%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Thu Sep 24 01:25:29 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 9 unt; 9 def)
% Number of atoms : 260 ( 23 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 281 ( 100 ~; 103 |; 56 &)
% ( 16 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 77 ( 67 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( X = Y
| smaller(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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') ).
fof(f8,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') ).
fof(f9,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') ).
fof(f10,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)],[f9]) ).
fof(f11,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)],[f1]) ).
fof(f12,plain,
( ! [X,Y] :
( ( X != Y
& ~ smaller(X,Y) )
| smaller_or_equal(X,Y) )
& ! [X,Y] :
( X = Y
| smaller(X,Y)
| ~ smaller_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ smaller(X0,X1)
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( X0 != X1
| smaller_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,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)],[f2]) ).
fof(f17,plain,
( ! [X,Y] :
( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ! [X,Y] :
( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
( ! [X,Y] :
( ~ greater(Y,X)
| smaller(X,Y) )
& ! [X,Y] :
( greater(Y,X)
| ~ smaller(X,Y) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| smaller(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f31,plain,
! [X] :
( fragile_position(X)
<=> ! [T] :
( ( ~ positional_advantage(X,T)
| ~ greater(age(X,T),sigma) )
& ( positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),sigma) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f32,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)],[f31]) ).
fof(f33,plain,
( ! [X] :
( ? [T] :
( positional_advantage(X,T)
& greater(age(X,T),sigma) )
| ? [T] :
( ~ positional_advantage(X,T)
& smaller_or_equal(age(X,T),sigma) )
| fragile_position(X) )
& ! [X] :
( ( ! [T] :
( ~ positional_advantage(X,T)
| ~ greater(age(X,T),sigma) )
& ! [T] :
( positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),sigma) ) )
| ~ fragile_position(X) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [X] :
( ( positional_advantage(X,sK1_skl(X))
& greater(age(X,sK1_skl(X)),sigma) )
| ( ~ positional_advantage(X,sK0_skl(X))
& smaller_or_equal(age(X,sK0_skl(X)),sigma) )
| fragile_position(X) )
& ! [X] :
( ( ! [T] :
( ~ positional_advantage(X,T)
| ~ greater(age(X,T),sigma) )
& ! [T] :
( positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),sigma) ) )
| ~ fragile_position(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl(X)),skolemize(T,sK1_skl(X))],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),sigma)
| ~ fragile_position(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f41,plain,
! [X] :
( robust_position(X)
<=> ! [T] :
( ( positional_advantage(X,T)
| ~ greater(age(X,T),tau) )
& ( ~ positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),tau) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f42,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)],[f41]) ).
fof(f43,plain,
( ! [X] :
( ? [T] :
( ~ positional_advantage(X,T)
& greater(age(X,T),tau) )
| ? [T] :
( positional_advantage(X,T)
& smaller_or_equal(age(X,T),tau) )
| robust_position(X) )
& ! [X] :
( ( ! [T] :
( positional_advantage(X,T)
| ~ greater(age(X,T),tau) )
& ! [T] :
( ~ positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),tau) ) )
| ~ robust_position(X) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [X] :
( ( ~ positional_advantage(X,sK3_skl(X))
& greater(age(X,sK3_skl(X)),tau) )
| ( positional_advantage(X,sK2_skl(X))
& smaller_or_equal(age(X,sK2_skl(X)),tau) )
| robust_position(X) )
& ! [X] :
( ( ! [T] :
( positional_advantage(X,T)
| ~ greater(age(X,T),tau) )
& ! [T] :
( ~ positional_advantage(X,T)
| ~ smaller_or_equal(age(X,T),tau) ) )
| ~ robust_position(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(T,sK2_skl(X)),skolemize(T,sK3_skl(X))],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ positional_advantage(X0,X1)
| ~ smaller_or_equal(age(X0,X1),tau)
| ~ robust_position(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f51,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(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f52,plain,
( robust_position(sK4_skl)
& fragile_position(sK4_skl)
& greater_or_equal(tau,zero)
& greater_or_equal(sigma,zero)
& age(sK4_skl,sK5_skl) = zero
& organization(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(T0,sK5_skl)],[f51]) ).
