%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT056-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:16:12 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of clauses : 82 ( 21 unt; 20 nHn; 73 RR)
% Number of literals : 177 ( 51 equ; 80 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_smaller_or_equal_2,axiom,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ) ).
cnf(definition_greater_or_equal_4,axiom,
( ~ greater_or_equal(A,B)
| greater(A,B)
| A = B ) ).
cnf(definition_smaller_8,axiom,
( ~ greater(A,B)
| smaller(B,A) ) ).
cnf(meaning_postulate_greater_transitive_10,axiom,
( ~ greater(A,B)
| ~ greater(B,C)
| greater(A,C) ) ).
cnf(definition_1_32,axiom,
( ~ has_endowment(A)
| ~ smaller_or_equal(age(A,B),eta)
| has_immunity(A,B) ) ).
cnf(definition_1_33,axiom,
( ~ has_endowment(A)
| ~ greater(age(A,B),eta)
| ~ has_immunity(A,B) ) ).
cnf(assumption_2_38,axiom,
( ~ organization(A)
| ~ has_immunity(A,B)
| ~ has_immunity(A,C)
| hazard_of_mortality(A,B) = hazard_of_mortality(A,C) ) ).
cnf(assumption_3_39,axiom,
( ~ organization(A)
| ~ has_immunity(A,B)
| has_immunity(A,C)
| greater(hazard_of_mortality(A,C),hazard_of_mortality(A,B)) ) ).
cnf(lemma_9_40,negated_conjecture,
organization(sk2) ).
cnf(lemma_9_41,negated_conjecture,
has_endowment(sk2) ).
cnf(lemma_9_42,negated_conjecture,
age(sk2,sk3) = zero ).
cnf(lemma_9_43,negated_conjecture,
smaller_or_equal(age(sk2,sk4),eta) ).
cnf(lemma_9_44,negated_conjecture,
greater(age(sk2,sk5),eta) ).
cnf(lemma_9_45,negated_conjecture,
greater_or_equal(eta,sigma) ).
cnf(lemma_9_46,negated_conjecture,
greater(sigma,zero) ).
cnf(lemma_9_47,negated_conjecture,
( ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))
| hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3) ) ).
cnf(refute_0_0,plain,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3))
| greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) ),
introduced(tautology,[equality,[$cnf( ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) ),[1],$fot(hazard_of_mortality(sk2,sk3))]]) ).
cnf(refute_0_1,plain,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)) ),
inference(resolve,[$cnf( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) )],[refute_0_0,lemma_9_47]) ).
cnf(refute_0_2,plain,
( ~ has_endowment(sk2)
| ~ smaller_or_equal(age(sk2,sk4),eta)
| has_immunity(sk2,sk4) ),
inference(subst,[],[definition_1_32:[bind(A,$fot(sk2)),bind(B,$fot(sk4))]]) ).
cnf(refute_0_3,plain,
( ~ has_endowment(sk2)
| has_immunity(sk2,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk2,sk4),eta) )],[lemma_9_43,refute_0_2]) ).
cnf(refute_0_4,plain,
has_immunity(sk2,sk4),
inference(resolve,[$cnf( has_endowment(sk2) )],[lemma_9_41,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ has_immunity(sk2,X_82)
| ~ has_immunity(sk2,sk4)
| ~ organization(sk2)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,X_82) ),
inference(subst,[],[assumption_2_38:[bind(A,$fot(sk2)),bind(B,$fot(sk4)),bind(C,$fot(X_82))]]) ).
cnf(refute_0_6,plain,
( ~ has_immunity(sk2,X_82)
| ~ organization(sk2)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,X_82) ),
inference(resolve,[$cnf( has_immunity(sk2,sk4) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ has_immunity(sk2,X_82)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,X_82) ),
inference(resolve,[$cnf( organization(sk2) )],[lemma_9_40,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ has_immunity(sk2,sk3)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
inference(subst,[],[refute_0_7:[bind(X_82,$fot(sk3))]]) ).
cnf(refute_0_9,plain,
( ~ has_endowment(sk2)
| ~ smaller_or_equal(age(sk2,sk3),eta)
| has_immunity(sk2,sk3) ),
inference(subst,[],[definition_1_32:[bind(A,$fot(sk2)),bind(B,$fot(sk3))]]) ).
cnf(refute_0_10,plain,
( age(sk2,sk3) != zero
| ~ smaller_or_equal(zero,eta)
| smaller_or_equal(age(sk2,sk3),eta) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(sk2,sk3),eta) ),[0],$fot(zero)]]) ).
