%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT050-1 : 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 : n018.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 08:02:59 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.39s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 68 ( 22 unt; 0 def)
% Number of atoms : 159 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 80 ~; 91 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 18 sgn 32 !; 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_or_equal_1,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| smaller(VAR_0,VAR_1)
| ~ smaller_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_smaller_or_equal_1) ).
cnf(c_2,plain,
( A = B
| smaller(A,B)
| ~ smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal_1]) ).
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(assumption_4_42,axiom,
! [VAR_0,VAR_1,VAR_2] :
( smaller(hazard_of_mortality(VAR_0,VAR_2),hazard_of_mortality(VAR_0,VAR_1))
| ~ greater_or_equal(position(VAR_0,VAR_2),position(VAR_0,VAR_1))
| ~ greater(capability(VAR_0,VAR_2),capability(VAR_0,VAR_1))
| has_immunity(VAR_0,VAR_2)
| has_immunity(VAR_0,VAR_1)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_4_42) ).
cnf(c_6,plain,
( smaller(hazard_of_mortality(A,C),hazard_of_mortality(A,B))
| ~ greater_or_equal(position(A,C),position(A,B))
| ~ greater(capability(A,C),capability(A,B))
| has_immunity(A,C)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_4_42]) ).
fof(assumption_5_46,axiom,
! [VAR_0,VAR_1,VAR_2] :
( smaller(capability(VAR_0,VAR_1),capability(VAR_0,VAR_2))
| ~ greater(internal_friction(VAR_0,VAR_1),internal_friction(VAR_0,VAR_2))
| ~ smaller_or_equal(stock_of_knowledge(VAR_0,VAR_1),stock_of_knowledge(VAR_0,VAR_2))
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_5_46) ).
cnf(c_8,plain,
( smaller(capability(A,B),capability(A,C))
| ~ greater(internal_friction(A,B),internal_friction(A,C))
| ~ smaller_or_equal(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_5_46]) ).
fof(theorem_3_53,axiom,
organization(sk1),
file('theBenchmark.p',theorem_3_53) ).
cnf(c_9,plain,
organization(sk1),
inference(clausify,[status(thm)],[theorem_3_53]) ).
cnf(c_10,plain,
( greater(hazard_of_mortality(A,B),hazard_of_mortality(A,C))
| ~ greater_or_equal(position(A,C),position(A,B))
| ~ greater(capability(A,C),capability(A,B))
| has_immunity(A,C)
| has_immunity(A,B)
| ~ organization(A) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_11,plain,
( smaller_or_equal(hazard_of_mortality(A,C),hazard_of_mortality(A,B))
| ~ greater_or_equal(position(A,C),position(A,B))
| ~ greater(capability(A,C),capability(A,B))
| has_immunity(A,C)
| has_immunity(A,B)
| ~ organization(A) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_14,plain,
( greater(capability(A,C),capability(A,B))
| ~ greater(internal_friction(A,B),internal_friction(A,C))
| ~ smaller_or_equal(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ organization(A) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
fof(assumption_12_52,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(internal_friction(VAR_0,VAR_1),internal_friction(VAR_0,VAR_2))
| ~ greater(age(VAR_0,VAR_1),age(VAR_0,VAR_2))
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_12_52) ).
cnf(c_16,plain,
( greater(internal_friction(A,B),internal_friction(A,C))
| ~ greater(age(A,B),age(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_12_52]) ).
fof(assumption_11_51,axiom,
! [VAR_0,VAR_1,VAR_2] :
( external_ties(VAR_0,VAR_1) = external_ties(VAR_0,VAR_2)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_11_51) ).
cnf(c_17,plain,
( external_ties(A,B) = external_ties(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_11_51]) ).
fof(assumption_10_50,axiom,
! [VAR_0,VAR_1,VAR_2] :
( stock_of_knowledge(VAR_0,VAR_1) = stock_of_knowledge(VAR_0,VAR_2)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_10_50) ).
cnf(c_18,plain,
( stock_of_knowledge(A,B) = stock_of_knowledge(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_10_50]) ).
fof(assumption_6_49,axiom,
! [VAR_0,VAR_1,VAR_2] :
( position(VAR_0,VAR_1) = position(VAR_0,VAR_2)
| external_ties(VAR_0,VAR_1) != external_ties(VAR_0,VAR_2)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_6_49) ).
