%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT057+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 01:25:29 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 12 unt; 8 def)
% Number of atoms : 217 ( 20 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 236 ( 84 ~; 81 |; 53 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 71 ( 64 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( X = Y
| smaller(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( has_endowment(X)
<=> ! [T] :
( ( greater(age(X,T),eta)
=> ~ has_immunity(X,T) )
& ( smaller_or_equal(age(X,T),eta)
=> has_immunity(X,T) )
& organization(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,T0,T] :
( ( has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> hazard_of_mortality(X,T0) = hazard_of_mortality(X,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,T0,T] :
( ( ~ has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [X,T0,T1,T2] :
( ( greater(eta,zero)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) )
=> ( hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0)
& greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [X,T0,T1,T2] :
( ( greater(eta,zero)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) )
=> ( hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0)
& greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X,Y] :
( ( ( X != Y
& ~ smaller(X,Y) )
| smaller_or_equal(X,Y) )
& ( X = Y
| smaller(X,Y)
| ~ smaller_or_equal(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
( ! [X,Y] :
( ( X != Y
& ~ smaller(X,Y) )
| smaller_or_equal(X,Y) )
& ! [X,Y] :
( X = Y
| smaller(X,Y)
| ~ smaller_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( ~ smaller(X0,X1)
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f22,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
( ! [X,Y] :
( ~ greater(Y,X)
| smaller(X,Y) )
& ! [X,Y] :
( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| smaller(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f32,plain,
! [X] :
( has_endowment(X)
<=> ! [T] :
( ( ~ has_immunity(X,T)
| ~ greater(age(X,T),eta) )
& ( has_immunity(X,T)
| ~ smaller_or_equal(age(X,T),eta) )
& organization(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
! [X] :
( ( ? [T] :
( ( has_immunity(X,T)
& greater(age(X,T),eta) )
| ( ~ has_immunity(X,T)
& smaller_or_equal(age(X,T),eta) )
| ~ organization(X) )
| has_endowment(X) )
& ( ! [T] :
( ( ~ has_immunity(X,T)
| ~ greater(age(X,T),eta) )
& ( has_immunity(X,T)
| ~ smaller_or_equal(age(X,T),eta) )
& organization(X) )
| ~ has_endowment(X) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [X] :
( ? [T] :
( has_immunity(X,T)
& greater(age(X,T),eta) )
| ? [T] :
( ~ has_immunity(X,T)
& smaller_or_equal(age(X,T),eta) )
| ~ organization(X)
| has_endowment(X) )
& ! [X] :
( ( ! [T] :
( ~ has_immunity(X,T)
| ~ greater(age(X,T),eta) )
& ! [T] :
( has_immunity(X,T)
| ~ smaller_or_equal(age(X,T),eta) )
& organization(X) )
| ~ has_endowment(X) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [X] :
( ( has_immunity(X,sK1_skl(X))
& greater(age(X,sK1_skl(X)),eta) )
| ( ~ has_immunity(X,sK0_skl(X))
& smaller_or_equal(age(X,sK0_skl(X)),eta) )
| ~ organization(X)
| has_endowment(X) )
& ! [X] :
( ( ! [T] :
( ~ has_immunity(X,T)
| ~ greater(age(X,T),eta) )
& ! [T] :
( has_immunity(X,T)
| ~ smaller_or_equal(age(X,T),eta) )
& organization(X) )
| ~ has_endowment(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl(X)),skolemize(T,sK1_skl(X))],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( has_immunity(X0,X1)
| ~ smaller_or_equal(age(X0,X1),eta)
| ~ has_endowment(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( ~ has_immunity(X0,X1)
| ~ greater(age(X0,X1),eta)
| ~ has_endowment(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f43,plain,
! [X,T0,T] :
( hazard_of_mortality(X,T0) = hazard_of_mortality(X,T)
| ~ has_immunity(X,T)
| ~ has_immunity(X,T0)
| ~ organization(X) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
! [X0,X1,X2] :
( hazard_of_mortality(X0,X1) = hazard_of_mortality(X0,X2)
| ~ has_immunity(X0,X2)
| ~ has_immunity(X0,X1)
| ~ organization(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X,T0,T] :
( greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0))
| has_immunity(X,T)
| ~ has_immunity(X,T0)
| ~ organization(X) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f46,plain,
! [X0,X1,X2] :
( greater(hazard_of_mortality(X0,X2),hazard_of_mortality(X0,X1))
| has_immunity(X0,X2)
| ~ has_immunity(X0,X1)
| ~ organization(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
? [X,T0,T1,T2] :
( ( hazard_of_mortality(X,T1) != hazard_of_mortality(X,T0)
| ~ greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) )
& greater(eta,zero)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f48,plain,
( ( hazard_of_mortality(sK2_skl,sK4_skl) != hazard_of_mortality(sK2_skl,sK3_skl)
| ~ greater(hazard_of_mortality(sK2_skl,sK5_skl),hazard_of_mortality(sK2_skl,sK4_skl)) )
& greater(eta,zero)
& greater(age(sK2_skl,sK5_skl),eta)
& smaller_or_equal(age(sK2_skl,sK4_skl),eta)
& age(sK2_skl,sK3_skl) = zero
& has_endowment(sK2_skl)
& organization(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK2_skl),skolemize(T0,sK3_skl),skolemize(T1,sK4_skl),skolemize(T2,sK5_skl)],[f47]) ).