cnf(refute_0_11,plain,
( ~ smaller_or_equal(zero,eta)
| smaller_or_equal(age(sk2,sk3),eta) ),
inference(resolve,[$cnf( $equal(age(sk2,sk3),zero) )],[lemma_9_42,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ has_endowment(sk2)
| ~ smaller_or_equal(zero,eta)
| has_immunity(sk2,sk3) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk2,sk3),eta) )],[refute_0_11,refute_0_9]) ).
cnf(refute_0_13,plain,
( ~ smaller_or_equal(zero,eta)
| has_immunity(sk2,sk3) ),
inference(resolve,[$cnf( has_endowment(sk2) )],[lemma_9_41,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ greater(sigma,zero)
| smaller(zero,sigma) ),
inference(subst,[],[definition_smaller_8:[bind(A,$fot(sigma)),bind(B,$fot(zero))]]) ).
cnf(refute_0_15,plain,
smaller(zero,sigma),
inference(resolve,[$cnf( greater(sigma,zero) )],[lemma_9_46,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ smaller(zero,sigma)
| smaller_or_equal(zero,sigma) ),
inference(subst,[],[definition_smaller_or_equal_2:[bind(A,$fot(zero)),bind(B,$fot(sigma))]]) ).
cnf(refute_0_17,plain,
smaller_or_equal(zero,sigma),
inference(resolve,[$cnf( smaller(zero,sigma) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ smaller(zero,eta)
| smaller_or_equal(zero,eta) ),
inference(subst,[],[definition_smaller_or_equal_2:[bind(A,$fot(zero)),bind(B,$fot(eta))]]) ).
cnf(refute_0_19,plain,
( ~ greater(eta,zero)
| smaller(zero,eta) ),
inference(subst,[],[definition_smaller_8:[bind(A,$fot(eta)),bind(B,$fot(zero))]]) ).
cnf(refute_0_20,plain,
( ~ greater_or_equal(eta,sigma)
| eta = sigma
| greater(eta,sigma) ),
inference(subst,[],[definition_greater_or_equal_4:[bind(A,$fot(eta)),bind(B,$fot(sigma))]]) ).
cnf(refute_0_21,plain,
( eta = sigma
| greater(eta,sigma) ),
inference(resolve,[$cnf( greater_or_equal(eta,sigma) )],[lemma_9_45,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ greater(X_24,sigma)
| ~ greater(sigma,zero)
| greater(X_24,zero) ),
inference(subst,[],[meaning_postulate_greater_transitive_10:[bind(A,$fot(X_24)),bind(B,$fot(sigma)),bind(C,$fot(zero))]]) ).
cnf(refute_0_23,plain,
( ~ greater(X_24,sigma)
| greater(X_24,zero) ),
inference(resolve,[$cnf( greater(sigma,zero) )],[lemma_9_46,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ greater(eta,sigma)
| greater(eta,zero) ),
inference(subst,[],[refute_0_23:[bind(X_24,$fot(eta))]]) ).
cnf(refute_0_25,plain,
( eta = sigma
| greater(eta,zero) ),
inference(resolve,[$cnf( greater(eta,sigma) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( eta = sigma
| smaller(zero,eta) ),
inference(resolve,[$cnf( greater(eta,zero) )],[refute_0_25,refute_0_19]) ).
cnf(refute_0_27,plain,
( eta = sigma
| smaller_or_equal(zero,eta) ),
inference(resolve,[$cnf( smaller(zero,eta) )],[refute_0_26,refute_0_18]) ).
cnf(refute_0_28,plain,
( eta = sigma
| has_immunity(sk2,sk3) ),
inference(resolve,[$cnf( smaller_or_equal(zero,eta) )],[refute_0_27,refute_0_13]) ).
cnf(refute_0_29,plain,
( ~ has_immunity(sk2,sk3)
| ~ organization(sk2)
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_89) ),
inference(subst,[],[assumption_3_39:[bind(A,$fot(sk2)),bind(B,$fot(sk3)),bind(C,$fot(X_89))]]) ).
cnf(refute_0_30,plain,
( ~ organization(sk2)
| eta = sigma
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_89) ),
inference(resolve,[$cnf( has_immunity(sk2,sk3) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( eta = sigma
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_89) ),
inference(resolve,[$cnf( organization(sk2) )],[lemma_9_40,refute_0_30]) ).
cnf(refute_0_32,plain,
( eta = sigma
| greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,sk5) ),
inference(subst,[],[refute_0_31:[bind(X_89,$fot(sk5))]]) ).
cnf(refute_0_33,plain,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| eta = sigma
| has_immunity(sk2,sk5) ),
inference(resolve,[$cnf( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)) )],[refute_0_32,refute_0_1]) ).
cnf(refute_0_34,plain,
( ~ greater(age(sk2,sk5),eta)
| ~ has_endowment(sk2)
| ~ has_immunity(sk2,sk5) ),
inference(subst,[],[definition_1_33:[bind(A,$fot(sk2)),bind(B,$fot(sk5))]]) ).
