%------------------------------------------------------------------------------
% 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 : n010.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 : Theorem 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 132 ( 27 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 136 ( 44 ~; 41 |; 35 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 53 ( 0 sgn 21 !; 3 ?)
% 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(assumption_4,axiom,
! [X,T0,T] :
( ( ~ has_immunity(X,T)
& ~ has_immunity(X,T0)
& organization(X) )
=> ( ( ( position(X,T) = position(X,T0)
& capability(X,T) = capability(X,T0) )
=> hazard_of_mortality(X,T) = hazard_of_mortality(X,T0) )
& ( ( greater(position(X,T),position(X,T0))
& greater_or_equal(capability(X,T),capability(X,T0)) )
=> smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) )
& ( ( greater_or_equal(position(X,T),position(X,T0))
& greater(capability(X,T),capability(X,T0)) )
=> smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ) ),
file('theBenchmark.p',assumption_4) ).
fof(assumption_5,axiom,
! [X,T0,T] :
( organization(X)
=> ( ( ( internal_friction(X,T) = internal_friction(X,T0)
& stock_of_knowledge(X,T) = stock_of_knowledge(X,T0) )
=> capability(X,T) = capability(X,T0) )
& ( ( greater(internal_friction(X,T),internal_friction(X,T0))
& smaller_or_equal(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) )
=> smaller(capability(X,T),capability(X,T0)) )
& ( ( smaller_or_equal(internal_friction(X,T),internal_friction(X,T0))
& greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) )
=> greater(capability(X,T),capability(X,T0)) ) ) ),
file('theBenchmark.p',assumption_5) ).
fof(assumption_6,axiom,
! [X,T0,T] :
( organization(X)
=> ( ( external_ties(X,T) = external_ties(X,T0)
=> position(X,T) = position(X,T0) )
& ( greater(external_ties(X,T),external_ties(X,T0))
=> greater(position(X,T),position(X,T0)) ) ) ),
file('theBenchmark.p',assumption_6) ).
fof(lemma_2,conjecture,
! [X,T0,T] :
( ( external_ties(X,T0) = external_ties(X,T)
& greater(internal_friction(X,T),internal_friction(X,T0))
& stock_of_knowledge(X,T) = stock_of_knowledge(X,T0)
& ~ has_immunity(X,T)
& ~ has_immunity(X,T0)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
file('theBenchmark.p',lemma_2) ).
fof(lemma_2_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( external_ties(X,T0) = external_ties(X,T)
& greater(internal_friction(X,T),internal_friction(X,T0))
& stock_of_knowledge(X,T) = stock_of_knowledge(X,T0)
& ~ has_immunity(X,T)
& ~ has_immunity(X,T0)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
inference(assume_negation,[status(cth)],[lemma_2]) ).
cnf(c_13,plain,
( greater(B,A)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_16,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]) ).
cnf(c_18,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]) ).
fof(nnf_10,plain,
? [X,T0,T] :
( ~ greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0))
& external_ties(X,T) = external_ties(X,T0)
& greater(internal_friction(X,T),internal_friction(X,T0))
& stock_of_knowledge(X,T) = stock_of_knowledge(X,T0)
& ~ has_immunity(X,T)
& ~ has_immunity(X,T0)
& organization(X) ),
inference(fof_nnf,[status(thm)],[lemma_2_neg]) ).
fof(sk_lemma_2_neg,plain,
( ~ greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1))
& external_ties(sK0,sK2) = external_ties(sK0,sK1)
& greater(internal_friction(sK0,sK2),internal_friction(sK0,sK1))
& stock_of_knowledge(sK0,sK2) = stock_of_knowledge(sK0,sK1)
& ~ has_immunity(sK0,sK2)
& ~ has_immunity(sK0,sK1)
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(T0,sK1),skolemize(T,sK2)],[nnf_10]) ).
cnf(c_19,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_20,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_16,c_13]) ).
cnf(c_24,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_18,c_13]) ).
cnf(c_26,plain,
( position(A,B) = position(A,C)
| external_ties(A,B) != external_ties(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_6]) ).
