%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT060+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:03:01 AM UTC 2026
% Result : Theorem 57.65s 9.64s
% Output : CNFRefutation 57.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 25 unt; 0 def)
% Number of atoms : 204 ( 43 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 184 ( 53 ~; 100 |; 20 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(meaning_postulate_greater_transitive,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('theBenchmark.p',meaning_postulate_greater_transitive) ).
fof(meaning_postulate_greater_comparable,axiom,
! [X,Y] :
( greater(X,Y)
| X = Y
| smaller(X,Y) ),
file('theBenchmark.p',meaning_postulate_greater_comparable) ).
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(assumption_3,conjecture,
! [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('theBenchmark.p',assumption_3) ).
fof(assumption_3_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( ~ has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ),
inference(assume_negation,[status(cth)],[assumption_3]) ).
cnf(c_12,plain,
( greater(B,A)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_14,plain,
( greater(A,B)
| B = A
| smaller(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_comparable]) ).
cnf(c_18,plain,
( hazard_of_mortality(A,B) = high
| positional_advantage(A,B)
| is_aligned(A,B)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_17]) ).
fof(nnf_8,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(fof_nnf,[status(thm)],[assumption_3_neg]) ).
fof(sk_assumption_3_neg,plain,
( ~ greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1))
& ~ has_immunity(sK0,sK2)
& has_immunity(sK0,sK1)
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(T0,sK1),skolemize(T,sK2)],[nnf_8]) ).
cnf(c_19,negated_conjecture,
organization(sK0),
inference(split_conjunct,[status(thm)],[sk_assumption_3_neg]) ).
cnf(c_20,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_21,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_22,plain,
( hazard_of_mortality(A,B) = low
| ~ positional_advantage(A,B)
| ~ is_aligned(A,B)
| has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_17]) ).
cnf(c_23,plain,
( hazard_of_mortality(A,B) = very_low
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(clausify,[status(thm)],[assumption_17]) ).
cnf(c_24,negated_conjecture,
( hazard_of_mortality(sK0,A) = very_low
| ~ has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_25,negated_conjecture,
( hazard_of_mortality(sK0,A) = low
| ~ positional_advantage(sK0,A)
| ~ is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_26,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_21,c_19]) ).
cnf(c_27,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_20,c_19]) ).
cnf(c_28,negated_conjecture,
( hazard_of_mortality(sK0,A) = high
| positional_advantage(sK0,A)
| is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_29,plain,
( greater(B,A)
| A = B
| greater(A,B) ),
inference(resolve,[status(thm)],[c_12,c_14]) ).
cnf(c_30,plain,
( ~ greater(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_strict]) ).
cnf(c_31,plain,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[meaning_postulate_greater_transitive]) ).
fof(assumption_18a,axiom,
greater(high,mod1),
file('theBenchmark.p',assumption_18a) ).
cnf(c_32,plain,
greater(high,mod1),
inference(clausify,[status(thm)],[assumption_18a]) ).
fof(assumption_18b,axiom,
greater(mod1,low),
file('theBenchmark.p',assumption_18b) ).
cnf(c_33,plain,
greater(mod1,low),
inference(clausify,[status(thm)],[assumption_18b]) ).
fof(assumption_18c,axiom,
greater(low,very_low),
file('theBenchmark.p',assumption_18c) ).
cnf(c_34,plain,
greater(low,very_low),
inference(clausify,[status(thm)],[assumption_18c]) ).
fof(assumption_18e,axiom,
greater(mod2,low),
file('theBenchmark.p',assumption_18e) ).
cnf(c_36,plain,
greater(mod2,low),
inference(clausify,[status(thm)],[assumption_18e]) ).
cnf(c_37,negated_conjecture,
has_immunity(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_assumption_3_neg]) ).
cnf(c_38,negated_conjecture,
~ has_immunity(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_assumption_3_neg]) ).
cnf(c_39,negated_conjecture,
~ greater(hazard_of_mortality(sK0,sK2),hazard_of_mortality(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_assumption_3_neg]) ).
