%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT062+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 08:03:02 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 32 unt; 0 def)
% Number of atoms : 225 ( 49 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 233 ( 91 ~; 73 |; 49 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 92 ( 9 sgn 26 !; 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(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_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(definition_4,axiom,
! [X] :
( robust_position(X)
<=> ! [T] :
( ( greater(age(X,T),tau)
=> positional_advantage(X,T) )
& ( smaller_or_equal(age(X,T),tau)
=> ~ positional_advantage(X,T) ) ) ),
file('theBenchmark.p',definition_4) ).
fof(assumption_17,axiom,
! [X,T] :
( organization(X)
=> ( ( ~ has_immunity(X,T)
=> ( ( ( ~ positional_advantage(X,T)
& ~ is_aligned(X,T) )
=> hazard_of_mortality(X,T) = high )
& ( ( ~ positional_advantage(X,T)
& is_aligned(X,T) )
=> hazard_of_mortality(X,T) = mod2 )
& ( ( positional_advantage(X,T)
& ~ is_aligned(X,T) )
=> hazard_of_mortality(X,T) = mod1 )
& ( ( positional_advantage(X,T)
& is_aligned(X,T) )
=> hazard_of_mortality(X,T) = low ) ) )
& ( has_immunity(X,T)
=> hazard_of_mortality(X,T) = very_low ) ) ),
file('theBenchmark.p',assumption_17) ).
fof(theorem_8,conjecture,
! [X,T0,T1,T2] :
( ( greater(age(X,T2),sigma)
& smaller_or_equal(age(X,T1),sigma)
& sigma = tau
& greater(tau,zero)
& greater(sigma,zero)
& age(X,T0) = zero
& ~ has_endowment(X)
& robust_position(X)
& organization(X) )
=> ( hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0)
& smaller(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ) ),
file('theBenchmark.p',theorem_8) ).
fof(theorem_8_neg,negated_conjecture,
~ ! [X,T0,T1,T2] :
( ( greater(age(X,T2),sigma)
& smaller_or_equal(age(X,T1),sigma)
& sigma = tau
& greater(tau,zero)
& greater(sigma,zero)
& age(X,T0) = zero
& ~ has_endowment(X)
& robust_position(X)
& organization(X) )
=> ( hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0)
& smaller(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) ) ),
inference(assume_negation,[status(cth)],[theorem_8]) ).
fof(nnf_13,plain,
? [X,T0,T1,T2] :
( ( hazard_of_mortality(X,T1) != hazard_of_mortality(X,T0)
| ~ smaller(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1)) )
& greater(age(X,T2),sigma)
& smaller_or_equal(age(X,T1),sigma)
& tau = sigma
& greater(tau,zero)
& greater(sigma,zero)
& age(X,T0) = zero
& ~ has_endowment(X)
& robust_position(X)
& organization(X) ),
inference(fof_nnf,[status(thm)],[theorem_8_neg]) ).
fof(sk_theorem_8_neg,plain,
( ( hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK3)
| ~ smaller(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)) )
& greater(age(sK0,sK1),sigma)
& smaller_or_equal(age(sK0,sK2),sigma)
& tau = sigma
& greater(tau,zero)
& greater(sigma,zero)
& age(sK0,sK3) = zero
& ~ has_endowment(sK0)
& robust_position(sK0)
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK2,sK1]),skolemize(X,sK0),skolemize(T0,sK3),skolemize(T1,sK2),skolemize(T2,sK1)],[nnf_13]) ).
cnf(c_18,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_19,plain,
( hazard_of_mortality(A,B) = mod2
| positional_advantage(A,B)
| ~ is_aligned(A,B)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_17]) ).
cnf(c_20,plain,
( hazard_of_mortality(A,B) = mod1
| ~ positional_advantage(A,B)
| is_aligned(A,B)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_17]) ).
cnf(c_23,plain,
( ~ dissimilar(A,B,C)
| greater(age(A,C),sigma)
| age(A,B) != zero
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_15]) ).
cnf(c_24,plain,
( dissimilar(A,B,C)
| ~ greater(age(A,C),sigma)
| age(A,B) != zero
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_15]) ).
cnf(c_25,plain,
( is_aligned(A,B)
| age(A,B) != zero
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_13]) ).
cnf(c_27,plain,
( is_aligned(A,C)
| ~ is_aligned(A,B)
| ~ organization(A)
| dissimilar(A,B,C) ),
inference(clausify,[status(thm)],[definition_2]) ).
cnf(c_28,plain,
( organization(A)
| ~ dissimilar(A,B,C) ),
inference(clausify,[status(thm)],[definition_2]) ).
cnf(c_29,plain,
( ~ has_immunity(A,B)
| has_endowment(A)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_1]) ).
cnf(c_31,plain,
( positional_advantage(A,B)
| ~ greater(age(A,B),tau)
| ~ robust_position(A) ),
inference(clausify,[status(thm)],[definition_4]) ).
