%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT058+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 : n012.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 0.04s 0.32s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 108 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 32 ~; 31 |; 20 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 12 !; 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_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('theBenchmark.p',definition_greater_or_equal) ).
fof(definition_smaller,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('theBenchmark.p',definition_smaller) ).
fof(definition_3,axiom,
! [X] :
( fragile_position(X)
<=> ! [T] :
( ( greater(age(X,T),sigma)
=> ~ positional_advantage(X,T) )
& ( smaller_or_equal(age(X,T),sigma)
=> positional_advantage(X,T) ) ) ),
file('theBenchmark.p',definition_3) ).
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(lemma_10,conjecture,
! [X] :
( ( greater_or_equal(tau,zero)
& greater_or_equal(sigma,zero)
& ? [T0] : age(X,T0) = zero
& organization(X) )
=> ~ ( robust_position(X)
& fragile_position(X) ) ),
file('theBenchmark.p',lemma_10) ).
fof(lemma_10_neg,negated_conjecture,
~ ! [X] :
( ( greater_or_equal(tau,zero)
& greater_or_equal(sigma,zero)
& ? [T0] : age(X,T0) = zero
& organization(X) )
=> ~ ( robust_position(X)
& fragile_position(X) ) ),
inference(assume_negation,[status(cth)],[lemma_10]) ).
cnf(c_10,plain,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_13,plain,
( ~ greater(B,A)
| smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller]) ).
cnf(c_15,plain,
( B = A
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal]) ).
fof(nnf_9,plain,
? [X] :
( robust_position(X)
& fragile_position(X)
& greater_or_equal(tau,zero)
& greater_or_equal(sigma,zero)
& ? [T0] : age(X,T0) = zero
& organization(X) ),
inference(fof_nnf,[status(thm)],[lemma_10_neg]) ).
fof(sk_lemma_10_neg,plain,
( robust_position(sK0)
& fragile_position(sK0)
& greater_or_equal(tau,zero)
& greater_or_equal(sigma,zero)
& age(sK0,sK1) = zero
& organization(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(T0,sK1)],[nnf_9]) ).
cnf(c_18,negated_conjecture,
greater_or_equal(sigma,zero),
inference(split_conjunct,[status(thm)],[sk_lemma_10_neg]) ).
cnf(c_19,negated_conjecture,
greater_or_equal(tau,zero),
inference(split_conjunct,[status(thm)],[sk_lemma_10_neg]) ).
cnf(c_22,plain,
( positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),sigma)
| ~ fragile_position(A) ),
inference(clausify,[status(thm)],[definition_3]) ).
cnf(c_25,negated_conjecture,
fragile_position(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_10_neg]) ).
cnf(c_30,negated_conjecture,
robust_position(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_10_neg]) ).
cnf(c_31,plain,
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
inference(clausify,[status(thm)],[definition_4]) ).
cnf(c_32,negated_conjecture,
( positional_advantage(sK0,A)
| ~ smaller_or_equal(age(sK0,A),sigma) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_42,plain,
( smaller_or_equal(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_44,negated_conjecture,
age(sK0,sK1) = zero,
inference(split_conjunct,[status(thm)],[sk_lemma_10_neg]) ).
cnf(c_47,plain,
( B != A
| smaller_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal]) ).
cnf(c_48,negated_conjecture,
( zero = sigma
| greater(sigma,zero) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_49,negated_conjecture,
( zero = tau
| greater(tau,zero) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_57,negated_conjecture,
( ~ positional_advantage(sK0,A)
| ~ smaller_or_equal(age(sK0,A),tau) ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
cnf(c_69,plain,
( positional_advantage(sK0,sK1)
| ~ smaller_or_equal(zero,sigma) ),
inference(paramod,[status(thm)],[c_44,c_32]) ).
cnf(c_76,plain,
smaller_or_equal(A,A),
inference(xxres,[status(thm)],[c_47]) ).
cnf(c_80,plain,
( smaller_or_equal(zero,sigma)
| zero = sigma ),
inference(resolve,[status(thm)],[c_48,c_42]) ).
cnf(c_84,plain,
( smaller_or_equal(zero,tau)
| zero = tau ),
inference(resolve,[status(thm)],[c_49,c_42]) ).
cnf(c_100,plain,
( ~ positional_advantage(sK0,sK1)
| ~ smaller_or_equal(zero,tau) ),
inference(paramod,[status(thm)],[c_44,c_57]) ).
cnf(c_104,plain,
( positional_advantage(sK0,sK1)
| zero = sigma ),
inference(resolve,[status(thm)],[c_80,c_69]) ).
cnf(c_105,plain,
( ~ positional_advantage(sK0,sK1)
| zero = tau ),
inference(resolve,[status(thm)],[c_84,c_100]) ).
cnf(c_108,plain,
( ~ smaller_or_equal(zero,tau)
| zero = sigma ),
inference(resolve,[status(thm)],[c_104,c_100]) ).
cnf(c_109,plain,
( zero = sigma
| zero = tau ),
inference(resolve,[status(thm)],[c_105,c_104]) ).
cnf(c_131,plain,
( ~ smaller_or_equal(tau,tau)
| zero = sigma
| zero = sigma ),
inference(paramod,[status(thm)],[c_109,c_108]) ).
cnf(c_132,plain,
( ~ smaller_or_equal(tau,tau)
| zero = sigma ),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_117,plain,
zero = sigma,
inference(resolve,[status(thm)],[c_76,c_132]) ).
cnf(c_133,plain,
( ~ positional_advantage(sK0,sK1)
| sigma = tau ),
inference(paramod,[status(thm)],[c_117,c_105]) ).
cnf(c_118,plain,
( ~ positional_advantage(sK0,sK1)
| tau = sigma ),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_119,plain,
( ~ positional_advantage(sK0,sK1)
| ~ smaller_or_equal(sigma,tau) ),
inference(paramod,[status(thm)],[c_117,c_100]) ).
cnf(c_134,plain,
( positional_advantage(sK0,sK1)
| ~ smaller_or_equal(sigma,sigma) ),
inference(paramod,[status(thm)],[c_117,c_69]) ).
cnf(c_125,plain,
positional_advantage(sK0,sK1),
inference(resolve,[status(thm)],[c_76,c_134]) ).
cnf(c_128,plain,
~ smaller_or_equal(sigma,tau),
inference(resolve,[status(thm)],[c_125,c_119]) ).
cnf(c_129,plain,
tau = sigma,
inference(resolve,[status(thm)],[c_125,c_118]) ).
cnf(c_135,plain,
~ smaller_or_equal(sigma,sigma),
inference(paramod,[status(thm)],[c_129,c_128]) ).
cnf(c_130,plain,
$false,
inference(resolve,[status(thm)],[c_76,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 00:10:06 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.31 % Process 3403985 was started by sandbox2 on n012,
% 0.04/0.31 % Sat Sep 26 00:10:06 2026
% 0.04/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 0.04/0.32
% 0.04/0.32 % SZS status Theorem for theBenchmark
% 0.04/0.32
% 0.04/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/0.32 % Length of proof is 38.
% 0.04/0.32 % Level of proof is 9.
% 0.04/0.32 % Maximum clause weight is 18.000.
% 0.04/0.32 % Given clauses 46.
% 0.04/0.32
% 0.04/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------