%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 : Fri Sep 25 02:11:52 PM UTC 2026
% Result : Theorem 24.34s 18.95s
% Output : Proof 24.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 12 unt; 0 def)
% Number of atoms : 183 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 190 ( 65 ~; 68 |; 46 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
fof(f8_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(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,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(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( robust_position(sk2)
& fragile_position(sk2)
& greater_or_equal(tau,zero)
& greater_or_equal(sigma,zero)
& age(sk2,sk3) = zero
& organization(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f8_nnf]) ).
cnf(c24,plain,
age(sk2,sk3) = zero,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f7,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('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_4) ).
fof(f7_nnf,plain,
! [X] :
( ( ? [T] :
( ( ~ positional_advantage(X,T)
& greater(age(X,T),tau) )
| ( positional_advantage(X,T)
& smaller_or_equal(age(X,T),tau) ) )
| robust_position(X) )
& ( ! [T] :
( ( positional_advantage(X,T)
| ~ greater(age(X,T),tau) )
& ( ~ positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),tau) ) )
| ~ robust_position(X) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,T] :
( ( ( ~ positional_advantage(X,sk1(X))
& greater(age(X,sk1(X)),tau) )
| ( positional_advantage(X,sk1(X))
& smaller_or_equal(age(X,sk1(X)),tau) )
| robust_position(X) )
& ( ( ( positional_advantage(X,T)
| ~ greater(age(X,T),tau) )
& ( ~ positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),tau) ) )
| ~ robust_position(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c17,plain,
( ~ positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),tau)
| ~ robust_position(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c28,plain,
robust_position(sk2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p96,plain,
( ~ positional_advantage(sk2,X0)
| ~ smaller_or_equal(age(sk2,X0),tau) ),
inference(resolution,[status(thm)],[c17,c28]) ).
cnf(p97,plain,
( ~ positional_advantage(sk2,sk3)
| ~ smaller_or_equal(zero,tau) ),
inference(superposition,[status(thm)],[c24,p96]) ).
fof(f2,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller) ).
fof(f2_nnf,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c7,plain,
( ~ greater(X1,X0)
| smaller(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f1,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_greater_or_equal) ).
fof(f1_nnf,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c26,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p31,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolution,[status(thm)],[c3,c26]) ).
cnf(p34,plain,
( tau = zero
| smaller(zero,tau) ),
inference(resolution,[status(thm)],[c7,p31]) ).
fof(f0,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( X = Y
| smaller(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller_or_equal) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ( X != Y
& ~ smaller(X,Y) )
| smaller_or_equal(X,Y) )
& ( X = Y
| smaller(X,Y)
| ~ smaller_or_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( X != Y
& ~ smaller(X,Y) )
| smaller_or_equal(X,Y) )
& ( X = Y
| smaller(X,Y)
| ~ smaller_or_equal(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( ~ smaller(X0,X1)
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p39,plain,
( smaller_or_equal(zero,tau)
| tau = zero ),
inference(resolution,[status(thm)],[p34,c1]) ).
cnf(p99,plain,
( tau = zero
| ~ positional_advantage(sk2,sk3) ),
inference(resolution,[status(thm)],[p97,p39]) ).
fof(f6,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('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_3) ).
fof(f6_nnf,plain,
! [X] :
( ( ? [T] :
( ( positional_advantage(X,T)
& greater(age(X,T),sigma) )
| ( ~ positional_advantage(X,T)
& smaller_or_equal(age(X,T),sigma) ) )
| fragile_position(X) )
& ( ! [T] :
( ( ~ positional_advantage(X,T)
| ~ greater(age(X,T),sigma) )
& ( positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),sigma) ) )
| ~ fragile_position(X) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,T] :
( ( ( positional_advantage(X,sk0(X))
& greater(age(X,sk0(X)),sigma) )
| ( ~ positional_advantage(X,sk0(X))
& smaller_or_equal(age(X,sk0(X)),sigma) )
| fragile_position(X) )
& ( ( ( ~ positional_advantage(X,T)
| ~ greater(age(X,T),sigma) )
& ( positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),sigma) ) )
| ~ fragile_position(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c11,plain,
( positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),sigma)
| ~ fragile_position(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c27,plain,
fragile_position(sk2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p58,plain,
( positional_advantage(sk2,X0)
| ~ smaller_or_equal(age(sk2,X0),sigma) ),
inference(resolution,[status(thm)],[c11,c27]) ).
