X3,X2,X5)
    | ~ meet(X2,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',modularity1) ).

cnf(meet_c2_and_r1,negated_conjecture,
    meet(c2,r1,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c2_and_r1) ).

cnf(absorbtion2,axiom,
    ( meet(X1,X3,X1)
    | ~ join(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',absorbtion2) ).

cnf(join_0_and_x,axiom,
    join(n0,X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',join_0_and_x) ).

cnf(join_total_function_2,axiom,
    ( X3 = X4
    | ~ join(X1,X2,X3)
    | ~ join(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',join_total_function_2) ).

cnf(associativity_of_meet1,axiom,
    ( meet(X3,X4,X6)
    | ~ meet(X1,X2,X3)
    | ~ meet(X2,X4,X5)
    | ~ meet(X1,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',associativity_of_meet1) ).

cnf(meet_a_and_b,negated_conjecture,
    meet(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a_and_b) ).

cnf(meet_c_and_r2,negated_conjecture,
    meet(c,r2,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c_and_r2) ).

cnf(meet_total_function_2,axiom,
    ( X3 = X4
    | ~ meet(X1,X2,X3)
    | ~ meet(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',meet_total_function_2) ).

cnf(join_total_function_1,axiom,
    join(X1,X2,join_of(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',join_total_function_1) ).

cnf(meet_total_function_1,axiom,
    meet(X1,X2,meet_of(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',meet_total_function_1) ).

cnf(associativity_of_meet2,axiom,
    ( meet(X1,X5,X6)
    | ~ meet(X1,X2,X3)
    | ~ meet(X2,X4,X5)
    | ~ meet(X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',associativity_of_meet2) ).

cnf(meet_0_and_x,axiom,
    meet(n0,X1,n0),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT002-0.ax',meet_0_and_x) ).

cnf(join_r1_and_e,negated_conjecture,
    join(r1,e,a2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_e) ).

cnf(meet_a2_and_b2,negated_conjecture,
    ~ meet(a2,b2,r1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a2_and_b2) ).

cnf(c_0_23,axiom,
    ( meet(X2,X1,X3)
    | ~ meet(X1,X2,X3) ),
    commutativity_of_meet ).

cnf(c_0_24,negated_conjecture,
    meet(r2,a,d),
    meet_r2_and_a ).

cnf(c_0_25,axiom,
    ( join(X1,X5,X6)
    | ~ join(X1,X2,X3)
    | ~ join(X2,X4,X5)
    | ~ join(X3,X4,X6) ),
    associativity_of_join2 ).

cnf(c_0_26,negated_conjecture,
    join(a,b,c2),
    join_a_and_b ).

cnf(c_0_27,axiom,
    ( join(X1,X3,X1)
    | ~ meet(X1,X2,X3) ),
    absorbtion1 ).

cnf(c_0_28,negated_conjecture,
    meet(a,r2,d),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    ( join(X1,X2,c2)
    | ~ join(X3,b,X2)
    | ~ join(X1,X3,a) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,axiom,
    ( join(X2,X1,X3)
    | ~ join(X1,X2,X3) ),
    commutativity_of_join ).

cnf(c_0_31,negated_conjecture,
    join(a,d,a),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    join(r1,d,b2),
    join_r1_and_d ).

cnf(c_0_33,negated_conjecture,
    ( join(X1,c2,c2)
    | ~ join(X1,a,a) ),
    inference(spm,[status(thm)],[c_0_29,c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    join(d,a,a),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    meet(r2,b,e),
    meet_r2_and_b ).

cnf(c_0_36,axiom,
    ( join(X1,X5,X6)
    | ~ meet(X1,X2,X1)
    | ~ join(X1,X3,X4)
    | ~ meet(X3,X2,X5)
    | ~ meet(X2,X4,X6) ),
    modularity1 ).

cnf(c_0_37,negated_conjecture,
    join(d,r1,b2),
    inference(spm,[status(thm)],[c_0_30,c_0_32]) ).

cnf(c_0_38,negated_conjecture,
    meet(c2,r1,n0),
    meet_c2_and_r1 ).

cnf(c_0_39,axiom,
    ( meet(X1,X3,X1)
    | ~ join(X1,X2,X3) ),
    absorbtion2 ).

