%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT043-1 : 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 : n001.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 08:02:57 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 22 unt; 0 def)
% Number of atoms : 94 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 49 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_38,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_38) ).
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_38]) ).
fof(assumption_5_42,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_42) ).
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_42]) ).
fof(lemma_2_46,axiom,
organization(sk1),
file('theBenchmark.p',lemma_2_46) ).
cnf(c_9,plain,
organization(sk1),
inference(clausify,[status(thm)],[lemma_2_46]) ).
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_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_6_45,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_45) ).
cnf(c_16,plain,
( position(A,B) = position(A,C)
| external_ties(A,B) != external_ties(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_6_45]) ).
cnf(c_25,plain,
( position(sk1,A) = position(sk1,B)
| external_ties(sk1,A) != external_ties(sk1,B) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_27,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_31,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_32,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_35,plain,
( greater_or_equal(A,B)
| A != B ),
inference(clausify,[status(thm)],[definition_greater_or_equal_6]) ).
fof(lemma_2_47,axiom,
~ has_immunity(sk1,sk2),
file('theBenchmark.p',lemma_2_47) ).
cnf(c_38,plain,
~ has_immunity(sk1,sk2),
inference(clausify,[status(thm)],[lemma_2_47]) ).
fof(lemma_2_48,axiom,
~ has_immunity(sk1,sk3),
file('theBenchmark.p',lemma_2_48) ).
cnf(c_39,plain,
~ has_immunity(sk1,sk3),
inference(clausify,[status(thm)],[lemma_2_48]) ).
fof(lemma_2_49,axiom,
stock_of_knowledge(sk1,sk3) = stock_of_knowledge(sk1,sk2),
file('theBenchmark.p',lemma_2_49) ).
cnf(c_40,plain,
stock_of_knowledge(sk1,sk3) = stock_of_knowledge(sk1,sk2),
inference(clausify,[status(thm)],[lemma_2_49]) ).
fof(lemma_2_50,axiom,
greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2)),
file('theBenchmark.p',lemma_2_50) ).
cnf(c_41,plain,
greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2)),
inference(clausify,[status(thm)],[lemma_2_50]) ).
fof(lemma_2_51,axiom,
external_ties(sk1,sk2) = external_ties(sk1,sk3),
file('theBenchmark.p',lemma_2_51) ).
cnf(c_42,plain,
external_ties(sk1,sk2) = external_ties(sk1,sk3),
inference(clausify,[status(thm)],[lemma_2_51]) ).
cnf(c_43,plain,
external_ties(sk1,sk3) = external_ties(sk1,sk2),
inference(copy,[status(thm)],[c_42]) ).
fof(lemma_2_52,axiom,
~ greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)),
file('theBenchmark.p',lemma_2_52) ).
cnf(c_44,plain,
~ greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)),
inference(clausify,[status(thm)],[lemma_2_52]) ).
cnf(c_54,plain,
smaller_or_equal(A,A),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_55,plain,
greater_or_equal(A,A),
inference(xxres,[status(thm)],[c_35]) ).
cnf(c_60,plain,
( greater(capability(sk1,A),capability(sk1,sk3))
| ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,A))
| ~ smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,A)) ),
inference(paramod,[status(thm)],[c_40,c_27]) ).
cnf(c_66,plain,
position(sk1,sk3) = position(sk1,sk2),
inference(resolve,[status(thm)],[c_43,c_25]) ).
cnf(c_129,plain,
( greater(capability(sk1,sk2),capability(sk1,sk3))
| ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_60,c_54]) ).
cnf(c_121,plain,
greater(capability(sk1,sk2),capability(sk1,sk3)),
inference(resolve,[status(thm)],[c_41,c_129]) ).
cnf(c_130,plain,
( greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,A))
| ~ greater_or_equal(position(sk1,A),position(sk1,sk3))
| ~ greater(capability(sk1,A),capability(sk1,sk3))
| has_immunity(sk1,A) ),
inference(resolve,[status(thm)],[c_31,c_39]) ).
cnf(c_131,plain,
( greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2))
| ~ greater_or_equal(position(sk1,sk2),position(sk1,sk3))
| ~ greater(capability(sk1,sk2),capability(sk1,sk3)) ),
inference(resolve,[status(thm)],[c_130,c_38]) ).
cnf(c_132,plain,
( greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2))
| ~ greater_or_equal(position(sk1,sk2),position(sk1,sk3)) ),
inference(resolve,[status(thm)],[c_131,c_121]) ).
cnf(c_133,plain,
~ greater_or_equal(position(sk1,sk2),position(sk1,sk3)),
inference(resolve,[status(thm)],[c_132,c_44]) ).
cnf(c_134,plain,
~ greater_or_equal(position(sk1,sk2),position(sk1,sk2)),
inference(paramod,[status(thm)],[c_66,c_133]) ).
cnf(c_128,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT043-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n001.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 00:14:31 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 396702 was started by sandbox on n001,
% 0.09/5.37 % Sat Sep 26 00:14:31 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/5.39 % Length of proof is 25.
% 0.09/5.39 % Level of proof is 5.
% 0.09/5.39 % Maximum clause weight is 27.000.
% 0.09/5.39 % Given clauses 56.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------