fof(f54,plain,
age(sK4_skl,sK5_skl) = zero,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
fragile_position(sK4_skl),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f58,plain,
robust_position(sK4_skl),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f59,plain,
! [X0] : smaller_or_equal(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f61,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolution,[status(thm)],[f18,f56]) ).
fof(f62,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolution,[status(thm)],[f18,f55]) ).
fof(f64,definition,
( sQ0_spl
<=> greater(tau,zero) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ0_spl
| greater(tau,zero) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ1_spl
<=> tau = zero ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ1_spl
| tau = zero ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f64,f67]) ).
fof(f71,definition,
( sQ2_spl
<=> greater(sigma,zero) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ2_spl
| greater(sigma,zero) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
( sQ3_spl
<=> sigma = zero ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ3_spl
| sigma = zero ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f62,f71,f74]) ).
fof(f80,plain,
( positional_advantage(sK4_skl,sK5_skl)
| ~ smaller_or_equal(zero,sigma)
| ~ fragile_position(sK4_skl) ),
inference(paramodulation,[status(thm)],[f54,f35]) ).
fof(f81,definition,
( sQ4_spl
<=> fragile_position(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ4_spl
| ~ fragile_position(sK4_skl) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ5_spl
<=> smaller_or_equal(zero,sigma) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ5_spl
| ~ smaller_or_equal(zero,sigma) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ6_spl
<=> positional_advantage(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f80,f81,f84,f87]) ).
fof(f96,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f57]) ).
fof(f97,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f98,plain,
( ~ positional_advantage(sK4_skl,sK5_skl)
| ~ smaller_or_equal(zero,tau)
| ~ robust_position(sK4_skl) ),
inference(paramodulation,[status(thm)],[f54,f45]) ).
fof(f99,definition,
( sQ8_spl
<=> robust_position(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ8_spl
| ~ robust_position(sK4_skl) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ9_spl
<=> smaller_or_equal(zero,tau) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( sQ9_spl
| ~ smaller_or_equal(zero,tau) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f98,f99,f102,f87]) ).
fof(f111,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f58]) ).
fof(f112,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
( ~ sQ0_spl
| smaller(zero,tau) ),
inference(resolution,[status(thm)],[f24,f65]) ).
fof(f114,plain,
( ~ sQ2_spl
| smaller(zero,sigma) ),
inference(resolution,[status(thm)],[f24,f72]) ).
fof(f116,plain,
( ~ sQ0_spl
| smaller_or_equal(zero,tau) ),
inference(resolution,[status(thm)],[f113,f14]) ).
fof(f117,plain,
( ~ sQ0_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f104]) ).
fof(f118,plain,
( ~ sQ0_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ9_spl
| ~ sQ1_spl
| ~ smaller_or_equal(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f68,f104]) ).
fof(f124,plain,
( sQ9_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f59]) ).
fof(f125,plain,
( sQ9_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ2_spl
| smaller_or_equal(zero,sigma) ),
inference(resolution,[status(thm)],[f114,f14]) ).
fof(f128,plain,
( ~ sQ2_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f86]) ).
fof(f129,plain,
( ~ sQ2_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ smaller_or_equal(zero,zero) ),
inference(backward_demodulation,[status(thm)],[f75,f86]) ).
fof(f135,plain,
( sQ5_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f59]) ).
fof(f136,plain,
( sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
$false,
inference(sat_refutation,[status(thm)],[f70,f77,f90,f97,f105,f112,f118,f125,f129,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT058+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 01:25:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.058905 seconds
% 0.10/0.44 % CPU time: 0.146847 seconds
% 0.10/0.44 % Total memory used: 102.285 MB
% 0.10/0.44 % Net memory used: 102.014 MB
%------------------------------------------------------------------------------