TSTP Solution File: MGT058+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : MGT058+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:28:51 EDT 2024
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 88 ( 10 unt; 0 def)
% Number of atoms : 287 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 305 ( 106 ~; 119 |; 57 &)
% ( 17 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 97 ( 87 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( smaller(X,Y)
| X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( greater(X,Y)
| 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(f4,axiom,
! [X,Y] :
~ ( greater(X,Y)
& greater(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( smaller(X,Y)
| X = Y
| greater(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( fragile_position(X)
<=> ! [T] :
( ( smaller_or_equal(age(X,T),sigma)
=> positional_advantage(X,T) )
& ( greater(age(X,T),sigma)
=> ~ positional_advantage(X,T) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( robust_position(X)
<=> ! [T] :
( ( smaller_or_equal(age(X,T),tau)
=> ~ positional_advantage(X,T) )
& ( greater(age(X,T),tau)
=> positional_advantage(X,T) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [X] :
( ( organization(X)
& ? [T0] : age(X,T0) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X)
& robust_position(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [X] :
( ( organization(X)
& ? [T0] : age(X,T0) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X)
& robust_position(X) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X,Y] :
( ( ~ smaller_or_equal(X,Y)
| smaller(X,Y)
| X = Y )
& ( smaller_or_equal(X,Y)
| ( ~ smaller(X,Y)
& X != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f12,plain,
( ! [X,Y] :
( ~ smaller_or_equal(X,Y)
| smaller(X,Y)
| X = Y )
& ! [X,Y] :
( smaller_or_equal(X,Y)
| ( ~ smaller(X,Y)
& X != Y ) ) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| ~ smaller(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( smaller_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f16,plain,
! [X,Y] :
( ( ~ greater_or_equal(X,Y)
| greater(X,Y)
| X = Y )
& ( greater_or_equal(X,Y)
| ( ~ greater(X,Y)
& X != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
( ! [X,Y] :
( ~ greater_or_equal(X,Y)
| greater(X,Y)
| X = Y )
& ! [X,Y] :
( greater_or_equal(X,Y)
| ( ~ greater(X,Y)
& X != Y ) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [X,Y] :
( ( ~ smaller(X,Y)
| greater(Y,X) )
& ( smaller(X,Y)
| ~ greater(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
( ! [X,Y] :
( ~ smaller(X,Y)
| greater(Y,X) )
& ! [X,Y] :
( smaller(X,Y)
| ~ greater(Y,X) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ smaller(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( smaller(X0,X1)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X,Y] :
( ~ greater(X,Y)
| ~ greater(Y,X) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f30,plain,
! [X0,X1] :
( smaller(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f31,plain,
! [X] :
( fragile_position(X)
<=> ! [T] :
( ( ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) )
& ( ~ greater(age(X,T),sigma)
| ~ positional_advantage(X,T) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f32,plain,
! [X] :
( ( ~ fragile_position(X)
| ! [T] :
( ( ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) )
& ( ~ greater(age(X,T),sigma)
| ~ positional_advantage(X,T) ) ) )
& ( fragile_position(X)
| ? [T] :
( ( smaller_or_equal(age(X,T),sigma)
& ~ positional_advantage(X,T) )
| ( greater(age(X,T),sigma)
& positional_advantage(X,T) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
( ! [X] :
( ~ fragile_position(X)
| ( ! [T] :
( ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) )
& ! [T] :
( ~ greater(age(X,T),sigma)
| ~ positional_advantage(X,T) ) ) )
& ! [X] :
( fragile_position(X)
| ? [T] :
( smaller_or_equal(age(X,T),sigma)
& ~ positional_advantage(X,T) )
| ? [T] :
( greater(age(X,T),sigma)
& positional_advantage(X,T) ) ) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f34,plain,
( ! [X] :
( ~ fragile_position(X)