cnf(c_0_40,negated_conjecture,
    join(d,c2,c2),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,axiom,
    join(n0,X1,X1),
    join_0_and_x ).

cnf(c_0_42,negated_conjecture,
    meet(b,r2,e),
    inference(spm,[status(thm)],[c_0_23,c_0_35]) ).

cnf(c_0_43,negated_conjecture,
    ( join(d,X1,X2)
    | ~ meet(d,X3,d)
    | ~ meet(r1,X3,X1)
    | ~ meet(X3,b2,X2) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_44,negated_conjecture,
    meet(r1,c2,n0),
    inference(spm,[status(thm)],[c_0_23,c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    meet(d,c2,d),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,axiom,
    ( X3 = X4
    | ~ join(X1,X2,X3)
    | ~ join(X1,X2,X4) ),
    join_total_function_2 ).

cnf(c_0_47,plain,
    join(X1,n0,X1),
    inference(spm,[status(thm)],[c_0_30,c_0_41]) ).

cnf(c_0_48,axiom,
    ( meet(X3,X4,X6)
    | ~ meet(X1,X2,X3)
    | ~ meet(X2,X4,X5)
    | ~ meet(X1,X5,X6) ),
    associativity_of_meet1 ).

cnf(c_0_49,negated_conjecture,
    meet(a,b,c),
    meet_a_and_b ).

cnf(c_0_50,negated_conjecture,
    meet(c,r2,n0),
    meet_c_and_r2 ).

cnf(c_0_51,axiom,
    ( X3 = X4
    | ~ meet(X1,X2,X3)
    | ~ meet(X1,X2,X4) ),
    meet_total_function_2 ).

cnf(c_0_52,negated_conjecture,
    join(b,e,b),
    inference(spm,[status(thm)],[c_0_27,c_0_42]) ).

cnf(c_0_53,negated_conjecture,
    join(b,a,c2),
    inference(spm,[status(thm)],[c_0_30,c_0_26]) ).

cnf(c_0_54,axiom,
    join(X1,X2,join_of(X1,X2)),
    join_total_function_1 ).

cnf(c_0_55,negated_conjecture,
    ( join(d,n0,X1)
    | ~ meet(c2,b2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_56,axiom,
    meet(X1,X2,meet_of(X1,X2)),
    meet_total_function_1 ).

cnf(c_0_57,plain,
    ( X1 = X2
    | ~ join(X2,n0,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_58,negated_conjecture,
    ( meet(X1,b,X2)
    | ~ meet(X3,c,X2)
    | ~ meet(X3,a,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_59,negated_conjecture,
    meet(r2,c,n0),
    inference(spm,[status(thm)],[c_0_23,c_0_50]) ).

cnf(c_0_60,negated_conjecture,
    ( X1 = d
    | ~ meet(r2,a,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_24]) ).

cnf(c_0_61,negated_conjecture,
    join(e,b,b),
    inference(spm,[status(thm)],[c_0_30,c_0_52]) ).

cnf(c_0_62,axiom,
    ( meet(X1,X5,X6)
    | ~ meet(X1,X2,X3)
    | ~ meet(X2,X4,X5)
    | ~ meet(X3,X4,X6) ),
    associativity_of_meet2 ).

cnf(c_0_63,negated_conjecture,
    meet(b,c2,b),
    inference(spm,[status(thm)],[c_0_39,c_0_53]) ).

cnf(c_0_64,plain,
    ( X1 = join_of(X2,X3)
    | ~ join(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_54]) ).

cnf(c_0_65,negated_conjecture,
    join(d,n0,meet_of(c2,b2)),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_66,plain,
    join_of(X1,n0) = X1,
    inference(spm,[status(thm)],[c_0_57,c_0_54]) ).

cnf(c_0_67,plain,
    meet(X1,X2,meet_of(X2,X1)),
    inference(spm,[status(thm)],[c_0_23,c_0_56]) ).

cnf(c_0_68,negated_conjecture,
    ( meet(X1,b,n0)
    | ~ meet(r2,a,X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_69,negated_conjecture,
    meet_of(r2,a) = d,
    inference(spm,[status(thm)],[c_0_60,c_0_56]) ).

cnf(c_0_70,negated_conjecture,
    meet(e,b,e),
    inference(spm,[status(thm)],[c_0_39,c_0_61]) ).