cnf(c_19,plain,
( position(A,B) = position(A,C)
| external_ties(A,B) != external_ties(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_6_49]) ).
fof(assumption_1_41,axiom,
! [VAR_0,VAR_1] :
( ~ has_immunity(VAR_0,VAR_1)
| has_endowment(VAR_0)
| ~ organization(VAR_0) ),
file('theBenchmark.p',assumption_1_41) ).
cnf(c_24,plain,
( ~ has_immunity(A,B)
| has_endowment(A)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_1_41]) ).
cnf(c_25,plain,
( ~ has_immunity(sk1,A)
| has_endowment(sk1) ),
inference(resolve,[status(thm)],[c_24,c_9]) ).
cnf(c_30,plain,
( position(sk1,A) = position(sk1,B)
| external_ties(sk1,A) != external_ties(sk1,B) ),
inference(resolve,[status(thm)],[c_19,c_9]) ).
cnf(c_31,plain,
stock_of_knowledge(sk1,A) = stock_of_knowledge(sk1,B),
inference(resolve,[status(thm)],[c_18,c_9]) ).
cnf(c_32,plain,
external_ties(sk1,A) = external_ties(sk1,B),
inference(resolve,[status(thm)],[c_17,c_9]) ).
cnf(c_33,plain,
( greater(internal_friction(sk1,A),internal_friction(sk1,B))
| ~ greater(age(sk1,A),age(sk1,B)) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_35,plain,
( greater(capability(sk1,B),capability(sk1,A))
| ~ greater(internal_friction(sk1,A),internal_friction(sk1,B))
| ~ smaller_or_equal(stock_of_knowledge(sk1,A),stock_of_knowledge(sk1,B)) ),
inference(resolve,[status(thm)],[c_9,c_14]) ).
cnf(c_38,plain,
( smaller_or_equal(hazard_of_mortality(sk1,B),hazard_of_mortality(sk1,A))
| ~ greater_or_equal(position(sk1,B),position(sk1,A))
| ~ greater(capability(sk1,B),capability(sk1,A))
| has_immunity(sk1,B)
| has_immunity(sk1,A) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_39,plain,
( greater(hazard_of_mortality(sk1,A),hazard_of_mortality(sk1,B))
| ~ greater_or_equal(position(sk1,B),position(sk1,A))
| ~ greater(capability(sk1,B),capability(sk1,A))
| has_immunity(sk1,B)
| has_immunity(sk1,A) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
fof(definition_smaller_or_equal_3,axiom,
! [VAR_0,VAR_1] :
( smaller_or_equal(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',definition_smaller_or_equal_3) ).
cnf(c_40,plain,
( smaller_or_equal(A,B)
| A != B ),
inference(clausify,[status(thm)],[definition_smaller_or_equal_3]) ).
fof(definition_greater_or_equal_6,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',definition_greater_or_equal_6) ).
cnf(c_43,plain,
( greater_or_equal(A,B)
| A != B ),
inference(clausify,[status(thm)],[definition_greater_or_equal_6]) ).
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_44,plain,
( ~ greater(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_strict_9]) ).
fof(theorem_3_54,axiom,
~ has_endowment(sk1),
file('theBenchmark.p',theorem_3_54) ).
cnf(c_46,plain,
~ has_endowment(sk1),
inference(clausify,[status(thm)],[theorem_3_54]) ).
fof(theorem_3_55,axiom,
greater(age(sk1,sk3),age(sk1,sk2)),
file('theBenchmark.p',theorem_3_55) ).
cnf(c_47,plain,
greater(age(sk1,sk3),age(sk1,sk2)),
inference(clausify,[status(thm)],[theorem_3_55]) ).
fof(theorem_3_56,axiom,
~ greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)),
file('theBenchmark.p',theorem_3_56) ).
cnf(c_48,plain,
~ greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)),
inference(clausify,[status(thm)],[theorem_3_56]) ).
cnf(c_49,plain,
( B = A
| ~ smaller_or_equal(B,A)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_54,plain,
position(sk1,A) = position(sk1,B),
inference(resolve,[status(thm)],[c_32,c_30]) ).
cnf(c_59,plain,
~ greater(A,A),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_60,plain,
~ has_immunity(sk1,A),
inference(resolve,[status(thm)],[c_46,c_25]) ).
