%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT059+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 08:03:01 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 46 ( 16 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 44 ( 14 ~; 3 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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_2,conjecture,
! [X,T0,T] :
( ( has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> hazard_of_mortality(X,T0) = hazard_of_mortality(X,T) ),
file('theBenchmark.p',assumption_2) ).
fof(assumption_2_neg,negated_conjecture,
~ ! [X,T0,T] :
( ( has_immunity(X,T)
& has_immunity(X,T0)
& organization(X) )
=> hazard_of_mortality(X,T0) = hazard_of_mortality(X,T) ),
inference(assume_negation,[status(cth)],[assumption_2]) ).
fof(nnf_8,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(fof_nnf,[status(thm)],[assumption_2_neg]) ).
fof(sk_assumption_2_neg,plain,
( hazard_of_mortality(sK0,sK1) != hazard_of_mortality(sK0,sK2)
& 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_2_neg]) ).
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_32,negated_conjecture,
has_immunity(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_assumption_2_neg]) ).
cnf(c_33,negated_conjecture,
has_immunity(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_assumption_2_neg]) ).
cnf(c_34,negated_conjecture,
hazard_of_mortality(sK0,sK1) != hazard_of_mortality(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_assumption_2_neg]) ).
cnf(c_35,negated_conjecture,
hazard_of_mortality(sK0,sK2) != hazard_of_mortality(sK0,sK1),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_42,plain,
hazard_of_mortality(sK0,sK1) = very_low,
inference(resolve,[status(thm)],[c_32,c_24]) ).
cnf(c_43,negated_conjecture,
hazard_of_mortality(sK0,sK2) != very_low,
inference(paramod,[status(thm)],[c_42,c_35]) ).
cnf(c_45,negated_conjecture,
hazard_of_mortality(sK0,sK2) = very_low,
inference(resolve,[status(thm)],[c_33,c_24]) ).
cnf(c_44,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_43,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT059+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 00:10:18 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 613315 was started by sandbox2 on n005,
% 0.17/0.44 % Sat Sep 26 00:10:18 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.47
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47
% 0.17/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.47 % Length of proof is 12.
% 0.17/0.47 % Level of proof is 5.
% 0.17/0.47 % Maximum clause weight is 8.000.
% 0.17/0.47 % Given clauses 10.
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------