| ( ! [T] :
( ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) )
& ! [T] :
( ~ greater(age(X,T),sigma)
| ~ positional_advantage(X,T) ) ) )
& ! [X] :
( fragile_position(X)
| ( smaller_or_equal(age(X,sk0_0(X)),sigma)
& ~ positional_advantage(X,sk0_0(X)) )
| ( greater(age(X,sk0_1(X)),sigma)
& positional_advantage(X,sk0_1(X)) ) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ fragile_position(X0)
| ~ smaller_or_equal(age(X0,X1),sigma)
| positional_advantage(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f41,plain,
! [X] :
( robust_position(X)
<=> ! [T] :
( ( ~ smaller_or_equal(age(X,T),tau)
| ~ positional_advantage(X,T) )
& ( ~ greater(age(X,T),tau)
| positional_advantage(X,T) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f42,plain,
! [X] :
( ( ~ robust_position(X)
| ! [T] :
( ( ~ smaller_or_equal(age(X,T),tau)
| ~ positional_advantage(X,T) )
& ( ~ greater(age(X,T),tau)
| positional_advantage(X,T) ) ) )
& ( robust_position(X)
| ? [T] :
( ( smaller_or_equal(age(X,T),tau)
& positional_advantage(X,T) )
| ( greater(age(X,T),tau)
& ~ positional_advantage(X,T) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
( ! [X] :
( ~ robust_position(X)
| ( ! [T] :
( ~ smaller_or_equal(age(X,T),tau)
| ~ positional_advantage(X,T) )
& ! [T] :
( ~ greater(age(X,T),tau)
| positional_advantage(X,T) ) ) )
& ! [X] :
( robust_position(X)
| ? [T] :
( smaller_or_equal(age(X,T),tau)
& positional_advantage(X,T) )
| ? [T] :
( greater(age(X,T),tau)
& ~ positional_advantage(X,T) ) ) ),
inference(miniscoping,[status(esa)],[f42]) ).
fof(f44,plain,
( ! [X] :
( ~ robust_position(X)
| ( ! [T] :
( ~ smaller_or_equal(age(X,T),tau)
| ~ positional_advantage(X,T) )
& ! [T] :
( ~ greater(age(X,T),tau)
| positional_advantage(X,T) ) ) )
& ! [X] :
( robust_position(X)
| ( smaller_or_equal(age(X,sk0_2(X)),tau)
& positional_advantage(X,sk0_2(X)) )
| ( greater(age(X,sk0_3(X)),tau)
& ~ positional_advantage(X,sk0_3(X)) ) ) ),
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ robust_position(X0)
| ~ smaller_or_equal(age(X0,X1),tau)
| ~ positional_advantage(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f51,plain,
? [X] :
( organization(X)
& ? [T0] : age(X,T0) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero)
& fragile_position(X)
& robust_position(X) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f52,plain,
( organization(sk0_4)
& age(sk0_4,sk0_5) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero)
& fragile_position(sk0_4)
& robust_position(sk0_4) ),
inference(skolemization,[status(esa)],[f51]) ).
fof(f54,plain,
age(sk0_4,sk0_5) = zero,
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f55,plain,
greater_or_equal(sigma,zero),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f56,plain,
greater_or_equal(tau,zero),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f57,plain,
fragile_position(sk0_4),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f58,plain,
robust_position(sk0_4),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f59,plain,
! [X0] : smaller_or_equal(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f15]) ).
fof(f61,plain,
( spl0_0
<=> greater(tau,zero) ),
introduced(split_symbol_definition) ).
fof(f62,plain,
( greater(tau,zero)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( spl0_1
<=> tau = zero ),
introduced(split_symbol_definition) ).
fof(f65,plain,
( tau = zero
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( greater(tau,zero)
| tau = zero ),
inference(resolution,[status(thm)],[f18,f56]) ).
fof(f68,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f67,f61,f64]) ).
fof(f69,plain,
( spl0_2
<=> greater(sigma,zero) ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( greater(sigma,zero)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( spl0_3
<=> sigma = zero ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( sigma = zero
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( greater(sigma,zero)
| sigma = zero ),
inference(resolution,[status(thm)],[f18,f55]) ).
fof(f76,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f75,f69,f72]) ).
