%------------------------------------------------------------------------------
% 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 : n011.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 : Theorem 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 18 unt; 0 def)
% Number of atoms : 164 ( 33 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 144 ( 43 ~; 54 |; 36 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 75 ( 0 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(definition_smaller_or_equal,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( X = Y
| smaller(X,Y) ) ),
file('theBenchmark.p',definition_smaller_or_equal) ).
fof(definition_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('theBenchmark.p',definition_greater_or_equal) ).
fof(definition_smaller,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('theBenchmark.p',definition_smaller) ).
fof(meaning_postulate_greater_strict,axiom,
! [X,Y] :
~ ( greater(Y,X)
& greater(X,Y) ),
file('theBenchmark.p',meaning_postulate_greater_strict) ).
fof(meaning_postulate_greater_transitive,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('theBenchmark.p',meaning_postulate_greater_transitive) ).
fof(meaning_postulate_greater_comparable,axiom,
! [X,Y] :
( greater(X,Y)
| X = Y
| smaller(X,Y) ),
file('theBenchmark.p',meaning_postulate_greater_comparable) ).
fof(definition_1,axiom,
! [X] :
( has_endowment(X)
<=> ! [T] :
( ( greater(age(X,T),eta)
=> ~ has_immunity(X,T) )
& ( smaller_or_equal(age(X,T),eta)
=> has_immunity(X,T) )
& organization(X) ) ),
file('theBenchmark.p',definition_1) ).
fof(assumption_2,axiom,
! [X,T0,T] :
( ( has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> hazard_of_mortality(X,T0) = hazard_of_mortality(X,T) ),
file('theBenchmark.p',assumption_2) ).
fof(assumption_3,axiom,
! [X,T0,T] :
( ( ~ has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
file('theBenchmark.p',assumption_3) ).
fof(lemma_9,conjecture,
! [X,T0,T1,T2] :
( ( greater(sigma,zero)
& greater_or_equal(eta,sigma)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) )
=> ( hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0)
& greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ) ),
file('theBenchmark.p',lemma_9) ).
fof(lemma_9_neg,negated_conjecture,
~ ! [X,T0,T1,T2] :
( ( greater(sigma,zero)
& greater_or_equal(eta,sigma)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) )
=> ( hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0)
& greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ) ),
inference(assume_negation,[status(cth)],[lemma_9]) ).
cnf(c_11,plain,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_13,plain,
( greater(B,A)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_14,plain,
( ~ greater(B,A)
| smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_15,plain,
( greater(A,B)
| B = A
| smaller(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_comparable]) ).
cnf(c_16,plain,
( B = A
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal]) ).
fof(nnf_10,plain,
? [X,T0,T1,T2] :
( ( hazard_of_mortality(X,T1) != hazard_of_mortality(X,T0)
| ~ greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) )
& greater(sigma,zero)
& greater_or_equal(eta,sigma)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) ),
inference(fof_nnf,[status(thm)],[lemma_9_neg]) ).
fof(sk_lemma_9_neg,plain,
( ( hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK1)
| ~ greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK2)) )
& greater(sigma,zero)
& greater_or_equal(eta,sigma)
& greater(age(sK0,sK3),eta)
& smaller_or_equal(age(sK0,sK2),eta)
& age(sK0,sK1) = zero
& has_endowment(sK0)
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X,sK0),skolemize(T0,sK1),skolemize(T1,sK2),skolemize(T2,sK3)],[nnf_10]) ).
cnf(c_19,negated_conjecture,
greater_or_equal(eta,sigma),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_21,plain,
( ~ has_immunity(A,B)
| ~ greater(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1]) ).
cnf(c_22,plain,
( has_immunity(A,B)
| ~ smaller_or_equal(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1]) ).
cnf(c_26,negated_conjecture,
has_endowment(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_34,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_35,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]) ).
cnf(c_36,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]) ).
cnf(c_37,negated_conjecture,
( hazard_of_mortality(sK0,A) = hazard_of_mortality(sK0,B)
| ~ has_immunity(sK0,B)
| ~ has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_36,c_34]) ).
cnf(c_38,negated_conjecture,
( greater(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| has_immunity(sK0,B)
| ~ has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_35,c_34]) ).
cnf(c_45,negated_conjecture,
( sigma = eta
| greater(eta,sigma) ),
inference(resolve,[status(thm)],[c_16,c_19]) ).
cnf(c_47,plain,
( ~ greater(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_strict]) ).
cnf(c_48,plain,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_transitive]) ).