cnf(c_32,plain,
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
inference(clausify,[status(thm)],[definition_4]) ).
cnf(c_35,negated_conjecture,
robust_position(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_36,negated_conjecture,
( ~ positional_advantage(sK0,A)
| ~ smaller_or_equal(age(sK0,A),tau) ),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_37,negated_conjecture,
( positional_advantage(sK0,A)
| ~ greater(age(sK0,A),tau) ),
inference(resolve,[status(thm)],[c_35,c_31]) ).
cnf(c_44,negated_conjecture,
( hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK3)
| ~ smaller(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_45,negated_conjecture,
greater(age(sK0,sK1),sigma),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_46,negated_conjecture,
smaller_or_equal(age(sK0,sK2),sigma),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_47,negated_conjecture,
tau = sigma,
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_48,negated_conjecture,
sigma = tau,
inference(copy,[status(thm)],[c_47]) ).
cnf(c_49,negated_conjecture,
greater(tau,zero),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_51,negated_conjecture,
age(sK0,sK3) = zero,
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
cnf(c_52,negated_conjecture,
~ has_endowment(sK0),
inference(split_conjunct,[status(thm)],[sk_theorem_8_neg]) ).
fof(assumption_19,axiom,
greater(mod2,mod1),
file('theBenchmark.p',assumption_19) ).
cnf(c_53,plain,
greater(mod2,mod1),
inference(clausify,[status(thm)],[assumption_19]) ).
cnf(c_54,plain,
( ~ is_aligned(A,C)
| ~ is_aligned(A,B)
| ~ dissimilar(A,B,C) ),
inference(clausify,[status(thm)],[definition_2]) ).
cnf(c_59,plain,
( ~ greater(B,A)
| smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_62,plain,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_65,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod2
| positional_advantage(sK0,A)
| ~ is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_66,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod1
| ~ positional_advantage(sK0,A)
| is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_71,negated_conjecture,
( dissimilar(sK0,A,B)
| ~ greater(age(sK0,B),sigma)
| age(sK0,A) != zero ),
inference(resolve,[status(thm)],[c_24,c_18]) ).
cnf(c_72,negated_conjecture,
( dissimilar(sK0,A,B)
| ~ greater(age(sK0,B),tau)
| age(sK0,A) != zero ),
inference(paramod,[status(thm)],[c_48,c_71]) ).
cnf(c_73,negated_conjecture,
( is_aligned(sK0,A)
| age(sK0,A) != zero ),
inference(resolve,[status(thm)],[c_25,c_18]) ).
cnf(c_75,negated_conjecture,
( is_aligned(sK0,B)
| ~ is_aligned(sK0,A)
| dissimilar(sK0,A,B) ),
inference(resolve,[status(thm)],[c_27,c_18]) ).
cnf(c_81,plain,
( ~ dissimilar(A,D,E)
| greater(age(A,E),sigma)
| age(A,D) != zero
| ~ dissimilar(A,B,C) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_82,plain,
( ~ dissimilar(A,D,E)
| greater(age(A,E),tau)
| age(A,D) != zero
| ~ dissimilar(A,B,C) ),
inference(paramod,[status(thm)],[c_48,c_81]) ).
cnf(c_89,negated_conjecture,
( ~ has_immunity(sK0,A)
| has_endowment(sK0) ),
inference(resolve,[status(thm)],[c_29,c_18]) ).
cnf(c_90,negated_conjecture,
~ has_immunity(sK0,A),
inference(resolve,[status(thm)],[c_52,c_89]) ).
cnf(c_91,negated_conjecture,
smaller_or_equal(age(sK0,sK2),tau),
inference(paramod,[status(thm)],[c_48,c_46]) ).
cnf(c_92,negated_conjecture,
greater(age(sK0,sK1),tau),
inference(paramod,[status(thm)],[c_48,c_45]) ).
cnf(c_96,plain,
( greater(age(A,C),tau)
| age(A,B) != zero
| ~ dissimilar(A,B,C) ),
inference(factor,[status(thm)],[c_82]) ).
cnf(c_98,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod1
| ~ positional_advantage(sK0,A)
| is_aligned(sK0,A) ),
inference(resolve,[status(thm)],[c_90,c_66]) ).
cnf(c_99,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod2
| positional_advantage(sK0,A)
| ~ is_aligned(sK0,A) ),
inference(resolve,[status(thm)],[c_90,c_65]) ).
cnf(c_101,plain,
( ~ positional_advantage(sK0,sK3)
| ~ smaller_or_equal(zero,tau) ),
inference(paramod,[status(thm)],[c_51,c_36]) ).
cnf(c_111,plain,
smaller(zero,tau),
inference(resolve,[status(thm)],[c_59,c_49]) ).
