%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT058+1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 : Tue Sep 8 06:16:12 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 23 unt; 0 def)
% Number of atoms : 299 ( 66 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 319 ( 126 ~; 120 |; 51 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 51 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(definition_smaller_or_equal,axiom,
! [X,Y] :
( smaller_or_equal(X,Y)
<=> ( smaller(X,Y)
| X = Y ) ) ).
fof(definition_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( greater(X,Y)
| X = Y ) ) ).
fof(definition_smaller,axiom,
! [X,Y] :
( smaller(X,Y)
<=> greater(Y,X) ) ).
fof(definition_3,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) ) ) ) ).
fof(definition_4,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) ) ) ) ).
fof(lemma_10,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) ) ) ).
fof(subgoal_0,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(strip,[],[lemma_10]) ).
fof(negate_0_0,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(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] :
( ~ robust_position(X)
<=> ( ? [T] :
( ~ positional_advantage(X,T)
& greater(age(X,T),tau) )
| ? [T] :
( positional_advantage(X,T)
& smaller_or_equal(age(X,T),tau) ) ) ),
inference(canonicalize,[],[definition_4]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ robust_position(X)
<=> ( ? [T] :
( ~ positional_advantage(X,T)
& greater(age(X,T),tau) )
| ? [T] :
( positional_advantage(X,T)
& smaller_or_equal(age(X,T),tau) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [T,X] :
( ( ~ greater(age(X,T),tau)
| ~ robust_position(X)
| positional_advantage(X,T) )
& ( ~ positional_advantage(X,T)
| ~ robust_position(X)
| ~ smaller_or_equal(age(X,T),tau) )
& ( ~ positional_advantage(X,skolemFOFtoCNF_T_2(X))
| positional_advantage(X,skolemFOFtoCNF_T_3(X))
| robust_position(X) )
& ( ~ positional_advantage(X,skolemFOFtoCNF_T_2(X))
| robust_position(X)
| smaller_or_equal(age(X,skolemFOFtoCNF_T_3(X)),tau) )
& ( greater(age(X,skolemFOFtoCNF_T_2(X)),tau)
| positional_advantage(X,skolemFOFtoCNF_T_3(X))
| robust_position(X) )
& ( greater(age(X,skolemFOFtoCNF_T_2(X)),tau)
| robust_position(X)
| smaller_or_equal(age(X,skolemFOFtoCNF_T_3(X)),tau) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [T,X] :
( ~ positional_advantage(X,T)
| ~ robust_position(X)
| ~ smaller_or_equal(age(X,T),tau) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X] :
( fragile_position(X)
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero)
& organization(X)
& robust_position(X)
& ? [T0] : age(X,T0) = zero ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( fragile_position(skolemFOFtoCNF_X)
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero)
& organization(skolemFOFtoCNF_X)
& robust_position(skolemFOFtoCNF_X)
& ? [T0] : age(skolemFOFtoCNF_X,T0) = zero ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [T0] : age(skolemFOFtoCNF_X,T0) = zero,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) = zero,
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
robust_position(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ fragile_position(X)
<=> ( ? [T] :
( ~ positional_advantage(X,T)
& smaller_or_equal(age(X,T),sigma) )
| ? [T] :
( greater(age(X,T),sigma)
& positional_advantage(X,T) ) ) ),
inference(canonicalize,[],[definition_3]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ fragile_position(X)
<=> ( ? [T] :
( ~ positional_advantage(X,T)
& smaller_or_equal(age(X,T),sigma) )
| ? [T] :
( greater(age(X,T),sigma)
& positional_advantage(X,T) ) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [T,X] :
( ( ~ fragile_position(X)
| ~ greater(age(X,T),sigma)
| ~ positional_advantage(X,T) )
& ( ~ fragile_position(X)
| ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) )
& ( ~ positional_advantage(X,skolemFOFtoCNF_T(X))
| fragile_position(X)
| greater(age(X,skolemFOFtoCNF_T_1(X)),sigma) )
& ( ~ positional_advantage(X,skolemFOFtoCNF_T(X))
| fragile_position(X)
| positional_advantage(X,skolemFOFtoCNF_T_1(X)) )
& ( fragile_position(X)
| greater(age(X,skolemFOFtoCNF_T_1(X)),sigma)
| smaller_or_equal(age(X,skolemFOFtoCNF_T(X)),sigma) )
& ( fragile_position(X)
| positional_advantage(X,skolemFOFtoCNF_T_1(X))