cnf(c_163,plain,
( greater(hazard_of_mortality(sk1,B),hazard_of_mortality(sk1,A))
| ~ greater_or_equal(position(sk1,A),position(sk1,B))
| ~ greater(capability(sk1,A),capability(sk1,B))
| has_immunity(sk1,A) ),
inference(resolve,[status(thm)],[c_60,c_39]) ).
cnf(c_62,plain,
( greater(hazard_of_mortality(sk1,B),hazard_of_mortality(sk1,A))
| ~ greater_or_equal(position(sk1,A),position(sk1,B))
| ~ greater(capability(sk1,A),capability(sk1,B)) ),
inference(resolve,[status(thm)],[c_60,c_163]) ).
cnf(c_164,plain,
( smaller_or_equal(hazard_of_mortality(sk1,A),hazard_of_mortality(sk1,B))
| ~ greater_or_equal(position(sk1,A),position(sk1,B))
| ~ greater(capability(sk1,A),capability(sk1,B))
| has_immunity(sk1,A) ),
inference(resolve,[status(thm)],[c_60,c_38]) ).
cnf(c_63,plain,
( smaller_or_equal(hazard_of_mortality(sk1,A),hazard_of_mortality(sk1,B))
| ~ greater_or_equal(position(sk1,A),position(sk1,B))
| ~ greater(capability(sk1,A),capability(sk1,B)) ),
inference(resolve,[status(thm)],[c_60,c_164]) ).
cnf(c_71,plain,
( greater(capability(sk1,C),capability(sk1,A))
| ~ greater(internal_friction(sk1,A),internal_friction(sk1,C))
| ~ smaller_or_equal(stock_of_knowledge(sk1,A),stock_of_knowledge(sk1,B)) ),
inference(paramod,[status(thm)],[c_31,c_35]) ).
cnf(c_73,plain,
smaller_or_equal(stock_of_knowledge(sk1,A),stock_of_knowledge(sk1,B)),
inference(resolve,[status(thm)],[c_40,c_31]) ).
cnf(c_75,plain,
( greater(capability(sk1,B),capability(sk1,A))
| ~ greater(internal_friction(sk1,A),internal_friction(sk1,B)) ),
inference(resolve,[status(thm)],[c_73,c_71]) ).
cnf(c_84,plain,
greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2)),
inference(resolve,[status(thm)],[c_47,c_33]) ).
cnf(c_97,plain,
greater_or_equal(position(sk1,A),position(sk1,B)),
inference(resolve,[status(thm)],[c_54,c_43]) ).
cnf(c_99,plain,
( smaller_or_equal(hazard_of_mortality(sk1,A),hazard_of_mortality(sk1,B))
| ~ greater(capability(sk1,A),capability(sk1,B)) ),
inference(resolve,[status(thm)],[c_97,c_63]) ).
cnf(c_100,plain,
( greater(hazard_of_mortality(sk1,B),hazard_of_mortality(sk1,A))
| ~ greater(capability(sk1,A),capability(sk1,B)) ),
inference(resolve,[status(thm)],[c_97,c_62]) ).
cnf(c_104,plain,
greater(capability(sk1,sk2),capability(sk1,sk3)),
inference(resolve,[status(thm)],[c_84,c_75]) ).
cnf(c_138,plain,
smaller_or_equal(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3)),
inference(resolve,[status(thm)],[c_99,c_104]) ).
cnf(c_165,plain,
( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3)
| greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_138,c_49]) ).
cnf(c_166,plain,
( hazard_of_mortality(sk1,sk3) = hazard_of_mortality(sk1,sk2)
| greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)) ),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_141,plain,
hazard_of_mortality(sk1,sk3) = hazard_of_mortality(sk1,sk2),
inference(resolve,[status(thm)],[c_48,c_166]) ).
cnf(c_167,plain,
greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)),
inference(resolve,[status(thm)],[c_100,c_104]) ).
cnf(c_168,plain,
greater(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk2)),
inference(paramod,[status(thm)],[c_141,c_167]) ).
cnf(c_162,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT050-1 : 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 : n018.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
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sat Sep 26 00:11:51 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 3182548 was started by sandbox on n018,
% 0.02/0.36 % Sat Sep 26 00:11:51 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.39
% 0.02/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.39
% 0.02/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.02/0.39 % Length of proof is 45.
% 0.02/0.39 % Level of proof is 8.
% 0.02/0.39 % Maximum clause weight is 27.000.
% 0.02/0.39 % Given clauses 72.
% 0.02/0.39
% 0.02/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------