%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Unsatisfiable 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 20 unt; 0 def)
% Number of atoms : 78 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 40 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 38 ( 0 sgn 14 !; 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_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(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_10,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_11,plain,
( has_immunity(A,B)
| ~ smaller_or_equal(age(A,B),eta)
| ~ has_endowment(A) ),
inference(clausify,[status(thm)],[definition_1_32]) ).
fof(theorem_6_41,axiom,
has_endowment(sk2),
file('theBenchmark.p',theorem_6_41) ).
cnf(c_16,plain,
has_endowment(sk2),
inference(clausify,[status(thm)],[theorem_6_41]) ).
fof(theorem_6_40,axiom,
organization(sk2),
file('theBenchmark.p',theorem_6_40) ).
cnf(c_24,plain,
organization(sk2),
inference(clausify,[status(thm)],[theorem_6_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_25,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_26,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_27,plain,
( hazard_of_mortality(sk2,A) = hazard_of_mortality(sk2,B)
| ~ has_immunity(sk2,B)
| ~ has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_28,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_25,c_24]) ).
fof(theorem_6_42,axiom,
age(sk2,sk3) = zero,
file('theBenchmark.p',theorem_6_42) ).
cnf(c_38,plain,
age(sk2,sk3) = zero,
inference(clausify,[status(thm)],[theorem_6_42]) ).
fof(theorem_6_43,axiom,
smaller_or_equal(age(sk2,sk4),eta),
file('theBenchmark.p',theorem_6_43) ).
cnf(c_39,plain,
smaller_or_equal(age(sk2,sk4),eta),
inference(clausify,[status(thm)],[theorem_6_43]) ).
fof(theorem_6_44,axiom,
greater(age(sk2,sk5),eta),
file('theBenchmark.p',theorem_6_44) ).
cnf(c_40,plain,
greater(age(sk2,sk5),eta),
inference(clausify,[status(thm)],[theorem_6_44]) ).
fof(theorem_6_45,axiom,
greater(eta,zero),
file('theBenchmark.p',theorem_6_45) ).
cnf(c_41,plain,
greater(eta,zero),
inference(clausify,[status(thm)],[theorem_6_45]) ).
fof(theorem_6_46,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',theorem_6_46) ).
cnf(c_42,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)],[theorem_6_46]) ).
cnf(c_44,plain,
( smaller_or_equal(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_47,plain,
( ~ has_immunity(sk2,A)
| ~ greater(age(sk2,A),eta) ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_48,plain,
( has_immunity(sk2,A)
| ~ smaller_or_equal(age(sk2,A),eta) ),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_58,plain,
smaller_or_equal(zero,eta),
inference(resolve,[status(thm)],[c_44,c_41]) ).
cnf(c_66,plain,
~ has_immunity(sk2,sk5),
inference(resolve,[status(thm)],[c_47,c_40]) ).
cnf(c_68,plain,
has_immunity(sk2,sk4),
inference(resolve,[status(thm)],[c_48,c_39]) ).
cnf(c_128,plain,
( has_immunity(sk2,sk3)
| ~ smaller_or_equal(zero,eta) ),
inference(paramod,[status(thm)],[c_38,c_48]) ).
cnf(c_69,plain,
has_immunity(sk2,sk3),
inference(resolve,[status(thm)],[c_58,c_128]) ).
cnf(c_74,plain,
( greater(hazard_of_mortality(sk2,A),hazard_of_mortality(sk2,sk4))
| has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_68,c_28]) ).
cnf(c_109,plain,
greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4)),
inference(resolve,[status(thm)],[c_74,c_66]) ).
cnf(c_114,plain,
hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3),
inference(resolve,[status(thm)],[c_109,c_42]) ).
cnf(c_129,plain,
( hazard_of_mortality(sk2,A) = hazard_of_mortality(sk2,sk3)
| ~ has_immunity(sk2,A) ),
inference(resolve,[status(thm)],[c_27,c_69]) ).
cnf(c_130,plain,
~ has_immunity(sk2,sk4),
inference(resolve,[status(thm)],[c_129,c_114]) ).
cnf(c_127,plain,
$false,
inference(resolve,[status(thm)],[c_68,c_130]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n008.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 00:11:14 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 2239797 was started by sandbox2 on n008,
% 0.09/5.38 % Sat Sep 26 00:11:14 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.41
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.41
% 0.14/5.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/5.41 % Length of proof is 26.
% 0.14/5.41 % Level of proof is 6.
% 0.14/5.41 % Maximum clause weight is 14.000.
% 0.14/5.41 % Given clauses 52.
% 0.14/5.41
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------