cnf(c_0_71,plain,
    ( meet(X1,X2,meet_of(X3,X4))
    | ~ meet(X5,X4,X2)
    | ~ meet(X1,X5,X3) ),
    inference(spm,[status(thm)],[c_0_62,c_0_56]) ).

cnf(c_0_72,negated_conjecture,
    meet(c2,b,b),
    inference(spm,[status(thm)],[c_0_23,c_0_63]) ).

cnf(c_0_73,negated_conjecture,
    meet_of(c2,b2) = d,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).

cnf(c_0_74,plain,
    ( X1 = meet_of(X2,X3)
    | ~ meet(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_56]) ).

cnf(c_0_75,plain,
    ( X1 = meet_of(X2,X3)
    | ~ meet(X3,X2,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_67]) ).

cnf(c_0_76,negated_conjecture,
    meet(d,b,n0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_56]),c_0_69]) ).

cnf(c_0_77,axiom,
    meet(n0,X1,n0),
    meet_0_and_x ).

cnf(c_0_78,negated_conjecture,
    meet(b,e,e),
    inference(spm,[status(thm)],[c_0_23,c_0_70]) ).

cnf(c_0_79,negated_conjecture,
    ( meet(X1,b,meet_of(X2,b))
    | ~ meet(X1,c2,X2) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_80,negated_conjecture,
    meet(b2,c2,d),
    inference(spm,[status(thm)],[c_0_67,c_0_73]) ).

cnf(c_0_81,plain,
    meet_of(X1,X2) = meet_of(X2,X1),
    inference(spm,[status(thm)],[c_0_74,c_0_67]) ).

cnf(c_0_82,negated_conjecture,
    meet_of(b,d) = n0,
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_83,plain,
    ( X1 = n0
    | ~ meet(n0,X2,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_77]) ).

cnf(c_0_84,negated_conjecture,
    ( meet(X1,e,meet_of(X2,e))
    | ~ meet(X1,b,X2) ),
    inference(spm,[status(thm)],[c_0_71,c_0_78]) ).

cnf(c_0_85,negated_conjecture,
    meet(b2,b,n0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]) ).

cnf(c_0_86,plain,
    meet_of(n0,X1) = n0,
    inference(spm,[status(thm)],[c_0_83,c_0_56]) ).

cnf(c_0_87,negated_conjecture,
    join(r1,e,a2),
    join_r1_and_e ).

cnf(c_0_88,negated_conjecture,
    meet(b2,e,n0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).

cnf(c_0_89,negated_conjecture,
    ( join(r1,X1,X2)
    | ~ meet(r1,X3,r1)
    | ~ meet(e,X3,X1)
    | ~ meet(X3,a2,X2) ),
    inference(spm,[status(thm)],[c_0_36,c_0_87]) ).

cnf(c_0_90,negated_conjecture,
    meet(e,b2,n0),
    inference(spm,[status(thm)],[c_0_23,c_0_88]) ).

cnf(c_0_91,negated_conjecture,
    meet(r1,b2,r1),
    inference(spm,[status(thm)],[c_0_39,c_0_32]) ).

cnf(c_0_92,negated_conjecture,
    ( join(r1,n0,X1)
    | ~ meet(b2,a2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91])]) ).

cnf(c_0_93,negated_conjecture,
    join(r1,n0,meet_of(a2,b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_56]),c_0_81]) ).

cnf(c_0_94,negated_conjecture,
    meet_of(a2,b2) = r1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_93]),c_0_66]) ).

cnf(c_0_95,negated_conjecture,
    ~ meet(a2,b2,r1),
    meet_a2_and_b2 ).

cnf(c_0_96,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_94]),c_0_95]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : LAT005-5 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Thu Aug 24 06:15:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 1.14/1.25  % Version  : CSE_E---1.5
% 1.14/1.25  % Problem  : theBenchmark.p
% 1.14/1.25  % Proof found
% 1.14/1.25  % SZS status Theorem for theBenchmark.p
% 1.14/1.25  % SZS output start Proof
% See solution above
% 1.14/1.25  % Total time : 0.699000 s
% 1.14/1.25  % SZS output end Proof
% 1.14/1.25  % Total time : 0.702000 s
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