%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT056+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 02:11:51 PM UTC 2026
% Result : Theorem 22.05s 3.66s
% Output : Proof 22.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 17 unt; 0 def)
% Number of atoms : 219 ( 40 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 229 ( 78 ~; 85 |; 55 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 59 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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/sandbox2/benchmark/theBenchmark.p',assumption_3) ).
fof(f8_nnf,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(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,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(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c19,plain,
( 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(esa)],[f8_sk]) ).
fof(f9,conjecture,
! [X,T0,T1,T2] :
( ( greater(sigma,zero)
& greater_or_equal(eta,sigma)
& 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/sandbox2/benchmark/theBenchmark.p',lemma_9) ).
fof(f9_neg,negated_conjecture,
~ ! [X,T0,T1,T2] :
( ( greater(sigma,zero)
& greater_or_equal(eta,sigma)
& 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)],[f9]) ).
fof(f9_nnf,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(sigma,zero)
& greater_or_equal(eta,sigma)
& greater(age(X,T2),eta)
& smaller_or_equal(age(X,T1),eta)
& age(X,T0) = zero
& has_endowment(X)
& organization(X) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
( ( hazard_of_mortality(sk1,sk3) != hazard_of_mortality(sk1,sk2)
| ~ greater(hazard_of_mortality(sk1,sk4),hazard_of_mortality(sk1,sk3)) )
& greater(sigma,zero)
& greater_or_equal(eta,sigma)
& greater(age(sk1,sk4),eta)
& smaller_or_equal(age(sk1,sk3),eta)
& age(sk1,sk2) = zero
& has_endowment(sk1)
& organization(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4])],[f9_nnf]) ).
cnf(c20,plain,
organization(sk1),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p102,plain,
( greater(hazard_of_mortality(sk1,X1),hazard_of_mortality(sk1,X0))
| has_immunity(sk1,X1)
| ~ has_immunity(sk1,X0) ),
inference(resolution,[status(thm)],[c19,c20]) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',definition_1) ).
fof(f6_nnf,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)],[f6]) ).
fof(f6_sk,plain,
! [X,T] :
( ( ( has_immunity(X,sk0(X))
& greater(age(X,sk0(X)),eta) )
| ( ~ has_immunity(X,sk0(X))
& smaller_or_equal(age(X,sk0(X)),eta) )
| ~ organization(X)
| has_endowment(X) )
& ( ( ( ~ 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(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c12,plain,
( has_immunity(X0,X1)
| ~ smaller_or_equal(age(X0,X1),eta)
| ~ has_endowment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c21,plain,
has_endowment(sk1),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p64,plain,
( has_immunity(sk1,X0)
| ~ smaller_or_equal(age(sk1,X0),eta) ),
inference(resolution,[status(thm)],[c12,c21]) ).
cnf(c23,plain,
smaller_or_equal(age(sk1,sk3),eta),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p66,plain,
has_immunity(sk1,sk3),
inference(resolution,[status(thm)],[p64,c23]) ).
cnf(p211,plain,
( greater(hazard_of_mortality(sk1,X0),hazard_of_mortality(sk1,sk3))
| has_immunity(sk1,X0) ),
inference(resolution,[status(thm)],[p102,p66]) ).
cnf(c27,plain,
( hazard_of_mortality(sk1,sk3) != hazard_of_mortality(sk1,sk2)
| ~ greater(hazard_of_mortality(sk1,sk4),hazard_of_mortality(sk1,sk3)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p214,plain,
( hazard_of_mortality(sk1,sk3) != hazard_of_mortality(sk1,sk2)
| has_immunity(sk1,sk4) ),
inference(resolution,[status(thm)],[p211,c27]) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',assumption_2) ).
fof(f7_nnf,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(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,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(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c18,plain,
( hazard_of_mortality(X0,X1) = hazard_of_mortality(X0,X2)
| ~ has_immunity(X0,X2)
| ~ has_immunity(X0,X1)
| ~ organization(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p94,plain,
( hazard_of_mortality(sk1,X0) = hazard_of_mortality(sk1,X1)
| ~ has_immunity(sk1,X1)
| ~ has_immunity(sk1,X0) ),
inference(resolution,[status(thm)],[c18,c20]) ).