fof(f49,plain,
organization(sK2_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
has_endowment(sK2_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
age(sK2_skl,sK3_skl) = zero,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
smaller_or_equal(age(sK2_skl,sK4_skl),eta),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f53,plain,
greater(age(sK2_skl,sK5_skl),eta),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f54,plain,
greater(eta,zero),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f55,plain,
( hazard_of_mortality(sK2_skl,sK4_skl) != hazard_of_mortality(sK2_skl,sK3_skl)
| ~ greater(hazard_of_mortality(sK2_skl,sK5_skl),hazard_of_mortality(sK2_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f56,definition,
( sQ0_spl
<=> greater(hazard_of_mortality(sK2_skl,sK5_skl),hazard_of_mortality(sK2_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ0_spl
| ~ greater(hazard_of_mortality(sK2_skl,sK5_skl),hazard_of_mortality(sK2_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ1_spl
<=> hazard_of_mortality(sK2_skl,sK4_skl) = hazard_of_mortality(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ1_spl
| hazard_of_mortality(sK2_skl,sK4_skl) != hazard_of_mortality(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f56,f59]) ).
fof(f73,plain,
( has_immunity(sK2_skl,sK4_skl)
| ~ has_endowment(sK2_skl) ),
inference(resolution,[status(thm)],[f37,f52]) ).
fof(f74,plain,
( has_immunity(sK2_skl,sK3_skl)
| ~ smaller_or_equal(zero,eta)
| ~ has_endowment(sK2_skl) ),
inference(paramodulation,[status(thm)],[f51,f37]) ).
fof(f75,definition,
( sQ2_spl
<=> has_endowment(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ2_spl
| ~ has_endowment(sK2_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ3_spl
<=> has_immunity(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f73,f75,f78]) ).
fof(f82,definition,
( sQ4_spl
<=> smaller_or_equal(zero,eta) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ4_spl
| ~ smaller_or_equal(zero,eta) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ5_spl
<=> has_immunity(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f74,f75,f82,f85]) ).
fof(f89,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f50]) ).
fof(f90,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( ~ has_immunity(sK2_skl,sK5_skl)
| ~ has_endowment(sK2_skl) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f93,definition,
( sQ6_spl
<=> has_immunity(sK2_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f91,f75,f93]) ).
fof(f106,plain,
smaller(zero,eta),
inference(resolution,[status(thm)],[f25,f54]) ).
fof(f108,plain,
smaller_or_equal(zero,eta),
inference(resolution,[status(thm)],[f106,f15]) ).
fof(f109,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f84]) ).
fof(f110,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f180,plain,
( sQ0_spl
| has_immunity(sK2_skl,sK5_skl)
| ~ has_immunity(sK2_skl,sK4_skl)
| ~ organization(sK2_skl) ),
inference(resolution,[status(thm)],[f46,f58]) ).
fof(f185,definition,
( sQ15_spl
<=> organization(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ15_spl
| ~ organization(sK2_skl) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ0_spl
| sQ6_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f180,f185,f78,f93,f56]) ).
fof(f189,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f49]) ).
fof(f190,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f254,plain,
( sQ1_spl
| ~ has_immunity(sK2_skl,sK3_skl)
| ~ has_immunity(sK2_skl,sK4_skl)
| ~ organization(sK2_skl) ),
inference(resolution,[status(thm)],[f61,f44]) ).
fof(f256,plain,
( sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f254,f185,f78,f85,f59]) ).
fof(f258,plain,
$false,
inference(sat_refutation,[status(thm)],[f62,f81,f88,f90,f96,f110,f188,f190,f256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT057+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:23:58 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.051955 seconds
% 0.14/0.41 % CPU time: 0.140046 seconds
% 0.14/0.41 % Total memory used: 61.029 MB
% 0.14/0.41 % Net memory used: 60.861 MB
%------------------------------------------------------------------------------