%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT054+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 : n005.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 08:03:00 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 17 unt; 0 def)
% Number of atoms : 164 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 167 ( 65 ~; 58 |; 32 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 94 ( 7 sgn 30 !; 4 ?)
% 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_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(definition_2,axiom,
! [X,T0,T] :
( dissimilar(X,T0,T)
<=> ( ~ ( is_aligned(X,T0)
<=> is_aligned(X,T) )
& organization(X) ) ),
file('theBenchmark.p',definition_2) ).
fof(assumption_13,axiom,
! [X,T] :
( ( age(X,T) = zero
& organization(X) )
=> is_aligned(X,T) ),
file('theBenchmark.p',assumption_13) ).
fof(assumption_14,axiom,
! [X,T0,T] :
( ( ~ is_aligned(X,T)
& is_aligned(X,T0)
& organization(X) )
=> greater(capability(X,T0),capability(X,T)) ),
file('theBenchmark.p',assumption_14) ).
fof(assumption_15,axiom,
! [X,T0,T] :
( ( age(X,T0) = zero
& organization(X) )
=> ( greater(age(X,T),sigma)
<=> dissimilar(X,T0,T) ) ),
file('theBenchmark.p',assumption_15) ).
fof(assumption_16,axiom,
! [X,T0,T] :
( ( greater(capability(X,T),capability(X,T0))
& ~ has_immunity(X,T)
& ~ has_immunity(X,T0)
& organization(X) )
=> greater(hazard_of_mortality(X,T0),hazard_of_mortality(X,T)) ),
file('theBenchmark.p',assumption_16) ).
fof(theorem_5,conjecture,
! [X,T0,T1,T2] :
( ( greater(sigma,zero)
& greater(age(X,T2),sigma)
& smaller_or_equal(age(X,T1),sigma)
& age(X,T0) = zero
& ~ has_endowment(X)
& organization(X) )
=> greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ),
file('theBenchmark.p',theorem_5) ).
fof(theorem_5_neg,negated_conjecture,
~ ! [X,T0,T1,T2] :
( ( greater(sigma,zero)
& greater(age(X,T2),sigma)
& smaller_or_equal(age(X,T1),sigma)
& age(X,T0) = zero
& ~ has_endowment(X)
& organization(X) )
=> greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ),
inference(assume_negation,[status(cth)],[theorem_5]) ).
cnf(c_16,plain,
( B = A
| smaller(A,B)
| ~ smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
fof(nnf_14,plain,
? [X,T0,T1,T2] :
( ~ greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1))
& greater(sigma,zero)
& greater(age(X,T2),sigma)
& smaller_or_equal(age(X,T1),sigma)
& age(X,T0) = zero
& ~ has_endowment(X)
& organization(X) ),
inference(fof_nnf,[status(thm)],[theorem_5_neg]) ).
fof(sk_theorem_5_neg,plain,
( ~ greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK1))
& greater(sigma,zero)
& greater(age(sK0,sK3),sigma)
& smaller_or_equal(age(sK0,sK1),sigma)
& age(sK0,sK2) = zero
& ~ has_endowment(sK0)
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1,sK3]),skolemize(X,sK0),skolemize(T0,sK2),skolemize(T1,sK1),skolemize(T2,sK3)],[nnf_14]) ).
cnf(c_18,negated_conjecture,
smaller_or_equal(age(sK0,sK1),sigma),
inference(split_conjunct,[status(thm)],[sk_theorem_5_neg]) ).
cnf(c_19,plain,
( greater(B,A)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_22,negated_conjecture,
( sigma = age(sK0,sK1)
| smaller(age(sK0,sK1),sigma) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_26,plain,
( greater(hazard_of_mortality(A,B),hazard_of_mortality(A,C))
| ~ greater(capability(A,C),capability(A,B))
| has_immunity(A,C)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_16]) ).
cnf(c_27,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_5_neg]) ).
cnf(c_28,plain,
( ~ dissimilar(A,B,C)
| greater(age(A,C),sigma)
| age(A,B) != zero
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_15]) ).
cnf(c_29,plain,
( dissimilar(A,B,C)
| ~ greater(age(A,C),sigma)
| age(A,B) != zero
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_15]) ).
cnf(c_30,plain,
( greater(capability(A,B),capability(A,C))
| is_aligned(A,C)
| ~ is_aligned(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_14]) ).
cnf(c_31,plain,
( is_aligned(A,B)
| age(A,B) != zero
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_13]) ).
cnf(c_33,plain,
( is_aligned(A,C)
| ~ is_aligned(A,B)
| ~ organization(A)
| dissimilar(A,B,C) ),
inference(clausify,[status(thm)],[definition_2]) ).
cnf(c_34,plain,
( organization(A)
| ~ dissimilar(A,B,C) ),
inference(clausify,[status(thm)],[definition_2]) ).
cnf(c_36,plain,
( ~ has_immunity(A,B)
| has_endowment(A)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_1]) ).
cnf(c_37,negated_conjecture,
( ~ has_immunity(sK0,A)
| has_endowment(sK0) ),
inference(resolve,[status(thm)],[c_36,c_27]) ).
cnf(c_42,plain,
( ~ dissimilar(A,D,E)
| greater(age(A,E),sigma)
| age(A,D) != zero
| ~ dissimilar(A,B,C) ),
inference(resolve,[status(thm)],[c_34,c_28]) ).
cnf(c_48,negated_conjecture,
( is_aligned(sK0,B)
| ~ is_aligned(sK0,A)
| dissimilar(sK0,A,B) ),
inference(resolve,[status(thm)],[c_33,c_27]) ).
