%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 18 unt; 0 def)
% Number of atoms : 180 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 184 ( 69 ~; 69 |; 26 &)
% ( 3 <=>; 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 : 120 ( 18 sgn 34 !; 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(meaning_postulate_greater_strict,axiom,
! [X,Y] :
~ ( greater(Y,X)
& greater(X,Y) ),
file('theBenchmark.p',meaning_postulate_greater_strict) ).
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_10,axiom,
! [X,T0,T] :
( organization(X)
=> stock_of_knowledge(X,T) = stock_of_knowledge(X,T0) ),
file('theBenchmark.p',assumption_10) ).
fof(assumption_11,axiom,
! [X,T0,T] :
( organization(X)
=> external_ties(X,T) = external_ties(X,T0) ),
file('theBenchmark.p',assumption_11) ).
fof(assumption_12,axiom,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& organization(X) )
=> greater(internal_friction(X,T),internal_friction(X,T0)) ),
file('theBenchmark.p',assumption_12) ).
fof(theorem_3,conjecture,
! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& ~ has_endowment(X)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
file('theBenchmark.p',theorem_3) ).
fof(theorem_3_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( greater(age(X,T),age(X,T0))
& ~ has_endowment(X)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
inference(assume_negation,[status(cth)],[theorem_3]) ).
cnf(c_15,plain,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_16,plain,
( B = A
| smaller(A,B)
| ~ smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_17,plain,
( greater(B,A)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_20,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_22,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_14,plain,
? [X,T0,T] :
( ~ greater(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_3_neg]) ).
fof(sk_theorem_3_neg,plain,
( ~ greater(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_23,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_3_neg]) ).
cnf(c_24,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_20,c_17]) ).
cnf(c_25,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_20,c_15]) ).
cnf(c_28,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_22,c_17]) ).
cnf(c_30,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]) ).
cnf(c_31,plain,
( external_ties(A,B) = external_ties(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_11]) ).
cnf(c_32,plain,
( stock_of_knowledge(A,B) = stock_of_knowledge(A,C)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_10]) ).
cnf(c_33,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_38,plain,
( ~ has_immunity(A,B)
| has_endowment(A)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_1]) ).
cnf(c_39,negated_conjecture,
( ~ has_immunity(sK0,A)
| has_endowment(sK0) ),
inference(resolve,[status(thm)],[c_38,c_23]) ).
cnf(c_44,negated_conjecture,
( position(sK0,A) = position(sK0,B)
| external_ties(sK0,A) != external_ties(sK0,B) ),
inference(resolve,[status(thm)],[c_33,c_23]) ).
cnf(c_45,negated_conjecture,
stock_of_knowledge(sK0,A) = stock_of_knowledge(sK0,B),
inference(resolve,[status(thm)],[c_32,c_23]) ).
cnf(c_46,negated_conjecture,
external_ties(sK0,A) = external_ties(sK0,B),
inference(resolve,[status(thm)],[c_31,c_23]) ).
cnf(c_47,negated_conjecture,
( greater(internal_friction(sK0,A),internal_friction(sK0,B))
| ~ greater(age(sK0,A),age(sK0,B)) ),
inference(resolve,[status(thm)],[c_30,c_23]) ).
cnf(c_49,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_23,c_28]) ).
cnf(c_52,negated_conjecture,
( smaller_or_equal(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| ~ 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_23,c_25]) ).
cnf(c_53,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_23,c_24]) ).
cnf(c_54,plain,
( B != A
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_57,plain,
( B != A
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal]) ).
cnf(c_58,plain,
( ~ greater(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_strict]) ).
cnf(c_60,negated_conjecture,
~ has_endowment(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_3_neg]) ).
cnf(c_61,negated_conjecture,
greater(age(sK0,sK1),age(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_theorem_3_neg]) ).
cnf(c_62,negated_conjecture,
~ greater(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_theorem_3_neg]) ).
cnf(c_63,plain,
( A = B
| ~ smaller_or_equal(B,A)
| greater(A,B) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_68,negated_conjecture,
position(sK0,A) = position(sK0,B),
inference(resolve,[status(thm)],[c_46,c_44]) ).