fof(f77,plain,
( spl0_4
<=> fragile_position(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( ~ fragile_position(sk0_4)
| spl0_4 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( spl0_5
<=> smaller_or_equal(zero,sigma) ),
introduced(split_symbol_definition) ).
fof(f83,plain,
( spl0_6
<=> positional_advantage(sk0_4,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f86,plain,
( ~ fragile_position(sk0_4)
| ~ smaller_or_equal(zero,sigma)
| positional_advantage(sk0_4,sk0_5) ),
inference(paramodulation,[status(thm)],[f54,f35]) ).
fof(f87,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f86,f77,f80,f83]) ).
fof(f93,plain,
( spl0_8
<=> robust_position(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f95,plain,
( ~ robust_position(sk0_4)
| spl0_8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( spl0_9
<=> smaller_or_equal(zero,tau) ),
introduced(split_symbol_definition) ).
fof(f98,plain,
( ~ smaller_or_equal(zero,tau)
| spl0_9 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( ~ robust_position(sk0_4)
| ~ smaller_or_equal(zero,tau)
| ~ positional_advantage(sk0_4,sk0_5) ),
inference(paramodulation,[status(thm)],[f54,f45]) ).
fof(f100,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f99,f93,f96,f83]) ).
fof(f101,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f58]) ).
fof(f102,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f111,plain,
! [X0,X1] :
( smaller(X0,X1)
| X0 = X1
| smaller(X1,X0) ),
inference(resolution,[status(thm)],[f30,f24]) ).
fof(f114,plain,
! [X0,X1] :
( X0 = X1
| smaller(X1,X0)
| smaller_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f111,f14]) ).
fof(f119,plain,
! [X0,X1] :
( X0 = X1
| smaller_or_equal(X0,X1)
| greater(X0,X1) ),
inference(resolution,[status(thm)],[f114,f23]) ).
fof(f123,plain,
! [X0,X1] :
( X0 = X1
| smaller_or_equal(X0,X1)
| ~ greater(X1,X0) ),
inference(resolution,[status(thm)],[f119,f26]) ).
fof(f157,plain,
( zero = sigma
| smaller_or_equal(zero,sigma)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f70,f123]) ).
fof(f158,plain,
( spl0_3
| spl0_5
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f157,f72,f80,f69]) ).
fof(f162,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f57]) ).
fof(f163,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
( age(sk0_4,sk0_5) = sigma
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f73,f54]) ).
fof(f189,plain,
( spl0_14
<=> smaller_or_equal(sigma,sigma) ),
introduced(split_symbol_definition) ).
fof(f191,plain,
( ~ smaller_or_equal(sigma,sigma)
| spl0_14 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f204,plain,
( ~ fragile_position(sk0_4)
| ~ smaller_or_equal(sigma,sigma)
| positional_advantage(sk0_4,sk0_5)
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f164,f35]) ).
fof(f205,plain,
( ~ spl0_4
| ~ spl0_14
| spl0_6
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f204,f77,f189,f83,f72]) ).
fof(f206,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f59]) ).
fof(f207,plain,
spl0_14,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f219,plain,
( ~ smaller_or_equal(tau,tau)
| ~ spl0_1
| spl0_9 ),
inference(backward_demodulation,[status(thm)],[f65,f98]) ).
fof(f220,plain,
( $false
| ~ spl0_1
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f59]) ).
fof(f221,plain,
( ~ spl0_1
| spl0_9 ),
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f245,plain,
( zero = tau
| smaller_or_equal(zero,tau)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f62,f123]) ).
fof(f246,plain,
( spl0_1
| spl0_9
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f245,f64,f96,f61]) ).
fof(f250,plain,
$false,
inference(sat_refutation,[status(thm)],[f68,f76,f87,f100,f102,f158,f163,f205,f207,f221,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : MGT058+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:34:55 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.6.0
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.33 % Elapsed time: 0.016931 seconds
% 0.15/0.33 % CPU time: 0.037479 seconds
% 0.15/0.33 % Total memory used: 15.044 MB
% 0.15/0.33 % Net memory used: 14.977 MB
%------------------------------------------------------------------------------