| smaller_or_equal(age(X,skolemFOFtoCNF_T(X)),sigma) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [T,X] :
( ~ fragile_position(X)
| ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
fragile_position(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ smaller_or_equal(X,Y)
<=> ( X != Y
& ~ smaller(X,Y) ) ),
inference(canonicalize,[],[definition_smaller_or_equal]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ smaller_or_equal(X,Y)
<=> ( X != Y
& ~ smaller(X,Y) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ( X != Y
| smaller_or_equal(X,Y) )
& ( ~ smaller(X,Y)
| smaller_or_equal(X,Y) )
& ( ~ smaller_or_equal(X,Y)
| X = Y
| smaller(X,Y) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ smaller(X,Y)
| smaller_or_equal(X,Y) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ greater(Y,X)
<=> ~ smaller(X,Y) ),
inference(canonicalize,[],[definition_smaller]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ greater(Y,X)
<=> ~ smaller(X,Y) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ( ~ greater(Y,X)
| smaller(X,Y) )
& ( ~ smaller(X,Y)
| greater(Y,X) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ greater(Y,X)
| smaller(X,Y) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
greater_or_equal(sigma,zero),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
<=> ( X != Y
& ~ greater(X,Y) ) ),
inference(canonicalize,[],[definition_greater_or_equal]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
<=> ( X != Y
& ~ greater(X,Y) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ( X != Y
| greater_or_equal(X,Y) )
& ( ~ greater(X,Y)
| greater_or_equal(X,Y) )
& ( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
greater_or_equal(tau,zero),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( X != Y
| smaller_or_equal(X,Y) ),
inference(conjunct,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
( ~ positional_advantage(X,T)
| ~ robust_position(X)
| ~ smaller_or_equal(age(X,T),tau) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| ~ robust_position(skolemFOFtoCNF_X)
| ~ smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),tau) ),
inference(subst,[],[refute_0_0:[bind(T,$fot(skolemFOFtoCNF_T0)),bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) = zero,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) != zero
| ~ smaller_or_equal(zero,tau)
| smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),tau) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),tau) ),[0],$fot(zero)]]) ).
cnf(refute_0_4,plain,
( ~ smaller_or_equal(zero,tau)
| smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),tau) ),
inference(resolve,[$cnf( $equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),zero) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| ~ robust_position(skolemFOFtoCNF_X)
| ~ smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),tau) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
robust_position(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| ~ smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( robust_position(skolemFOFtoCNF_X) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ fragile_position(X)
| ~ smaller_or_equal(age(X,T),sigma)
| positional_advantage(X,T) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ fragile_position(skolemFOFtoCNF_X)
| ~ smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),sigma)
| positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) ),
inference(subst,[],[refute_0_8:[bind(T,$fot(skolemFOFtoCNF_T0)),bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_10,plain,
( age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) != zero
| ~ smaller_or_equal(zero,sigma)
| smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),sigma) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),sigma) ),[0],$fot(zero)]]) ).
cnf(refute_0_11,plain,
( ~ smaller_or_equal(zero,sigma)
| smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),sigma) ),
inference(resolve,[$cnf( $equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),zero) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ fragile_position(skolemFOFtoCNF_X)
| ~ smaller_or_equal(zero,sigma)
| positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) ),
inference(resolve,[$cnf( smaller_or_equal(age(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),sigma) )],[refute_0_11,refute_0_9]) ).