cnf(c_40,plain,
~ greater(A,A),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_2015,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod2
| positional_advantage(sK0,A)
| has_immunity(sK0,A)
| hazard_of_mortality(sK0,A) = high
| positional_advantage(sK0,A)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_28,c_27]) ).
cnf(c_2016,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod2
| positional_advantage(sK0,A)
| hazard_of_mortality(sK0,A) = high
| positional_advantage(sK0,A)
| has_immunity(sK0,A) ),
inference(copy,[status(thm)],[c_2015]) ).
cnf(c_42,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod2
| hazard_of_mortality(sK0,A) = high
| positional_advantage(sK0,A)
| has_immunity(sK0,A) ),
inference(copy,[status(thm)],[c_2016]) ).
cnf(c_2017,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod1
| is_aligned(sK0,A)
| has_immunity(sK0,A)
| hazard_of_mortality(sK0,A) = high
| is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(resolve,[status(thm)],[c_28,c_26]) ).
cnf(c_2018,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod1
| is_aligned(sK0,A)
| hazard_of_mortality(sK0,A) = high
| is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(copy,[status(thm)],[c_2017]) ).
cnf(c_43,negated_conjecture,
( hazard_of_mortality(sK0,A) = mod1
| hazard_of_mortality(sK0,A) = high
| is_aligned(sK0,A)
| has_immunity(sK0,A) ),
inference(copy,[status(thm)],[c_2018]) ).
cnf(c_46,plain,
( hazard_of_mortality(sK0,B) = low
| ~ positional_advantage(A,B)
| ~ is_aligned(sK0,B)
| has_immunity(sK0,B)
| greater(A,sK0)
| greater(sK0,A) ),
inference(paramod,[status(thm)],[c_29,c_25]) ).
cnf(c_60,plain,
( greater(high,A)
| ~ greater(mod1,A) ),
inference(resolve,[status(thm)],[c_32,c_31]) ).
cnf(c_65,plain,
( greater(mod1,A)
| ~ greater(low,A) ),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_69,plain,
( greater(A,very_low)
| ~ greater(A,low) ),
inference(resolve,[status(thm)],[c_34,c_31]) ).
cnf(c_72,plain,
( greater(A,very_low)
| greater(A,low)
| greater(low,A) ),
inference(paramod,[status(thm)],[c_29,c_34]) ).
cnf(c_84,plain,
hazard_of_mortality(sK0,sK1) = very_low,
inference(resolve,[status(thm)],[c_37,c_24]) ).
cnf(c_87,negated_conjecture,
~ greater(hazard_of_mortality(sK0,sK2),very_low),
inference(paramod,[status(thm)],[c_84,c_39]) ).
cnf(c_143,plain,
greater(mod1,very_low),
inference(resolve,[status(thm)],[c_65,c_34]) ).
cnf(c_146,plain,
greater(high,very_low),
inference(resolve,[status(thm)],[c_143,c_60]) ).
cnf(c_155,plain,
greater(mod2,very_low),
inference(resolve,[status(thm)],[c_69,c_36]) ).
cnf(c_167,negated_conjecture,
~ greater(hazard_of_mortality(sK0,sK2),low),
inference(resolve,[status(thm)],[c_69,c_87]) ).
cnf(c_2019,plain,
( ~ greater(high,very_low)
| hazard_of_mortality(sK0,sK2) = mod2
| positional_advantage(sK0,sK2)
| has_immunity(sK0,sK2) ),
inference(paramod,[status(thm)],[c_42,c_87]) ).
cnf(c_2020,negated_conjecture,
( ~ greater(high,very_low)
| hazard_of_mortality(sK0,sK2) = mod2
| positional_advantage(sK0,sK2) ),
inference(resolve,[status(thm)],[c_38,c_2019]) ).
cnf(c_176,negated_conjecture,
( hazard_of_mortality(sK0,sK2) = mod2
| positional_advantage(sK0,sK2) ),
inference(resolve,[status(thm)],[c_146,c_2020]) ).
cnf(c_2021,plain,
( ~ greater(high,very_low)
| hazard_of_mortality(sK0,sK2) = mod1
| is_aligned(sK0,sK2)
| has_immunity(sK0,sK2) ),
inference(paramod,[status(thm)],[c_43,c_87]) ).
