%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT057-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 47 ( 16 unt; 5 nHn; 43 RR)
% Number of literals : 97 ( 18 equ; 53 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_smaller_or_equal_2,axiom,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ) ).
cnf(definition_smaller_8,axiom,
( ~ greater(A,B)
| smaller(B,A) ) ).
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(theorem_6_40,negated_conjecture,
organization(sk2) ).
cnf(theorem_6_41,negated_conjecture,
has_endowment(sk2) ).
cnf(theorem_6_42,negated_conjecture,
age(sk2,sk3) = zero ).
cnf(theorem_6_43,negated_conjecture,
smaller_or_equal(age(sk2,sk4),eta) ).
cnf(theorem_6_44,negated_conjecture,
greater(age(sk2,sk5),eta) ).
cnf(theorem_6_45,negated_conjecture,
greater(eta,zero) ).
cnf(theorem_6_46,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,[$cnf( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) )],[refute_0_0,theorem_6_46]) ).
cnf(refute_0_2,plain,
( ~ has_endowment(sk2)
| ~ smaller_or_equal(age(sk2,sk3),eta)
| has_immunity(sk2,sk3) ),
inference(subst,[],[definition_1_32:[bind(A,$fot(sk2)),bind(B,$fot(sk3))]]) ).
cnf(refute_0_3,plain,
( age(sk2,sk3) != zero
| ~ smaller_or_equal(zero,eta)
| smaller_or_equal(age(sk2,sk3),eta) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(sk2,sk3),eta) ),[0],$fot(zero)]]) ).
cnf(refute_0_4,plain,
( ~ smaller_or_equal(zero,eta)
| smaller_or_equal(age(sk2,sk3),eta) ),
inference(resolve,[$cnf( $equal(age(sk2,sk3),zero) )],[theorem_6_42,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ has_endowment(sk2)
| ~ smaller_or_equal(zero,eta)
| has_immunity(sk2,sk3) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk2,sk3),eta) )],[refute_0_4,refute_0_2]) ).
cnf(refute_0_6,plain,
( ~ smaller_or_equal(zero,eta)
| has_immunity(sk2,sk3) ),
inference(resolve,[$cnf( has_endowment(sk2) )],[theorem_6_41,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ smaller(zero,eta)
| smaller_or_equal(zero,eta) ),
inference(subst,[],[definition_smaller_or_equal_2:[bind(A,$fot(zero)),bind(B,$fot(eta))]]) ).
cnf(refute_0_8,plain,
( ~ greater(eta,zero)
| smaller(zero,eta) ),
inference(subst,[],[definition_smaller_8:[bind(A,$fot(eta)),bind(B,$fot(zero))]]) ).
cnf(refute_0_9,plain,
smaller(zero,eta),
inference(resolve,[$cnf( greater(eta,zero) )],[theorem_6_45,refute_0_8]) ).
cnf(refute_0_10,plain,
smaller_or_equal(zero,eta),
inference(resolve,[$cnf( smaller(zero,eta) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
has_immunity(sk2,sk3),
inference(resolve,[$cnf( smaller_or_equal(zero,eta) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,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_13,plain,
( ~ has_endowment(sk2)
| has_immunity(sk2,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk2,sk4),eta) )],[theorem_6_43,refute_0_12]) ).
cnf(refute_0_14,plain,
has_immunity(sk2,sk4),
inference(resolve,[$cnf( has_endowment(sk2) )],[theorem_6_41,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ has_immunity(sk2,X_75)
| ~ has_immunity(sk2,sk4)
| ~ organization(sk2)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,X_75) ),
inference(subst,[],[assumption_2_38:[bind(A,$fot(sk2)),bind(B,$fot(sk4)),bind(C,$fot(X_75))]]) ).
cnf(refute_0_16,plain,
( ~ has_immunity(sk2,X_75)
| ~ organization(sk2)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,X_75) ),
inference(resolve,[$cnf( has_immunity(sk2,sk4) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ has_immunity(sk2,X_75)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,X_75) ),
inference(resolve,[$cnf( organization(sk2) )],[theorem_6_40,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ has_immunity(sk2,sk3)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
inference(subst,[],[refute_0_17:[bind(X_75,$fot(sk3))]]) ).
cnf(refute_0_19,plain,
hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3),
inference(resolve,[$cnf( has_immunity(sk2,sk3) )],[refute_0_11,refute_0_18]) ).
cnf(refute_0_20,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
introduced(tautology,[equality,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) ),[1],$fot(hazard_of_mortality(sk2,sk3))]]) ).
cnf(refute_0_21,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,sk3) ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk4),hazard_of_mortality(sk2,sk3)) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
hazard_of_mortality(sk2,sk3) = hazard_of_mortality(sk2,sk3),
introduced(tautology,[refl,[$fot(hazard_of_mortality(sk2,sk3))]]) ).
cnf(refute_0_24,plain,
~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)),
inference(resolve,[$cnf( $equal(hazard_of_mortality(sk2,sk3),hazard_of_mortality(sk2,sk3)) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( ~ has_immunity(sk2,sk3)
| ~ organization(sk2)
| greater(hazard_of_mortality(sk2,X_95),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_95) ),
inference(subst,[],[assumption_3_39:[bind(A,$fot(sk2)),bind(B,$fot(sk3)),bind(C,$fot(X_95))]]) ).
cnf(refute_0_26,plain,
( ~ organization(sk2)
| greater(hazard_of_mortality(sk2,X_95),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_95) ),
inference(resolve,[$cnf( has_immunity(sk2,sk3) )],[refute_0_11,refute_0_25]) ).
cnf(refute_0_27,plain,
( greater(hazard_of_mortality(sk2,X_95),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,X_95) ),
inference(resolve,[$cnf( organization(sk2) )],[theorem_6_40,refute_0_26]) ).
cnf(refute_0_28,plain,
( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3))
| has_immunity(sk2,sk5) ),
inference(subst,[],[refute_0_27:[bind(X_95,$fot(sk5))]]) ).
cnf(refute_0_29,plain,
has_immunity(sk2,sk5),
inference(resolve,[$cnf( greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk3)) )],[refute_0_28,refute_0_24]) ).
cnf(refute_0_30,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_31,plain,
( ~ has_endowment(sk2)
| ~ has_immunity(sk2,sk5) ),
inference(resolve,[$cnf( greater(age(sk2,sk5),eta) )],[theorem_6_44,refute_0_30]) ).
cnf(refute_0_32,plain,
~ has_immunity(sk2,sk5),
inference(resolve,[$cnf( has_endowment(sk2) )],[theorem_6_41,refute_0_31]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( has_immunity(sk2,sk5) )],[refute_0_29,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT057-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 13:30:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.10/0.46
%------------------------------------------------------------------------------