%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT056-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Sun Sep 27 08:03:00 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 25 unt; 0 def)
% Number of atoms : 143 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 127 ( 55 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(definition_smaller_or_equal_2,axiom,
! [VAR_0,VAR_1] :
( smaller_or_equal(VAR_0,VAR_1)
| ~ smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_smaller_or_equal_2) ).
cnf(c_1,plain,
( smaller_or_equal(A,B)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal_2]) ).
fof(definition_smaller_7,axiom,
! [VAR_0,VAR_1] :
( greater(VAR_1,VAR_0)
| ~ smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_smaller_7) ).
cnf(c_3,plain,
( greater(B,A)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_7]) ).
fof(definition_smaller_8,axiom,
! [VAR_0,VAR_1] :
( smaller(VAR_1,VAR_0)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_smaller_8) ).
cnf(c_4,plain,
( smaller(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_8]) ).
fof(meaning_postulate_greater_comparable_11,axiom,
! [VAR_0,VAR_1] :
( greater(VAR_0,VAR_1)
| VAR_0 = VAR_1
| smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',meaning_postulate_greater_comparable_11) ).
cnf(c_5,plain,
( greater(A,B)
| A = B
| smaller(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_comparable_11]) ).
fof(definition_greater_or_equal_4,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| greater(VAR_0,VAR_1)
| ~ greater_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_greater_or_equal_4) ).
cnf(c_6,plain,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal_4]) ).
fof(lemma_9_45,axiom,
greater_or_equal(eta,sigma),
file('theBenchmark.p',lemma_9_45) ).
cnf(c_9,plain,
greater_or_equal(eta,sigma),
inference(clausify,[status(thm)],[lemma_9_45]) ).
fof(definition_1_33,axiom,
! [VAR_0,VAR_1] :
( ~ has_immunity(VAR_0,VAR_1)
| ~ greater(age(VAR_0,VAR_1),eta)
| ~ has_endowment(VAR_0) ),
file('theBenchmark.p',definition_1_33) ).
cnf(c_11,plain,
( ~ has_immunity(A,B)
| ~ greater(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1_33]) ).
fof(definition_1_32,axiom,
! [VAR_0,VAR_1] :
( has_immunity(VAR_0,VAR_1)
| ~ smaller_or_equal(age(VAR_0,VAR_1),eta)
| ~ has_endowment(VAR_0) ),
file('theBenchmark.p',definition_1_32) ).
cnf(c_12,plain,
( has_immunity(A,B)
| ~ smaller_or_equal(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1_32]) ).
fof(lemma_9_41,axiom,
has_endowment(sk2),
file('theBenchmark.p',lemma_9_41) ).
cnf(c_17,plain,
has_endowment(sk2),
inference(clausify,[status(thm)],[lemma_9_41]) ).
fof(lemma_9_40,axiom,
organization(sk2),
file('theBenchmark.p',lemma_9_40) ).
cnf(c_25,plain,
organization(sk2),
inference(clausify,[status(thm)],[lemma_9_40]) ).
fof(assumption_3_39,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(hazard_of_mortality(VAR_0,VAR_2),hazard_of_mortality(VAR_0,VAR_1))
| has_immunity(VAR_0,VAR_2)
| ~ has_immunity(VAR_0,VAR_1)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_3_39) ).
cnf(c_26,plain,
( greater(hazard_of_mortality(A,C),hazard_of_mortality(A,B))
| has_immunity(A,C)
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_3_39]) ).
fof(assumption_2_38,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hazard_of_mortality(VAR_0,VAR_1) = hazard_of_mortality(VAR_0,VAR_2)
| ~ has_immunity(VAR_0,VAR_2)
| ~ has_immunity(VAR_0,VAR_1)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_2_38) ).
cnf(c_27,plain,
( hazard_of_mortality(A,B) = hazard_of_mortality(A,C)
| ~ has_immunity(A,C)
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_2_38]) ).
cnf(c_28,plain,
( hazard_of_mortality(sk2,A) = hazard_of_mortality(sk2,B)
| ~ has_immunity(sk2,B)
| ~ has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_29,plain,
( greater(hazard_of_mortality(sk2,B),hazard_of_mortality(sk2,A))
| has_immunity(sk2,B)
| ~ has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_26,c_25]) ).
cnf(c_36,plain,
( eta = sigma
| greater(eta,sigma) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_37,plain,
( sigma = eta
| greater(eta,sigma) ),
inference(copy,[status(thm)],[c_36]) ).
fof(meaning_postulate_greater_strict_9,axiom,
! [VAR_0,VAR_1] :
( ~ greater(VAR_1,VAR_0)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',meaning_postulate_greater_strict_9) ).
cnf(c_39,plain,
( ~ greater(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_strict_9]) ).
fof(meaning_postulate_greater_transitive_10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(VAR_0,VAR_2)
| ~ greater(VAR_1,VAR_2)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',meaning_postulate_greater_transitive_10) ).
cnf(c_40,plain,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_transitive_10]) ).
fof(lemma_9_42,axiom,
age(sk2,sk3) = zero,
file('theBenchmark.p',lemma_9_42) ).
cnf(c_41,plain,
age(sk2,sk3) = zero,
inference(clausify,[status(thm)],[lemma_9_42]) ).