cnf(c_117,plain,
is_aligned(sK0,sK3),
inference(resolve,[status(thm)],[c_73,c_51]) ).
cnf(c_122,plain,
~ positional_advantage(sK0,sK2),
inference(resolve,[status(thm)],[c_91,c_36]) ).
cnf(c_123,plain,
( dissimilar(sK0,A,sK1)
| age(sK0,A) != zero ),
inference(resolve,[status(thm)],[c_92,c_72]) ).
cnf(c_130,plain,
positional_advantage(sK0,sK1),
inference(resolve,[status(thm)],[c_92,c_37]) ).
cnf(c_137,negated_conjecture,
~ greater(age(sK0,sK2),tau),
inference(resolve,[status(thm)],[c_37,c_122]) ).
cnf(c_139,plain,
smaller_or_equal(zero,tau),
inference(resolve,[status(thm)],[c_111,c_62]) ).
cnf(c_140,plain,
~ positional_advantage(sK0,sK3),
inference(resolve,[status(thm)],[c_139,c_101]) ).
cnf(c_204,negated_conjecture,
( hazard_of_mortality(sK0,sK3) = mod2
| positional_advantage(sK0,sK3) ),
inference(resolve,[status(thm)],[c_117,c_99]) ).
cnf(c_141,negated_conjecture,
hazard_of_mortality(sK0,sK3) = mod2,
inference(resolve,[status(thm)],[c_140,c_204]) ).
cnf(c_142,plain,
( is_aligned(sK0,A)
| dissimilar(sK0,sK3,A) ),
inference(resolve,[status(thm)],[c_117,c_75]) ).
cnf(c_146,negated_conjecture,
( hazard_of_mortality(sK0,sK2) != mod2
| ~ smaller(hazard_of_mortality(sK0,sK1),hazard_of_mortality(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_141,c_44]) ).
cnf(c_147,plain,
( hazard_of_mortality(sK0,sK1) = mod1
| is_aligned(sK0,sK1) ),
inference(resolve,[status(thm)],[c_130,c_98]) ).
cnf(c_205,negated_conjecture,
( greater(age(sK0,A),tau)
| ~ dissimilar(sK0,sK3,A) ),
inference(resolve,[status(thm)],[c_96,c_51]) ).
cnf(c_153,negated_conjecture,
~ dissimilar(sK0,sK3,sK2),
inference(resolve,[status(thm)],[c_205,c_137]) ).
cnf(c_176,plain,
is_aligned(sK0,sK2),
inference(resolve,[status(thm)],[c_142,c_153]) ).
cnf(c_206,negated_conjecture,
( hazard_of_mortality(sK0,sK2) = mod2
| positional_advantage(sK0,sK2) ),
inference(resolve,[status(thm)],[c_176,c_99]) ).
cnf(c_185,negated_conjecture,
hazard_of_mortality(sK0,sK2) = mod2,
inference(resolve,[status(thm)],[c_122,c_206]) ).
cnf(c_207,negated_conjecture,
( hazard_of_mortality(sK0,sK2) != mod2
| ~ smaller(hazard_of_mortality(sK0,sK1),mod2) ),
inference(paramod,[status(thm)],[c_185,c_146]) ).
cnf(c_208,negated_conjecture,
( mod2 != mod2
| ~ smaller(hazard_of_mortality(sK0,sK1),mod2) ),
inference(paramod,[status(thm)],[c_185,c_207]) ).
cnf(c_190,negated_conjecture,
~ smaller(hazard_of_mortality(sK0,sK1),mod2),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_192,negated_conjecture,
~ greater(mod2,hazard_of_mortality(sK0,sK1)),
inference(resolve,[status(thm)],[c_59,c_190]) ).
cnf(c_198,plain,
dissimilar(sK0,sK3,sK1),
inference(resolve,[status(thm)],[c_123,c_51]) ).
cnf(c_209,plain,
( ~ is_aligned(sK0,sK1)
| ~ is_aligned(sK0,sK3) ),
inference(resolve,[status(thm)],[c_198,c_54]) ).
cnf(c_201,plain,
~ is_aligned(sK0,sK1),
inference(resolve,[status(thm)],[c_117,c_209]) ).
cnf(c_202,plain,
hazard_of_mortality(sK0,sK1) = mod1,
inference(resolve,[status(thm)],[c_201,c_147]) ).
cnf(c_210,negated_conjecture,
~ greater(mod2,mod1),
inference(paramod,[status(thm)],[c_202,c_192]) ).
cnf(c_203,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_53,c_210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT062+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.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 : Sat Sep 26 00:12:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1482248 was started by sandbox2 on n003,
% 0.09/0.36 % Sat Sep 26 00:12:23 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 72.
% 0.14/0.41 % Level of proof is 11.
% 0.14/0.41 % Maximum clause weight is 18.000.
% 0.14/0.41 % Given clauses 107.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------