cnf(c_49,negated_conjecture,
age(sK0,sK1) = zero,
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_50,negated_conjecture,
smaller_or_equal(age(sK0,sK2),eta),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_51,negated_conjecture,
greater(age(sK0,sK3),eta),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_52,negated_conjecture,
greater(sigma,zero),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_53,negated_conjecture,
( hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK1)
| ~ greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_lemma_9_neg]) ).
cnf(c_55,plain,
( smaller_or_equal(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_56,plain,
( greater(A,B)
| greater(B,A)
| A = B ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_58,negated_conjecture,
( ~ has_immunity(sK0,A)
| ~ greater(age(sK0,A),eta) ),
inference(resolve,[status(thm)],[c_26,c_21]) ).
cnf(c_59,negated_conjecture,
( has_immunity(sK0,A)
| ~ smaller_or_equal(age(sK0,A),eta) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_60,plain,
~ greater(A,A),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_63,plain,
( sigma = eta
| greater(eta,A)
| ~ greater(sigma,A) ),
inference(resolve,[status(thm)],[c_48,c_45]) ).
cnf(c_69,plain,
( greater(sigma,A)
| ~ greater(zero,A) ),
inference(resolve,[status(thm)],[c_52,c_48]) ).
cnf(c_82,plain,
~ has_immunity(sK0,sK3),
inference(resolve,[status(thm)],[c_58,c_51]) ).
cnf(c_85,plain,
has_immunity(sK0,sK2),
inference(resolve,[status(thm)],[c_59,c_50]) ).
cnf(c_86,plain,
( has_immunity(sK0,sK1)
| ~ smaller_or_equal(zero,eta) ),
inference(paramod,[status(thm)],[c_49,c_59]) ).
cnf(c_88,plain,
( sigma = eta
| greater(eta,zero) ),
inference(resolve,[status(thm)],[c_63,c_52]) ).
cnf(c_92,plain,
( greater(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,sK2))
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_85,c_38]) ).
cnf(c_95,plain,
( greater(A,zero)
| zero = A
| greater(sigma,A) ),
inference(resolve,[status(thm)],[c_69,c_56]) ).
cnf(c_105,plain,
( smaller_or_equal(zero,eta)
| sigma = eta ),
inference(resolve,[status(thm)],[c_88,c_55]) ).
cnf(c_109,plain,
( has_immunity(sK0,sK1)
| sigma = eta ),
inference(resolve,[status(thm)],[c_105,c_86]) ).
cnf(c_129,plain,
( smaller_or_equal(zero,A)
| zero = A
| greater(sigma,A) ),
inference(resolve,[status(thm)],[c_95,c_55]) ).
cnf(c_150,plain,
( has_immunity(sK0,sK1)
| zero = eta
| greater(sigma,eta) ),
inference(resolve,[status(thm)],[c_129,c_86]) ).
cnf(c_173,plain,
greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK2)),
inference(resolve,[status(thm)],[c_92,c_82]) ).
cnf(c_179,negated_conjecture,
hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK1),
inference(resolve,[status(thm)],[c_173,c_53]) ).
cnf(c_187,negated_conjecture,
( hazard_of_mortality(sK0,sK2) = hazard_of_mortality(sK0,A)
| ~ has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_37,c_85]) ).
cnf(c_180,negated_conjecture,
~ has_immunity(sK0,sK1),
inference(resolve,[status(thm)],[c_187,c_179]) ).
cnf(c_181,plain,
( zero = eta
| greater(sigma,eta) ),
inference(resolve,[status(thm)],[c_180,c_150]) ).
cnf(c_182,plain,
sigma = eta,
inference(resolve,[status(thm)],[c_180,c_109]) ).
cnf(c_188,plain,
( zero = eta
| greater(eta,eta) ),
inference(paramod,[status(thm)],[c_182,c_181]) ).
cnf(c_185,plain,
zero = eta,
inference(resolve,[status(thm)],[c_60,c_188]) ).
cnf(c_189,negated_conjecture,
greater(eta,zero),
inference(paramod,[status(thm)],[c_182,c_52]) ).
cnf(c_190,negated_conjecture,
greater(eta,eta),
inference(paramod,[status(thm)],[c_185,c_189]) ).
cnf(c_186,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_60,c_190]) ).
%------------------------------------------------------------------------------
%----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
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 00:10:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3235267 was started by sandbox on n011,
% 0.09/0.36 % Sat Sep 26 00:10:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.46 % Length of proof is 56.
% 0.13/0.46 % Level of proof is 10.
% 0.13/0.46 % Maximum clause weight is 24.000.
% 0.13/0.46 % Given clauses 66.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------