cnf(p59,plain,
( positional_advantage(sk2,sk3)
| ~ smaller_or_equal(zero,sigma) ),
inference(superposition,[status(thm)],[c24,p58]) ).
cnf(c25,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p30,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolution,[status(thm)],[c3,c25]) ).
cnf(p33,plain,
( sigma = zero
| smaller(zero,sigma) ),
inference(resolution,[status(thm)],[c7,p30]) ).
cnf(p35,plain,
( smaller_or_equal(zero,sigma)
| sigma = zero ),
inference(resolution,[status(thm)],[p33,c1]) ).
cnf(p60,plain,
( sigma = zero
| positional_advantage(sk2,sk3) ),
inference(resolution,[status(thm)],[p59,p35]) ).
cnf(p101,plain,
( sigma = zero
| tau = zero ),
inference(resolution,[status(thm)],[p99,p60]) ).
cnf(p103,plain,
( zero = tau
| sigma = zero ),
inference(superposition,[status(thm)],[p101,c24]) ).
cnf(c2,plain,
( X0 != X1
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p121,plain,
( smaller_or_equal(zero,tau)
| sigma = zero ),
inference(resolution,[status(thm)],[p103,c2]) ).
cnf(p123,plain,
( ~ positional_advantage(sk2,sk3)
| sigma = zero ),
inference(resolution,[status(thm)],[p121,p97]) ).
cnf(p128,plain,
( sigma = zero
| sigma = zero ),
inference(resolution,[status(thm)],[p123,p60]) ).
cnf(p129,plain,
sigma = zero,
inference(factoring,[status(thm)],[p128]) ).
cnf(p131,plain,
zero = sigma,
inference(superposition,[status(thm)],[p129,c24]) ).
cnf(p158,plain,
( tau = sigma
| ~ positional_advantage(sk2,sk3) ),
inference(demodulation,[status(thm)],[p131,p99]) ).
cnf(p143,plain,
( positional_advantage(sk2,sk3)
| ~ smaller_or_equal(sigma,sigma) ),
inference(demodulation,[status(thm)],[p131,p59]) ).
cnf(p29,plain,
smaller_or_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p163,plain,
positional_advantage(sk2,sk3),
inference(resolution,[status(thm)],[p143,p29]) ).
cnf(p164,plain,
tau = sigma,
inference(resolution,[status(thm)],[p158,p163]) ).
cnf(p156,plain,
( ~ positional_advantage(sk2,sk3)
| ~ smaller_or_equal(sigma,tau) ),
inference(demodulation,[status(thm)],[p131,p97]) ).
cnf(p176,plain,
( ~ positional_advantage(sk2,sk3)
| ~ smaller_or_equal(sigma,sigma) ),
inference(demodulation,[status(thm)],[p164,p156]) ).
cnf(p181,plain,
~ positional_advantage(sk2,sk3),
inference(resolution,[status(thm)],[p176,p29]) ).
cnf(p182,plain,
$false,
inference(resolution,[status(thm)],[p181,p163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/15.40 % Computer : n002.cluster.edu
% 0.11/15.40 % Model : x86_64 x86_64
% 0.11/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.40 % Memory : 8046.5625MB
% 0.11/15.40 % OS : Linux 6.8.0-71-generic
% 0.11/15.40 % CPULimit : 300
% 0.11/15.40 % WCLimit : 300
% 0.11/15.40 % DateTime : Thu Sep 24 01:19:11 UTC 2026
% 0.14/15.40 % CPUTime :
% 0.14/15.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.34/18.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.34/18.95 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------