cnf(c_35,negated_conjecture,
( position(sK0,A) = position(sK0,B)
| external_ties(sK0,A) != external_ties(sK0,B) ),
inference(resolve,[status(thm)],[c_26,c_19]) ).
cnf(c_37,negated_conjecture,
( greater(capability(sK0,B),capability(sK0,A))
| ~ greater(internal_friction(sK0,A),internal_friction(sK0,B))
| ~ smaller_or_equal(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(resolve,[status(thm)],[c_19,c_24]) ).
cnf(c_41,negated_conjecture,
( greater(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater_or_equal(position(sK0,B),position(sK0,A))
| ~ greater(capability(sK0,B),capability(sK0,A))
| has_immunity(sK0,B)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_42,plain,
( B != A
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_45,plain,
( B != A
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal]) ).
cnf(c_48,negated_conjecture,
~ has_immunity(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_49,negated_conjecture,
~ has_immunity(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_50,negated_conjecture,
stock_of_knowledge(sK0,sK2) = stock_of_knowledge(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_51,negated_conjecture,
greater(internal_friction(sK0,sK2),internal_friction(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_52,negated_conjecture,
external_ties(sK0,sK2) = external_ties(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_53,negated_conjecture,
~ greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_63,plain,
smaller_or_equal(A,A),
inference(xxres,[status(thm)],[c_42]) ).
cnf(c_64,plain,
greater_or_equal(A,A),
inference(xxres,[status(thm)],[c_45]) ).
cnf(c_124,negated_conjecture,
( greater(capability(sK0,sK1),capability(sK0,sK2))
| ~ smaller_or_equal(stock_of_knowledge(sK0,sK2),stock_of_knowledge(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_51,c_37]) ).
cnf(c_125,negated_conjecture,
( greater(capability(sK0,sK1),capability(sK0,sK2))
| ~ smaller_or_equal(stock_of_knowledge(sK0,sK1),stock_of_knowledge(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_50,c_124]) ).
cnf(c_77,negated_conjecture,
greater(capability(sK0,sK1),capability(sK0,sK2)),
inference(resolve,[status(thm)],[c_63,c_125]) ).
cnf(c_79,plain,
position(sK0,sK2) = position(sK0,sK1),
inference(resolve,[status(thm)],[c_52,c_35]) ).
cnf(c_126,negated_conjecture,
( greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1))
| ~ greater_or_equal(position(sK0,sK1),position(sK0,sK2))
| has_immunity(sK0,sK1)
| has_immunity(sK0,sK2) ),
inference(resolve,[status(thm)],[c_77,c_41]) ).
cnf(c_127,negated_conjecture,
( greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1))
| ~ greater_or_equal(position(sK0,sK1),position(sK0,sK1))
| has_immunity(sK0,sK1)
| has_immunity(sK0,sK2) ),
inference(paramod,[status(thm)],[c_79,c_126]) ).
cnf(c_128,negated_conjecture,
( greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1))
| ~ greater_or_equal(position(sK0,sK1),position(sK0,sK1))
| has_immunity(sK0,sK1) ),
inference(resolve,[status(thm)],[c_49,c_127]) ).
cnf(c_129,negated_conjecture,
( greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1))
| ~ greater_or_equal(position(sK0,sK1),position(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_48,c_128]) ).
cnf(c_130,negated_conjecture,
greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1)),
inference(resolve,[status(thm)],[c_64,c_129]) ).
cnf(c_123,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_53,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT043+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n010.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 00:09:00 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.46 % Process 1993305 was started by sandbox on n010,
% 0.17/0.46 % Sat Sep 26 00:09:00 2026
% 0.17/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.17/0.52
% 0.17/0.52 % SZS status Theorem for theBenchmark
% 0.17/0.52
% 0.17/0.52 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.52 % Length of proof is 30.
% 0.17/0.52 % Level of proof is 5.
% 0.17/0.52 % Maximum clause weight is 37.000.
% 0.17/0.52 % Given clauses 37.
% 0.17/0.52
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------