TSTP Solution File: MGT056+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : MGT056+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/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 09:08:43 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   82 (  17 unt;  18 typ;   0 def)
%            Number of atoms       :  202 (  36 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  202 (  64   ~;  79   |;  44   &)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  11   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   85 (   0 sgn;  57   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    organization: $i > $o ).

tff(decl_28,type,
    age: ( $i * $i ) > $i ).

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

tff(decl_30,type,
    has_immunity: ( $i * $i ) > $o ).

tff(decl_31,type,
    hazard_of_mortality: ( $i * $i ) > $i ).

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

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

tff(decl_34,type,
    esk1_1: $i > $i ).

tff(decl_35,type,
    esk2_1: $i > $i ).

tff(decl_36,type,
    esk3_0: $i ).

tff(decl_37,type,
    esk4_0: $i ).

tff(decl_38,type,
    esk5_0: $i ).

tff(decl_39,type,
    esk6_0: $i ).

fof(lemma_9,conjecture,
    ! [X1,X5,X6,X7] :
      ( ( organization(X1)
        & has_endowment(X1)
        & age(X1,X5) = zero
        & smaller_or_equal(age(X1,X6),eta)
        & greater(age(X1,X7),eta)
        & greater_or_equal(eta,sigma)
        & greater(sigma,zero) )
     => ( greater(hazard_of_mortality(X1,X7),hazard_of_mortality(X1,X6))
        & hazard_of_mortality(X1,X6) = hazard_of_mortality(X1,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_9) ).

fof(meaning_postulate_greater_transitive,axiom,
    ! [X1,X2,X3] :
      ( ( greater(X1,X2)
        & greater(X2,X3) )
     => greater(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax',meaning_postulate_greater_transitive) ).

fof(definition_greater_or_equal,axiom,
    ! [X1,X2] :
      ( greater_or_equal(X1,X2)
    <=> ( greater(X1,X2)
        | X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax',definition_greater_or_equal) ).

fof(definition_1,axiom,
    ! [X1] :
      ( has_endowment(X1)
    <=> ! [X4] :
          ( organization(X1)
          & ( smaller_or_equal(age(X1,X4),eta)
           => has_immunity(X1,X4) )
          & ( greater(age(X1,X4),eta)
           => ~ has_immunity(X1,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_1) ).

fof(definition_smaller,axiom,
    ! [X1,X2] :
      ( smaller(X1,X2)
    <=> greater(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax',definition_smaller) ).

fof(definition_smaller_or_equal,axiom,
    ! [X1,X2] :
      ( smaller_or_equal(X1,X2)
    <=> ( smaller(X1,X2)
        | X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax',definition_smaller_or_equal) ).

fof(assumption_3,axiom,
    ! [X1,X5,X4] :
      ( ( organization(X1)
        & has_immunity(X1,X5)
        & ~ has_immunity(X1,X4) )
     => greater(hazard_of_mortality(X1,X4),hazard_of_mortality(X1,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_3) ).

fof(assumption_2,axiom,
    ! [X1,X5,X4] :
      ( ( organization(X1)
        & has_immunity(X1,X5)
        & has_immunity(X1,X4) )
     => hazard_of_mortality(X1,X5) = hazard_of_mortality(X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2) ).

fof(meaning_postulate_greater_comparable,axiom,
    ! [X1,X2] :
      ( smaller(X1,X2)
      | X1 = X2
      | greater(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax',meaning_postulate_greater_comparable) ).

fof(meaning_postulate_greater_strict,axiom,
    ! [X1,X2] :
      ~ ( greater(X1,X2)
        & greater(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MGT001+0.ax',meaning_postulate_greater_strict) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X5,X6,X7] :
        ( ( organization(X1)
          & has_endowment(X1)
          & age(X1,X5) = zero
          & smaller_or_equal(age(X1,X6),eta)
          & greater(age(X1,X7),eta)
          & greater_or_equal(eta,sigma)
          & greater(sigma,zero) )
       => ( greater(hazard_of_mortality(X1,X7),hazard_of_mortality(X1,X6))
          & hazard_of_mortality(X1,X6) = hazard_of_mortality(X1,X5) ) ),
    inference(assume_negation,[status(cth)],[lemma_9]) ).

fof(c_0_11,plain,
    ! [X16,X17,X18] :
      ( ~ greater(X16,X17)
      | ~ greater(X17,X18)
      | greater(X16,X18) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[meaning_postulate_greater_transitive])]) ).

