%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT057+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 : n019.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 08:03:01 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 103 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 98 ( 33 ~; 26 |; 30 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 20 !; 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_smaller,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('theBenchmark.p',definition_smaller) ).
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(theorem_6,conjecture,
! [X,T0,T1,T2] :
( ( greater(eta,zero)
& 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',theorem_6) ).
fof(theorem_6_neg,negated_conjecture,
~ ! [X,T0,T1,T2] :
( ( greater(eta,zero)
& 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)],[theorem_6]) ).
cnf(c_11,plain,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_14,plain,
( ~ greater(B,A)
| smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_20,plain,
( ~ has_immunity(A,B)
| ~ greater(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1]) ).
cnf(c_21,plain,
( has_immunity(A,B)
| ~ smaller_or_equal(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1]) ).
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(eta,zero)
& 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)],[theorem_6_neg]) ).
fof(sk_theorem_6_neg,plain,
( ( hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK1)
| ~ greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK2)) )
& greater(eta,zero)
& 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_25,negated_conjecture,
has_endowment(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_6_neg]) ).
cnf(c_33,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_6_neg]) ).
cnf(c_34,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_35,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_36,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_35,c_33]) ).
cnf(c_37,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_34,c_33]) ).
cnf(c_47,negated_conjecture,
age(sK0,sK1) = zero,
inference(split_conjunct,[status(thm)],[sk_theorem_6_neg]) ).
cnf(c_48,negated_conjecture,
smaller_or_equal(age(sK0,sK2),eta),
inference(split_conjunct,[status(thm)],[sk_theorem_6_neg]) ).
cnf(c_49,negated_conjecture,
greater(age(sK0,sK3),eta),
inference(split_conjunct,[status(thm)],[sk_theorem_6_neg]) ).
cnf(c_50,negated_conjecture,
greater(eta,zero),
inference(split_conjunct,[status(thm)],[sk_theorem_6_neg]) ).
cnf(c_51,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_theorem_6_neg]) ).
cnf(c_53,plain,
( smaller_or_equal(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_56,negated_conjecture,
( ~ has_immunity(sK0,A)
| ~ greater(age(sK0,A),eta) ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_57,negated_conjecture,
( has_immunity(sK0,A)
| ~ smaller_or_equal(age(sK0,A),eta) ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_67,plain,
smaller_or_equal(zero,eta),
inference(resolve,[status(thm)],[c_53,c_50]) ).
cnf(c_75,negated_conjecture,
~ has_immunity(sK0,sK3),
inference(resolve,[status(thm)],[c_56,c_49]) ).
cnf(c_77,plain,
has_immunity(sK0,sK2),
inference(resolve,[status(thm)],[c_57,c_48]) ).
cnf(c_137,plain,
( has_immunity(sK0,sK1)
| ~ smaller_or_equal(zero,eta) ),
inference(paramod,[status(thm)],[c_47,c_57]) ).
cnf(c_78,plain,
has_immunity(sK0,sK1),
inference(resolve,[status(thm)],[c_67,c_137]) ).
cnf(c_83,plain,
( greater(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,sK2))
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_77,c_37]) ).
cnf(c_118,plain,
greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK2)),
inference(resolve,[status(thm)],[c_83,c_75]) ).
cnf(c_123,negated_conjecture,
hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK1),
inference(resolve,[status(thm)],[c_118,c_51]) ).
cnf(c_138,negated_conjecture,
( hazard_of_mortality(sK0,A) = hazard_of_mortality(sK0,sK1)
| ~ has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_36,c_78]) ).
cnf(c_139,negated_conjecture,
~ has_immunity(sK0,sK2),
inference(resolve,[status(thm)],[c_138,c_123]) ).
cnf(c_136,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_77,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT057+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 00:10:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4051786 was started by sandbox on n019,
% 0.10/0.37 % Sat Sep 26 00:10:33 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).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 32.
% 0.10/0.40 % Level of proof is 7.
% 0.10/0.40 % Maximum clause weight is 14.000.
% 0.10/0.40 % Given clauses 52.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------