fof(lemma_9_43,axiom,
smaller_or_equal(age(sk2,sk4),eta),
file('theBenchmark.p',lemma_9_43) ).
cnf(c_42,plain,
smaller_or_equal(age(sk2,sk4),eta),
inference(clausify,[status(thm)],[lemma_9_43]) ).
fof(lemma_9_44,axiom,
greater(age(sk2,sk5),eta),
file('theBenchmark.p',lemma_9_44) ).
cnf(c_43,plain,
greater(age(sk2,sk5),eta),
inference(clausify,[status(thm)],[lemma_9_44]) ).
fof(lemma_9_46,axiom,
greater(sigma,zero),
file('theBenchmark.p',lemma_9_46) ).
cnf(c_44,plain,
greater(sigma,zero),
inference(clausify,[status(thm)],[lemma_9_46]) ).
fof(lemma_9_47,axiom,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) ),
file('theBenchmark.p',lemma_9_47) ).
cnf(c_45,plain,
( hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3)
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)) ),
inference(clausify,[status(thm)],[lemma_9_47]) ).
cnf(c_47,plain,
( smaller_or_equal(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_48,plain,
( greater(B,A)
| greater(A,B)
| A = B ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_50,plain,
( ~ has_immunity(sk2,A)
| ~ greater(age(sk2,A),eta) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_51,plain,
( has_immunity(sk2,A)
| ~ smaller_or_equal(age(sk2,A),eta) ),
inference(resolve,[status(thm)],[c_17,c_12]) ).
cnf(c_52,plain,
~ greater(A,A),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_55,plain,
( sigma = eta
| greater(eta,A)
| ~ greater(sigma,A) ),
inference(resolve,[status(thm)],[c_40,c_37]) ).
cnf(c_61,plain,
( greater(sigma,A)
| ~ greater(zero,A) ),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_74,plain,
~ has_immunity(sk2,sk5),
inference(resolve,[status(thm)],[c_50,c_43]) ).
cnf(c_77,plain,
has_immunity(sk2,sk4),
inference(resolve,[status(thm)],[c_51,c_42]) ).
cnf(c_78,plain,
( has_immunity(sk2,sk3)
| ~ smaller_or_equal(zero,eta) ),
inference(paramod,[status(thm)],[c_41,c_51]) ).
cnf(c_80,plain,
( sigma = eta
| greater(eta,zero) ),
inference(resolve,[status(thm)],[c_55,c_44]) ).
cnf(c_84,plain,
( greater(hazard_of_mortality(sk2,A),hazard_of_mortality(sk2,sk4))
| has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_77,c_29]) ).
cnf(c_179,plain,
( greater(A,zero)
| A = zero
| greater(sigma,A) ),
inference(resolve,[status(thm)],[c_61,c_48]) ).
cnf(c_87,plain,
( greater(A,zero)
| zero = A
| greater(sigma,A) ),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_97,plain,
( smaller_or_equal(zero,eta)
| sigma = eta ),
inference(resolve,[status(thm)],[c_80,c_47]) ).
cnf(c_101,plain,
( has_immunity(sk2,sk3)
| sigma = eta ),
inference(resolve,[status(thm)],[c_97,c_78]) ).
cnf(c_121,plain,
( smaller_or_equal(zero,A)
| zero = A
| greater(sigma,A) ),
inference(resolve,[status(thm)],[c_87,c_47]) ).
cnf(c_142,plain,
( has_immunity(sk2,sk3)
| zero = eta
| greater(sigma,eta) ),
inference(resolve,[status(thm)],[c_121,c_78]) ).
cnf(c_165,plain,
greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)),
inference(resolve,[status(thm)],[c_84,c_74]) ).
cnf(c_171,plain,
hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3),
inference(resolve,[status(thm)],[c_165,c_45]) ).
cnf(c_180,plain,
( hazard_of_mortality(sk2,sk4) = hazard_of_mortality(sk2,A)
| ~ has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_28,c_77]) ).
cnf(c_172,plain,
~ has_immunity(sk2,sk3),
inference(resolve,[status(thm)],[c_180,c_171]) ).
cnf(c_173,plain,
( zero = eta
| greater(sigma,eta) ),
inference(resolve,[status(thm)],[c_172,c_142]) ).
cnf(c_174,plain,
sigma = eta,
inference(resolve,[status(thm)],[c_172,c_101]) ).
cnf(c_181,plain,
( zero = eta
| greater(eta,eta) ),
inference(paramod,[status(thm)],[c_174,c_173]) ).
cnf(c_177,plain,
zero = eta,
inference(resolve,[status(thm)],[c_52,c_181]) ).
cnf(c_182,plain,
greater(eta,zero),
inference(paramod,[status(thm)],[c_174,c_44]) ).
cnf(c_183,plain,
greater(eta,eta),
inference(paramod,[status(thm)],[c_177,c_182]) ).
cnf(c_178,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT056-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.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 : Sat Sep 26 00:10:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2895591 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 00:10:29 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.40
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.40
% 0.15/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.40 % Length of proof is 47.
% 0.15/0.40 % Level of proof is 9.
% 0.15/0.40 % Maximum clause weight is 24.000.
% 0.15/0.40 % Given clauses 66.
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------