cnf(refute_0_35,plain,
( ~ has_endowment(sk2)
| ~ has_immunity(sk2,sk5) ),
inference(resolve,[$cnf( greater(age(sk2,sk5),eta) )],[lemma_9_44,refute_0_34]) ).
cnf(refute_0_36,plain,
~ has_immunity(sk2,sk5),
inference(resolve,[$cnf( has_endowment(sk2) )],[lemma_9_41,refute_0_35]) ).
cnf(refute_0_37,plain,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| eta = sigma ),
inference(resolve,[$cnf( has_immunity(sk2,sk5) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( eta = sigma
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
inference(resolve,[$cnf( has_immunity(sk2,sk3) )],[refute_0_28,refute_0_8]) ).
cnf(refute_0_39,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
introduced(tautology,[equality,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) ),[1],$fot(hazard_of_mortality(sk2,sk3))]]) ).
cnf(refute_0_40,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| eta = sigma
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| eta = sigma ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_40,refute_0_37]) ).
cnf(refute_0_42,plain,
hazard_of_mortality(sk2,sk3) = hazard_of_mortality(sk2,sk3),
introduced(tautology,[refl,[$fot(hazard_of_mortality(sk2,sk3))]]) ).
cnf(refute_0_43,plain,
eta = sigma,
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk3),hazard_of_mortality(sk2,sk3)) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_45,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_46,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( eta != sigma
| sigma = eta ),
inference(subst,[],[refute_0_46:[bind(X,$fot(eta)),bind(Y,$fot(sigma))]]) ).
cnf(refute_0_48,plain,
sigma = eta,
inference(resolve,[$cnf( $equal(eta,sigma) )],[refute_0_43,refute_0_47]) ).
cnf(refute_0_49,plain,
( sigma != eta
| ~ smaller_or_equal(zero,sigma)
| smaller_or_equal(zero,eta) ),
introduced(tautology,[equality,[$cnf( smaller_or_equal(zero,sigma) ),[1],$fot(eta)]]) ).
cnf(refute_0_50,plain,
( ~ smaller_or_equal(zero,sigma)
| smaller_or_equal(zero,eta) ),
inference(resolve,[$cnf( $equal(sigma,eta) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
smaller_or_equal(zero,eta),
inference(resolve,[$cnf( smaller_or_equal(zero,sigma) )],[refute_0_17,refute_0_50]) ).
cnf(refute_0_52,plain,
has_immunity(sk2,sk3),
inference(resolve,[$cnf( smaller_or_equal(zero,eta) )],[refute_0_51,refute_0_13]) ).
cnf(refute_0_53,plain,
hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3),
inference(resolve,[$cnf( has_immunity(sk2,sk3) )],[refute_0_52,refute_0_8]) ).
cnf(refute_0_54,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_53,refute_0_39]) ).
cnf(refute_0_55,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_54,refute_0_1]) ).
cnf(refute_0_56,plain,
~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk3),hazard_of_mortality(sk2,sk3)) )],[refute_0_42,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ has_immunity(sk2,sk4)
| ~ organization(sk2)
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4))
| has_immunity(sk2,X_89) ),
inference(subst,[],[assumption_3_39:[bind(A,$fot(sk2)),bind(B,$fot(sk4)),bind(C,$fot(X_89))]]) ).
cnf(refute_0_58,plain,
( ~ organization(sk2)
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4))
| has_immunity(sk2,X_89) ),
inference(resolve,[$cnf( has_immunity(sk2,sk4) )],[refute_0_4,refute_0_57]) ).
cnf(refute_0_59,plain,
( greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4))
| has_immunity(sk2,X_89) ),
inference(resolve,[$cnf( organization(sk2) )],[lemma_9_40,refute_0_58]) ).
cnf(refute_0_60,plain,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4))
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4)) ),[1],$fot(hazard_of_mortality(sk2,sk3))]]) ).
cnf(refute_0_61,plain,
( ~ greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4))
| greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_53,refute_0_60]) ).
cnf(refute_0_62,plain,
( greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_89) ),
inference(resolve,[$cnf( greater(hazard_of_mortality(sk2,X_89),hazard_of_mortality(sk2,sk4)) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,sk5) ),
inference(subst,[],[refute_0_62:[bind(X_89,$fot(sk5))]]) ).
cnf(refute_0_64,plain,
has_immunity(sk2,sk5),
inference(resolve,[$cnf( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)) )],[refute_0_63,refute_0_56]) ).
cnf(refute_0_65,plain,
$false,
inference(resolve,[$cnf( has_immunity(sk2,sk5) )],[refute_0_64,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT056-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 13:30:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.40
%------------------------------------------------------------------------------