cnf(c_50,negated_conjecture,
( is_aligned(sK0,A)
| age(sK0,A) != zero ),
inference(resolve,[status(thm)],[c_31,c_27]) ).
cnf(c_51,negated_conjecture,
( greater(capability(sK0,A),capability(sK0,B))
| is_aligned(sK0,B)
| ~ is_aligned(sK0,A) ),
inference(resolve,[status(thm)],[c_30,c_27]) ).
cnf(c_52,negated_conjecture,
( dissimilar(sK0,A,B)
| ~ greater(age(sK0,B),sigma)
| age(sK0,A) != zero ),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_54,negated_conjecture,
( greater(hazard_of_mortality(sK0,A),hazard_of_mortality(sK0,B))
| ~ greater(capability(sK0,B),capability(sK0,A))
| has_immunity(sK0,B)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_55,negated_conjecture,
( sigma = age(sK0,sK1)
| greater(sigma,age(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_56,negated_conjecture,
( age(sK0,sK1) = sigma
| greater(sigma,age(sK0,sK1)) ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_58,plain,
( ~ greater(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_strict]) ).
cnf(c_61,plain,
( ~ is_aligned(A,C)
| ~ is_aligned(A,B)
| ~ dissimilar(A,B,C) ),
inference(clausify,[status(thm)],[definition_2]) ).
cnf(c_62,negated_conjecture,
~ has_endowment(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_5_neg]) ).
cnf(c_63,negated_conjecture,
age(sK0,sK2) = zero,
inference(split_conjunct,[status(thm)],[sk_theorem_5_neg]) ).
cnf(c_64,negated_conjecture,
greater(age(sK0,sK3),sigma),
inference(split_conjunct,[status(thm)],[sk_theorem_5_neg]) ).
cnf(c_66,negated_conjecture,
~ greater(hazard_of_mortality(sK0,sK3),hazard_of_mortality(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_theorem_5_neg]) ).
cnf(c_68,plain,
( greater(age(A,C),sigma)
| age(A,B) != zero
| ~ dissimilar(A,B,C) ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_70,plain,
~ greater(A,A),
inference(factor,[status(thm)],[c_58]) ).
cnf(c_73,negated_conjecture,
~ has_immunity(sK0,A),
inference(resolve,[status(thm)],[c_62,c_37]) ).
cnf(c_213,negated_conjecture,
( greater(hazard_of_mortality(sK0,B),hazard_of_mortality(sK0,A))
| ~ greater(capability(sK0,A),capability(sK0,B))
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_73,c_54]) ).
cnf(c_74,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_73,c_213]) ).
cnf(c_76,plain,
( age(sK0,sK1) = sigma
| ~ greater(age(sK0,sK1),sigma) ),
inference(resolve,[status(thm)],[c_58,c_56]) ).
cnf(c_83,plain,
is_aligned(sK0,sK2),
inference(resolve,[status(thm)],[c_63,c_50]) ).
cnf(c_88,plain,
( dissimilar(sK0,A,sK3)
| age(sK0,A) != zero ),
inference(resolve,[status(thm)],[c_64,c_52]) ).
cnf(c_95,negated_conjecture,
~ greater(capability(sK0,sK1),capability(sK0,sK3)),
inference(resolve,[status(thm)],[c_74,c_66]) ).
cnf(c_107,plain,
( is_aligned(sK0,A)
| dissimilar(sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_83,c_48]) ).
cnf(c_214,plain,
( greater(age(sK0,A),sigma)
| age(sK0,sK2) != zero
| is_aligned(sK0,A) ),
inference(resolve,[status(thm)],[c_107,c_68]) ).
cnf(c_112,negated_conjecture,
( greater(age(sK0,A),sigma)
| is_aligned(sK0,A) ),
inference(resolve,[status(thm)],[c_63,c_214]) ).
cnf(c_145,plain,
dissimilar(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_88,c_63]) ).
cnf(c_215,plain,
( ~ is_aligned(sK0,sK3)
| ~ is_aligned(sK0,sK2) ),
inference(resolve,[status(thm)],[c_145,c_61]) ).
cnf(c_163,plain,
~ is_aligned(sK0,sK3),
inference(resolve,[status(thm)],[c_83,c_215]) ).
cnf(c_216,negated_conjecture,
( greater(capability(sK0,A),capability(sK0,sK3))
| ~ is_aligned(sK0,A) ),
inference(resolve,[status(thm)],[c_51,c_163]) ).
cnf(c_168,negated_conjecture,
~ is_aligned(sK0,sK1),
inference(resolve,[status(thm)],[c_216,c_95]) ).
cnf(c_170,plain,
greater(age(sK0,sK1),sigma),
inference(resolve,[status(thm)],[c_168,c_112]) ).
cnf(c_175,plain,
age(sK0,sK1) = sigma,
inference(resolve,[status(thm)],[c_170,c_76]) ).
cnf(c_217,plain,
greater(sigma,sigma),
inference(paramod,[status(thm)],[c_175,c_170]) ).
cnf(c_212,plain,
$false,
inference(resolve,[status(thm)],[c_70,c_217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT054+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 00:10:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 612920 was started by sandbox2 on n005,
% 0.08/0.36 % Sat Sep 26 00:10:02 2026
% 0.08/0.36 % 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).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 54.
% 0.14/0.40 % Level of proof is 9.
% 0.14/0.40 % Maximum clause weight is 30.000.
% 0.14/0.40 % Given clauses 81.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------