fof(c_0_12,negated_conjecture,
    ( organization(esk3_0)
    & has_endowment(esk3_0)
    & age(esk3_0,esk4_0) = zero
    & smaller_or_equal(age(esk3_0,esk5_0),eta)
    & greater(age(esk3_0,esk6_0),eta)
    & greater_or_equal(eta,sigma)
    & greater(sigma,zero)
    & ( ~ greater(hazard_of_mortality(esk3_0,esk6_0),hazard_of_mortality(esk3_0,esk5_0))
      | hazard_of_mortality(esk3_0,esk5_0) != hazard_of_mortality(esk3_0,esk4_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_13,plain,
    ! [X10,X11] :
      ( ( ~ greater_or_equal(X10,X11)
        | greater(X10,X11)
        | X10 = X11 )
      & ( ~ greater(X10,X11)
        | greater_or_equal(X10,X11) )
      & ( X10 != X11
        | greater_or_equal(X10,X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_greater_or_equal])])]) ).

cnf(c_0_14,plain,
    ( greater(X1,X3)
    | ~ greater(X1,X2)
    | ~ greater(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    greater(sigma,zero),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    ( greater(X1,X2)
    | X1 = X2
    | ~ greater_or_equal(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    greater_or_equal(eta,sigma),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_18,plain,
    ! [X1] :
      ( has_endowment(X1)
    <=> ! [X4] :
          ( organization(X1)
          & ( smaller_or_equal(age(X1,X4),eta)
           => has_immunity(X1,X4) )
          & ( greater(age(X1,X4),eta)
           => ~ has_immunity(X1,X4) ) ) ),
    inference(fof_simplification,[status(thm)],[definition_1]) ).

fof(c_0_19,plain,
    ! [X12,X13] :
      ( ( ~ smaller(X12,X13)
        | greater(X13,X12) )
      & ( ~ greater(X13,X12)
        | smaller(X12,X13) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_smaller])]) ).

cnf(c_0_20,negated_conjecture,
    ( greater(X1,zero)
    | ~ greater(X1,sigma) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    ( sigma = eta
    | greater(eta,sigma) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_22,plain,
    ! [X21,X22,X23,X24] :
      ( ( organization(X21)
        | ~ has_endowment(X21) )
      & ( ~ smaller_or_equal(age(X21,X22),eta)
        | has_immunity(X21,X22)
        | ~ has_endowment(X21) )
      & ( ~ greater(age(X21,X23),eta)
        | ~ has_immunity(X21,X23)
        | ~ has_endowment(X21) )
      & ( greater(age(X24,esk2_1(X24)),eta)
        | smaller_or_equal(age(X24,esk1_1(X24)),eta)
        | ~ organization(X24)
        | has_endowment(X24) )
      & ( has_immunity(X24,esk2_1(X24))
        | smaller_or_equal(age(X24,esk1_1(X24)),eta)
        | ~ organization(X24)
        | has_endowment(X24) )
      & ( greater(age(X24,esk2_1(X24)),eta)
        | ~ has_immunity(X24,esk1_1(X24))
        | ~ organization(X24)
        | has_endowment(X24) )
      & ( has_immunity(X24,esk2_1(X24))
        | ~ has_immunity(X24,esk1_1(X24))
        | ~ organization(X24)
        | has_endowment(X24) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])]) ).

fof(c_0_23,plain,
    ! [X8,X9] :
      ( ( ~ smaller_or_equal(X8,X9)
        | smaller(X8,X9)
        | X8 = X9 )
      & ( ~ smaller(X8,X9)
        | smaller_or_equal(X8,X9) )
      & ( X8 != X9
        | smaller_or_equal(X8,X9) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_smaller_or_equal])])]) ).

cnf(c_0_24,plain,
    ( smaller(X2,X1)
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,negated_conjecture,
    ( sigma = eta
    | greater(eta,zero) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

fof(c_0_26,plain,
    ! [X1,X5,X4] :
      ( ( organization(X1)
        & has_immunity(X1,X5)
        & ~ has_immunity(X1,X4) )
     => greater(hazard_of_mortality(X1,X4),hazard_of_mortality(X1,X5)) ),
    inference(fof_simplification,[status(thm)],[assumption_3]) ).

fof(c_0_27,plain,
    ! [X27,X28,X29] :
      ( ~ organization(X27)
      | ~ has_immunity(X27,X28)
      | ~ has_immunity(X27,X29)
      | hazard_of_mortality(X27,X28) = hazard_of_mortality(X27,X29) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[assumption_2])]) ).

cnf(c_0_28,plain,
    ( has_immunity(X1,X2)
    | ~ smaller_or_equal(age(X1,X2),eta)
    | ~ has_endowment(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    smaller_or_equal(age(esk3_0,esk5_0),eta),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_30,negated_conjecture,
    has_endowment(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_31,negated_conjecture,
    age(esk3_0,esk4_0) = zero,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_32,plain,
    ( smaller_or_equal(X1,X2)
    | ~ smaller(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,negated_conjecture,
    ( sigma = eta
    | smaller(zero,eta) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_34,plain,
    ! [X30,X31,X32] :
      ( ~ organization(X30)
      | ~ has_immunity(X30,X31)
      | has_immunity(X30,X32)
      | greater(hazard_of_mortality(X30,X32),hazard_of_mortality(X30,X31)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).