cnf(c_2022,negated_conjecture,
( ~ greater(high,very_low)
| hazard_of_mortality(sK0,sK2) = mod1
| is_aligned(sK0,sK2) ),
inference(resolve,[status(thm)],[c_38,c_2021]) ).
cnf(c_178,negated_conjecture,
( hazard_of_mortality(sK0,sK2) = mod1
| is_aligned(sK0,sK2) ),
inference(resolve,[status(thm)],[c_146,c_2022]) ).
cnf(c_2023,plain,
( greater(hazard_of_mortality(sK0,sK2),very_low)
| greater(low,hazard_of_mortality(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_72,c_167]) ).
cnf(c_535,negated_conjecture,
greater(low,hazard_of_mortality(sK0,sK2)),
inference(resolve,[status(thm)],[c_87,c_2023]) ).
cnf(c_2024,plain,
( ~ greater(mod2,very_low)
| positional_advantage(sK0,sK2) ),
inference(paramod,[status(thm)],[c_176,c_87]) ).
cnf(c_1774,plain,
positional_advantage(sK0,sK2),
inference(resolve,[status(thm)],[c_155,c_2024]) ).
cnf(c_2025,plain,
( hazard_of_mortality(sK0,sK2) = low
| ~ is_aligned(sK0,sK2)
| has_immunity(sK0,sK2)
| greater(sK0,sK0)
| greater(sK0,sK0) ),
inference(resolve,[status(thm)],[c_1774,c_46]) ).
cnf(c_2026,plain,
( hazard_of_mortality(sK0,sK2) = low
| ~ is_aligned(sK0,sK2)
| has_immunity(sK0,sK2)
| greater(sK0,sK0) ),
inference(copy,[status(thm)],[c_2025]) ).
cnf(c_2027,plain,
( hazard_of_mortality(sK0,sK2) = low
| ~ is_aligned(sK0,sK2)
| has_immunity(sK0,sK2) ),
inference(resolve,[status(thm)],[c_40,c_2026]) ).
cnf(c_1778,negated_conjecture,
( hazard_of_mortality(sK0,sK2) = low
| ~ is_aligned(sK0,sK2) ),
inference(resolve,[status(thm)],[c_38,c_2027]) ).
cnf(c_2028,plain,
( ~ greater(mod1,very_low)
| is_aligned(sK0,sK2) ),
inference(paramod,[status(thm)],[c_178,c_87]) ).
cnf(c_2001,plain,
is_aligned(sK0,sK2),
inference(resolve,[status(thm)],[c_143,c_2028]) ).
cnf(c_2004,negated_conjecture,
hazard_of_mortality(sK0,sK2) = low,
inference(resolve,[status(thm)],[c_2001,c_1778]) ).
cnf(c_2029,negated_conjecture,
greater(low,low),
inference(paramod,[status(thm)],[c_2004,c_535]) ).
cnf(c_2014,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_40,c_2029]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT060+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.96 % Computer : n008.cluster.edu
% 0.10/0.96 % Model : x86_64 x86_64
% 0.10/0.96 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.96 % Memory : 8046.5625MB
% 0.10/0.96 % OS : Linux 6.8.0-71-generic
% 0.10/0.96 % CPULimit : 300
% 0.10/0.96 % WCLimit : 300
% 0.10/0.96 % DateTime : Sat Sep 26 00:11:26 UTC 2026
% 0.10/0.96 % CPUTime :
% 0.10/0.96 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.96 % Process 2240335 was started by sandbox on n008,
% 0.10/0.96 % Sat Sep 26 00:11:26 2026
% 0.10/0.96 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.97
% 0.10/0.97 % From the command line: assign(max_seconds, 300).
% 57.65/9.64
% 57.65/9.64 % SZS status Theorem for theBenchmark
% 57.65/9.64
% 57.65/9.64 % Proof 1 at 0.46 (+ 0.19) seconds.
% 57.65/9.64 % Length of proof is 51.
% 57.65/9.64 % Level of proof is 9.
% 57.65/9.64 % Maximum clause weight is 24.000.
% 57.65/9.64 % Given clauses 168.
% 57.65/9.64
% 57.65/9.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------