%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT046+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 : n006.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 08:02:58 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 132 ( 14 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 134 ( 49 ~; 40 |; 26 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 82 ( 10 sgn 30 !; 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(assumption_1,axiom,
! [X,T] :
( ( ~ has_endowment(X)
& organization(X) )
=> ~ has_immunity(X,T) ),
file('theBenchmark.p',assumption_1) ).
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(assumption_7,axiom,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) ),
file('theBenchmark.p',assumption_7) ).
fof(assumption_8,axiom,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(external_ties(X,T),external_ties(X,T0)) ),
file('theBenchmark.p',assumption_8) ).
fof(assumption_9,axiom,
! [X,T0,T] :
( organization(X)
=> internal_friction(X,T) = internal_friction(X,T0) ),
file('theBenchmark.p',assumption_9) ).
fof(theorem_1,conjecture,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& ~ has_endowment(X)
& organization(X) )
=> smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
file('theBenchmark.p',theorem_1) ).
fof(theorem_1_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& ~ has_endowment(X)
& organization(X) )
=> smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
inference(assume_negation,[status(cth)],[theorem_1]) ).
fof(nnf_14,plain,
? [X,T0,T] :
( ~ smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0))
& greater(age(X,T),age(X,T0))
& ~ has_endowment(X)
& organization(X) ),
inference(fof_nnf,[status(thm)],[theorem_1_neg]) ).
fof(sk_theorem_1_neg,plain,
( ~ smaller(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2))
& greater(age(sK0,sK1),age(sK0,sK2))
& ~ has_endowment(sK0)
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(T0,sK2),skolemize(T,sK1)],[nnf_14]) ).
cnf(c_15,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_1_neg]) ).
cnf(c_16,plain,
( internal_friction(A,B) = internal_friction(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_9]) ).
cnf(c_17,plain,
( greater(external_ties(A,B),external_ties(A,C))
| ~ greater(age(A,B),age(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_8]) ).
cnf(c_18,plain,
( greater(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ greater(age(A,B),age(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_7]) ).
cnf(c_20,plain,
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_6]) ).
cnf(c_23,plain,
( greater(capability(A,B),capability(A,C))
| ~ smaller_or_equal(internal_friction(A,B),internal_friction(A,C))
| ~ greater(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_5]) ).
cnf(c_25,plain,
( smaller(hazard_of_mortality(A,C),hazard_of_mortality(A,B))
| ~ greater(position(A,C),position(A,B))
| ~ greater_or_equal(capability(A,C),capability(A,B))
| has_immunity(A,C)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_4]) ).
cnf(c_27,plain,
( ~ has_immunity(A,B)
| has_endowment(A)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_1]) ).
cnf(c_28,negated_conjecture,
( ~ has_immunity(sK0,A)
| has_endowment(sK0) ),
inference(resolve,[status(thm)],[c_15,c_27]) ).
cnf(c_30,negated_conjecture,
( smaller(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| ~ greater(position(sK0,B),position(sK0,A))
| ~ greater_or_equal(capability(sK0,B),capability(sK0,A))
| has_immunity(sK0,B)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_15,c_25]) ).
cnf(c_32,negated_conjecture,
( greater(capability(sK0,A),capability(sK0,B))
| ~ smaller_or_equal(internal_friction(sK0,A),internal_friction(sK0,B))
| ~ greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(resolve,[status(thm)],[c_15,c_23]) ).
cnf(c_35,negated_conjecture,
( greater(position(sK0,A),position(sK0,B))
| ~ greater(external_ties(sK0,A),external_ties(sK0,B)) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_37,negated_conjecture,
( greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B))
| ~ greater(age(sK0,A),age(sK0,B)) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_38,negated_conjecture,
( greater(external_ties(sK0,A),external_ties(sK0,B))
| ~ greater(age(sK0,A),age(sK0,B)) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_39,negated_conjecture,
internal_friction(sK0,A) = internal_friction(sK0,B),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_40,negated_conjecture,
~ smaller(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_theorem_1_neg]) ).
cnf(c_41,negated_conjecture,
greater(age(sK0,sK1),age(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_theorem_1_neg]) ).
cnf(c_42,negated_conjecture,
~ has_endowment(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_1_neg]) ).
cnf(c_49,plain,
( ~ greater(A,B)
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal]) ).
cnf(c_51,plain,
( B != A
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_57,negated_conjecture,
~ has_immunity(sK0,A),
inference(resolve,[status(thm)],[c_42,c_28]) ).
cnf(c_141,negated_conjecture,
( smaller(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater(position(sK0,A),position(sK0,B))
| ~ greater_or_equal(capability(sK0,A),capability(sK0,B))
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_57,c_30]) ).
cnf(c_60,negated_conjecture,
( smaller(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater(position(sK0,A),position(sK0,B))
| ~ greater_or_equal(capability(sK0,A),capability(sK0,B)) ),
inference(resolve,[status(thm)],[c_57,c_141]) ).
cnf(c_63,plain,
( greater(capability(sK0,A),capability(sK0,B))
| ~ smaller_or_equal(internal_friction(sK0,A),internal_friction(sK0,C))
| ~ greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(paramod,[status(thm)],[c_39,c_32]) ).
cnf(c_64,plain,
greater(external_ties(sK0,sK1),external_ties(sK0,sK2)),
inference(resolve,[status(thm)],[c_41,c_38]) ).
cnf(c_65,plain,
greater(stock_of_knowledge(sK0,sK1),stock_of_knowledge(sK0,sK2)),
inference(resolve,[status(thm)],[c_41,c_37]) ).
cnf(c_76,plain,
smaller_or_equal(internal_friction(sK0,A),internal_friction(sK0,B)),
inference(resolve,[status(thm)],[c_51,c_39]) ).
cnf(c_78,plain,
( greater(capability(sK0,A),capability(sK0,B))
| ~ greater(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(resolve,[status(thm)],[c_76,c_63]) ).
cnf(c_86,plain,
greater(position(sK0,sK1),position(sK0,sK2)),
inference(resolve,[status(thm)],[c_64,c_35]) ).
cnf(c_142,negated_conjecture,
( smaller(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2))
| ~ greater_or_equal(capability(sK0,sK1),capability(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_60,c_86]) ).
cnf(c_106,negated_conjecture,
~ greater_or_equal(capability(sK0,sK1),capability(sK0,sK2)),
inference(resolve,[status(thm)],[c_142,c_40]) ).
cnf(c_109,plain,
~ greater(capability(sK0,sK1),capability(sK0,sK2)),
inference(resolve,[status(thm)],[c_49,c_106]) ).
cnf(c_143,plain,
greater(capability(sK0,sK1),capability(sK0,sK2)),
inference(resolve,[status(thm)],[c_78,c_65]) ).
cnf(c_140,plain,
$false,
inference(resolve,[status(thm)],[c_109,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT046+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 00:08:55 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 4092786 was started by sandbox on n006,
% 0.10/0.36 % Sat Sep 26 00:08:55 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 41.
% 0.12/0.39 % Level of proof is 7.
% 0.12/0.39 % Maximum clause weight is 27.000.
% 0.12/0.39 % Given clauses 69.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------