%------------------------------------------------------------------------------
% 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 : Unsatisfiable 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 17 unt; 0 def)
% Number of atoms : 90 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 36 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(definition_smaller_or_equal_2,axiom,
! [VAR_0,VAR_1] :
( smaller_or_equal(VAR_0,VAR_1)
| ~ smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_smaller_or_equal_2) ).
cnf(c_1,plain,
( smaller_or_equal(A,B)
| ~ smaller(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_or_equal_2]) ).
fof(definition_smaller_8,axiom,
! [VAR_0,VAR_1] :
( smaller(VAR_1,VAR_0)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_smaller_8) ).
cnf(c_4,plain,
( smaller(B,A)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[definition_smaller_8]) ).
fof(definition_greater_or_equal_4,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| greater(VAR_0,VAR_1)
| ~ greater_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',definition_greater_or_equal_4) ).
cnf(c_6,plain,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[definition_greater_or_equal_4]) ).
fof(lemma_10_44,axiom,
greater_or_equal(sigma,zero),
file('theBenchmark.p',lemma_10_44) ).
cnf(c_9,plain,
greater_or_equal(sigma,zero),
inference(clausify,[status(thm)],[lemma_10_44]) ).
fof(lemma_10_45,axiom,
greater_or_equal(tau,zero),
file('theBenchmark.p',lemma_10_45) ).
cnf(c_10,plain,
greater_or_equal(tau,zero),
inference(clausify,[status(thm)],[lemma_10_45]) ).
fof(definition_3_30,axiom,
! [VAR_0,VAR_1] :
( positional_advantage(VAR_0,VAR_1)
| ~ smaller_or_equal(age(VAR_0,VAR_1),sigma)
| ~ fragile_position(VAR_0) ),
file('theBenchmark.p',definition_3_30) ).
cnf(c_13,plain,
( positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),sigma)
| ~ fragile_position(A) ),
inference(clausify,[status(thm)],[definition_3_30]) ).
fof(lemma_10_46,axiom,
fragile_position(sk3),
file('theBenchmark.p',lemma_10_46) ).
cnf(c_17,plain,
fragile_position(sk3),
inference(clausify,[status(thm)],[lemma_10_46]) ).
fof(lemma_10_47,axiom,
robust_position(sk3),
file('theBenchmark.p',lemma_10_47) ).
cnf(c_23,plain,
robust_position(sk3),
inference(clausify,[status(thm)],[lemma_10_47]) ).
fof(definition_4_36,axiom,
! [VAR_0,VAR_1] :
( ~ positional_advantage(VAR_0,VAR_1)
| ~ smaller_or_equal(age(VAR_0,VAR_1),tau)
| ~ robust_position(VAR_0) ),
file('theBenchmark.p',definition_4_36) ).
cnf(c_24,plain,
( ~ positional_advantage(A,B)
| ~ smaller_or_equal(age(A,B),tau)
| ~ robust_position(A) ),
inference(clausify,[status(thm)],[definition_4_36]) ).
cnf(c_25,plain,
( positional_advantage(sk3,A)
| ~ smaller_or_equal(age(sk3,A),sigma) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_35,plain,
( smaller_or_equal(B,A)
| ~ greater(A,B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(lemma_10_43,axiom,
age(sk3,sk4) = zero,
file('theBenchmark.p',lemma_10_43) ).
cnf(c_37,plain,
age(sk3,sk4) = zero,
inference(clausify,[status(thm)],[lemma_10_43]) ).
fof(definition_smaller_or_equal_3,axiom,
! [VAR_0,VAR_1] :
( smaller_or_equal(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',definition_smaller_or_equal_3) ).
cnf(c_40,plain,
( smaller_or_equal(A,B)
| A != B ),
inference(clausify,[status(thm)],[definition_smaller_or_equal_3]) ).
cnf(c_41,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_42,plain,
( zero = sigma
| greater(sigma,zero) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolve,[status(thm)],[c_6,c_10]) ).
cnf(c_44,plain,
( zero = tau
| greater(tau,zero) ),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_52,plain,
( ~ positional_advantage(sk3,A)
| ~ smaller_or_equal(age(sk3,A),tau) ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_59,plain,
( positional_advantage(sk3,sk4)
| ~ smaller_or_equal(zero,sigma) ),
inference(paramod,[status(thm)],[c_37,c_25]) ).
cnf(c_65,plain,
smaller_or_equal(A,A),
inference(xxres,[status(thm)],[c_40]) ).
cnf(c_69,plain,
( smaller_or_equal(zero,sigma)
| zero = sigma ),
inference(resolve,[status(thm)],[c_42,c_35]) ).
cnf(c_73,plain,
( smaller_or_equal(zero,tau)
| zero = tau ),
inference(resolve,[status(thm)],[c_44,c_35]) ).
cnf(c_87,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(zero,tau) ),
inference(paramod,[status(thm)],[c_37,c_52]) ).
cnf(c_90,plain,
( positional_advantage(sk3,sk4)
| zero = sigma ),
inference(resolve,[status(thm)],[c_69,c_59]) ).
cnf(c_92,plain,
( ~ positional_advantage(sk3,sk4)
| zero = tau ),
inference(resolve,[status(thm)],[c_73,c_87]) ).
cnf(c_93,plain,
( zero = sigma
| zero = tau ),
inference(resolve,[status(thm)],[c_92,c_90]) ).
cnf(c_116,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(tau,tau)
| zero = sigma ),
inference(paramod,[status(thm)],[c_93,c_87]) ).
cnf(c_97,plain,
( ~ positional_advantage(sk3,sk4)
| zero = sigma ),
inference(resolve,[status(thm)],[c_65,c_116]) ).
cnf(c_117,plain,
( zero = sigma
| zero = sigma ),
inference(resolve,[status(thm)],[c_97,c_90]) ).
cnf(c_102,plain,
zero = sigma,
inference(copy,[status(thm)],[c_117]) ).
cnf(c_118,plain,
( ~ positional_advantage(sk3,sk4)
| sigma = tau ),
inference(paramod,[status(thm)],[c_102,c_92]) ).
cnf(c_103,plain,
( ~ positional_advantage(sk3,sk4)
| tau = sigma ),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_104,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(sigma,tau) ),
inference(paramod,[status(thm)],[c_102,c_87]) ).
cnf(c_119,plain,
( positional_advantage(sk3,sk4)
| ~ smaller_or_equal(sigma,sigma) ),
inference(paramod,[status(thm)],[c_102,c_59]) ).
cnf(c_110,plain,
positional_advantage(sk3,sk4),
inference(resolve,[status(thm)],[c_65,c_119]) ).
cnf(c_113,plain,
~ smaller_or_equal(sigma,tau),
inference(resolve,[status(thm)],[c_110,c_104]) ).
cnf(c_114,plain,
tau = sigma,
inference(resolve,[status(thm)],[c_110,c_103]) ).
cnf(c_120,plain,
~ smaller_or_equal(sigma,sigma),
inference(paramod,[status(thm)],[c_114,c_113]) ).
cnf(c_115,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_120]) ).
%------------------------------------------------------------------------------
%----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
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 00:10:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 3404380 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 00:10:22 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.03/0.31
% 0.03/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.31
% 0.03/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.31 % Length of proof is 34.
% 0.03/0.31 % Level of proof is 10.
% 0.03/0.31 % Maximum clause weight is 8.000.
% 0.03/0.31 % Given clauses 46.
% 0.03/0.31
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------