cnf(p201,plain,
( hazard_of_mortality(sk1,sk3) = hazard_of_mortality(sk1,X0)
| ~ has_immunity(sk1,X0) ),
inference(resolution,[status(thm)],[p94,p66]) ).
fof(f4,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_transitive) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f1,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_greater_or_equal) ).
fof(f1_nnf,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c25,plain,
greater_or_equal(eta,sigma),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p30,plain,
( eta = sigma
| greater(eta,sigma) ),
inference(resolution,[status(thm)],[c3,c25]) ).
cnf(p49,plain,
( eta = sigma
| greater(eta,X0)
| ~ greater(sigma,X0) ),
inference(resolution,[status(thm)],[c9,p30]) ).
cnf(c26,plain,
greater(sigma,zero),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p72,plain,
( eta = sigma
| greater(eta,zero) ),
inference(resolution,[status(thm)],[p49,c26]) ).
fof(f2,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller) ).
fof(f2_nnf,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c7,plain,
( ~ greater(X1,X0)
| smaller(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p75,plain,
( smaller(zero,eta)
| eta = sigma ),
inference(resolution,[status(thm)],[p72,c7]) ).
fof(f0,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( X = Y
| smaller(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_or_equal) ).
fof(f0_nnf,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)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( X != Y
& ~ smaller(X,Y) )
| smaller_or_equal(X,Y) )
& ( X = Y
| smaller(X,Y)
| ~ smaller_or_equal(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( ~ smaller(X0,X1)
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p79,plain,
( smaller_or_equal(zero,eta)
| eta = sigma ),
inference(resolution,[status(thm)],[p75,c1]) ).
cnf(c22,plain,
age(sk1,sk2) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p65,plain,
( has_immunity(sk1,sk2)
| ~ smaller_or_equal(zero,eta) ),
inference(superposition,[status(thm)],[c22,p64]) ).
cnf(p80,plain,
( has_immunity(sk1,sk2)
| eta = sigma ),
inference(resolution,[status(thm)],[p79,p65]) ).
cnf(p204,plain,
( eta = sigma
| hazard_of_mortality(sk1,sk3) = hazard_of_mortality(sk1,sk2) ),
inference(resolution,[status(thm)],[p201,p80]) ).
cnf(p221,plain,
( eta = sigma
| has_immunity(sk1,sk4) ),
inference(resolution,[status(thm)],[p214,p204]) ).
cnf(c13,plain,
( ~ has_immunity(X0,X1)
| ~ greater(age(X0,X1),eta)
| ~ has_endowment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p67,plain,
( ~ has_immunity(sk1,X0)
| ~ greater(age(sk1,X0),eta) ),
inference(resolution,[status(thm)],[c13,c21]) ).
cnf(c24,plain,
greater(age(sk1,sk4),eta),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p69,plain,
~ has_immunity(sk1,sk4),
inference(resolution,[status(thm)],[p67,c24]) ).
cnf(p222,plain,
eta = sigma,
inference(resolution,[status(thm)],[p221,p69]) ).
cnf(p36,plain,
smaller(zero,sigma),
inference(resolution,[status(thm)],[c7,c26]) ).
cnf(p39,plain,
smaller_or_equal(zero,sigma),
inference(resolution,[status(thm)],[p36,c1]) ).
cnf(p227,plain,
smaller_or_equal(zero,eta),
inference(superposition,[status(thm)],[p222,p39]) ).
cnf(p256,plain,
has_immunity(sk1,sk2),
inference(resolution,[status(thm)],[p227,p65]) ).
cnf(p258,plain,
hazard_of_mortality(sk1,sk3) = hazard_of_mortality(sk1,sk2),
inference(resolution,[status(thm)],[p256,p201]) ).
cnf(p262,plain,
( hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk2)
| has_immunity(sk1,sk4) ),
inference(demodulation,[status(thm)],[p258,p214]) ).
cnf(p331,plain,
has_immunity(sk1,sk4),
inference(equality_resolution,[status(thm)],[p262]) ).
cnf(p332,plain,
$false,
inference(resolution,[status(thm)],[p331,p69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT056+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 01:15:39 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.05/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.05/3.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------