fof(c_0_35,plain,
    ! [X19,X20] :
      ( smaller(X19,X20)
      | X19 = X20
      | greater(X19,X20) ),
    inference(variable_rename,[status(thm)],[meaning_postulate_greater_comparable]) ).

cnf(c_0_36,plain,
    ( hazard_of_mortality(X1,X2) = hazard_of_mortality(X1,X3)
    | ~ organization(X1)
    | ~ has_immunity(X1,X2)
    | ~ has_immunity(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,negated_conjecture,
    has_immunity(esk3_0,esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).

cnf(c_0_38,negated_conjecture,
    organization(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_39,negated_conjecture,
    ( has_immunity(esk3_0,esk4_0)
    | ~ smaller_or_equal(zero,eta) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_30])]) ).

cnf(c_0_40,negated_conjecture,
    ( sigma = eta
    | smaller_or_equal(zero,eta) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_41,plain,
    ( has_immunity(X1,X3)
    | greater(hazard_of_mortality(X1,X3),hazard_of_mortality(X1,X2))
    | ~ organization(X1)
    | ~ has_immunity(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_42,plain,
    ( ~ greater(age(X1,X2),eta)
    | ~ has_immunity(X1,X2)
    | ~ has_endowment(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_43,negated_conjecture,
    greater(age(esk3_0,esk6_0),eta),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_44,plain,
    ( smaller(X1,X2)
    | X1 = X2
    | greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

fof(c_0_45,plain,
    ! [X14,X15] :
      ( ~ greater(X14,X15)
      | ~ greater(X15,X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[meaning_postulate_greater_strict])]) ).

cnf(c_0_46,negated_conjecture,
    ( hazard_of_mortality(esk3_0,X1) = hazard_of_mortality(esk3_0,esk5_0)
    | ~ has_immunity(esk3_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).

cnf(c_0_47,negated_conjecture,
    ( sigma = eta
    | has_immunity(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ greater(hazard_of_mortality(esk3_0,esk6_0),hazard_of_mortality(esk3_0,esk5_0))
    | hazard_of_mortality(esk3_0,esk5_0) != hazard_of_mortality(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_49,negated_conjecture,
    ( has_immunity(esk3_0,X1)
    | greater(hazard_of_mortality(esk3_0,X1),hazard_of_mortality(esk3_0,esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_37]),c_0_38])]) ).

cnf(c_0_50,negated_conjecture,
    ~ has_immunity(esk3_0,esk6_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_30])]) ).

cnf(c_0_51,plain,
    ( X1 = X2
    | greater(X1,X2)
    | smaller_or_equal(X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_44]) ).

cnf(c_0_52,plain,
    ( ~ greater(X1,X2)
    | ~ greater(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_53,negated_conjecture,
    ( hazard_of_mortality(esk3_0,esk4_0) = hazard_of_mortality(esk3_0,esk5_0)
    | sigma = eta ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_54,negated_conjecture,
    hazard_of_mortality(esk3_0,esk4_0) != hazard_of_mortality(esk3_0,esk5_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).

cnf(c_0_55,negated_conjecture,
    ( zero = eta
    | has_immunity(esk3_0,esk4_0)
    | greater(zero,eta) ),
    inference(spm,[status(thm)],[c_0_39,c_0_51]) ).

cnf(c_0_56,negated_conjecture,
    ~ greater(zero,sigma),
    inference(spm,[status(thm)],[c_0_52,c_0_15]) ).

cnf(c_0_57,negated_conjecture,
    sigma = eta,
    inference(sr,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_58,negated_conjecture,
    ( hazard_of_mortality(esk3_0,esk4_0) = hazard_of_mortality(esk3_0,esk5_0)
    | zero = eta
    | greater(zero,eta) ),
    inference(spm,[status(thm)],[c_0_46,c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    ~ greater(zero,eta),
    inference(rw,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_60,negated_conjecture,
    zero = eta,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_58,c_0_54]),c_0_59]) ).

cnf(c_0_61,negated_conjecture,
    greater(eta,zero),
    inference(rw,[status(thm)],[c_0_15,c_0_57]) ).

cnf(c_0_62,negated_conjecture,
    ~ greater(eta,eta),
    inference(rw,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_60]),c_0_62]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : MGT056+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34  % Computer : n018.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Mon Aug 28 06:43:02 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.014000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.018000 s
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