cnf(c_73,plain,
~ greater(A,A),
inference(factor,[status(thm)],[c_58]) ).
cnf(c_74,negated_conjecture,
~ has_immunity(sK0,A),
inference(resolve,[status(thm)],[c_60,c_39]) ).
cnf(c_177,negated_conjecture,
( greater(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| ~ greater_or_equal(position(sK0,A),position(sK0,B))
| ~ greater(capability(sK0,A),capability(sK0,B))
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_74,c_53]) ).
cnf(c_76,negated_conjecture,
( greater(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| ~ greater_or_equal(position(sK0,A),position(sK0,B))
| ~ greater(capability(sK0,A),capability(sK0,B)) ),
inference(resolve,[status(thm)],[c_74,c_177]) ).
cnf(c_178,negated_conjecture,
( smaller_or_equal(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater_or_equal(position(sK0,A),position(sK0,B))
| ~ greater(capability(sK0,A),capability(sK0,B))
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_74,c_52]) ).
cnf(c_77,negated_conjecture,
( smaller_or_equal(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater_or_equal(position(sK0,A),position(sK0,B))
| ~ greater(capability(sK0,A),capability(sK0,B)) ),
inference(resolve,[status(thm)],[c_74,c_178]) ).
cnf(c_85,plain,
( greater(capability(sK0,C),capability(sK0,A))
| ~ greater(internal_friction(sK0,A),internal_friction(sK0,C))
| ~ smaller_or_equal(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)) ),
inference(paramod,[status(thm)],[c_45,c_49]) ).
cnf(c_87,plain,
smaller_or_equal(stock_of_knowledge(sK0,A),stock_of_knowledge(sK0,B)),
inference(resolve,[status(thm)],[c_54,c_45]) ).
cnf(c_89,plain,
( greater(capability(sK0,B),capability(sK0,A))
| ~ greater(internal_friction(sK0,A),internal_friction(sK0,B)) ),
inference(resolve,[status(thm)],[c_87,c_85]) ).
cnf(c_98,plain,
greater(internal_friction(sK0,sK1),internal_friction(sK0,sK2)),
inference(resolve,[status(thm)],[c_61,c_47]) ).
cnf(c_111,plain,
greater_or_equal(position(sK0,A),position(sK0,B)),
inference(resolve,[status(thm)],[c_68,c_57]) ).
cnf(c_113,negated_conjecture,
( smaller_or_equal(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater(capability(sK0,A),capability(sK0,B)) ),
inference(resolve,[status(thm)],[c_111,c_77]) ).
cnf(c_114,negated_conjecture,
( greater(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| ~ greater(capability(sK0,A),capability(sK0,B)) ),
inference(resolve,[status(thm)],[c_111,c_76]) ).
cnf(c_118,plain,
greater(capability(sK0,sK2),capability(sK0,sK1)),
inference(resolve,[status(thm)],[c_98,c_89]) ).
cnf(c_152,plain,
smaller_or_equal(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1)),
inference(resolve,[status(thm)],[c_113,c_118]) ).
cnf(c_179,plain,
( hazard_of_mortality(sK0,sK1) = hazard_of_mortality(sK0,sK2)
| greater(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_152,c_63]) ).
cnf(c_155,negated_conjecture,
hazard_of_mortality(sK0,sK1) = hazard_of_mortality(sK0,sK2),
inference(resolve,[status(thm)],[c_62,c_179]) ).
cnf(c_180,negated_conjecture,
greater(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)),
inference(resolve,[status(thm)],[c_114,c_118]) ).
cnf(c_181,negated_conjecture,
greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK2)),
inference(paramod,[status(thm)],[c_155,c_180]) ).
cnf(c_176,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_73,c_181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT050+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 00:11:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1478876 was started by sandbox2 on n003,
% 0.08/0.37 % Sat Sep 26 00:11:09 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % SZS status Theorem for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.08/0.40 % Length of proof is 57.
% 0.08/0.40 % Level of proof is 9.
% 0.08/0.40 % Maximum clause weight is 27.000.
% 0.08/0.40 % Given clauses 72.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------