cnf(refute_0_13,plain,
fragile_position(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( ~ smaller_or_equal(zero,sigma)
| positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) ),
inference(resolve,[$cnf( fragile_position(skolemFOFtoCNF_X) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
( ~ smaller(X,Y)
| smaller_or_equal(X,Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( ~ smaller(zero,sigma)
| smaller_or_equal(zero,sigma) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(zero)),bind(Y,$fot(sigma))]]) ).
cnf(refute_0_17,plain,
( ~ greater(Y,X)
| smaller(X,Y) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_18,plain,
( ~ greater(sigma,zero)
| smaller(zero,sigma) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(zero)),bind(Y,$fot(sigma))]]) ).
cnf(refute_0_19,plain,
greater_or_equal(sigma,zero),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_20,plain,
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_21,plain,
( ~ greater_or_equal(sigma,zero)
| sigma = zero
| greater(sigma,zero) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(sigma)),bind(Y,$fot(zero))]]) ).
cnf(refute_0_22,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolve,[$cnf( greater_or_equal(sigma,zero) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( sigma = zero
| smaller(zero,sigma) ),
inference(resolve,[$cnf( greater(sigma,zero) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( sigma = zero
| smaller_or_equal(zero,sigma) ),
inference(resolve,[$cnf( smaller(zero,sigma) )],[refute_0_23,refute_0_16]) ).
cnf(refute_0_25,plain,
( sigma = zero
| positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) ),
inference(resolve,[$cnf( smaller_or_equal(zero,sigma) )],[refute_0_24,refute_0_14]) ).
cnf(refute_0_26,plain,
( ~ smaller(zero,tau)
| smaller_or_equal(zero,tau) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(zero)),bind(Y,$fot(tau))]]) ).
cnf(refute_0_27,plain,
( ~ greater(tau,zero)
| smaller(zero,tau) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(zero)),bind(Y,$fot(tau))]]) ).
cnf(refute_0_28,plain,
greater_or_equal(tau,zero),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_29,plain,
( ~ greater_or_equal(tau,zero)
| tau = zero
| greater(tau,zero) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(tau)),bind(Y,$fot(zero))]]) ).
cnf(refute_0_30,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolve,[$cnf( greater_or_equal(tau,zero) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( tau = zero
| smaller(zero,tau) ),
inference(resolve,[$cnf( greater(tau,zero) )],[refute_0_30,refute_0_27]) ).
cnf(refute_0_32,plain,
( tau = zero
| smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( smaller(zero,tau) )],[refute_0_31,refute_0_26]) ).
cnf(refute_0_33,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| tau = zero ),
inference(resolve,[$cnf( smaller_or_equal(zero,tau) )],[refute_0_32,refute_0_7]) ).
cnf(refute_0_34,plain,
( sigma = zero
| tau = zero ),
inference(resolve,[$cnf( positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_36,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_37,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( tau != zero
| zero = tau ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(tau)),bind(Y0,$fot(zero))]]) ).
cnf(refute_0_39,plain,
( sigma = zero
| zero = tau ),
inference(resolve,[$cnf( $equal(tau,zero) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
( zero != tau
| ~ smaller_or_equal(tau,tau)
| smaller_or_equal(zero,tau) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(zero,tau) ),[0],$fot(tau)]]) ).
cnf(refute_0_41,plain,
( ~ smaller_or_equal(tau,tau)
| sigma = zero
| smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( $equal(zero,tau) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| ~ smaller_or_equal(tau,tau)
| sigma = zero ),
inference(resolve,[$cnf( smaller_or_equal(zero,tau) )],[refute_0_41,refute_0_7]) ).
cnf(refute_0_43,plain,
( X != Y
| smaller_or_equal(X,Y) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_44,plain,
( Y != Y
| smaller_or_equal(Y,Y) ),
inference(subst,[],[refute_0_43:[bind(X,$fot(Y))]]) ).
cnf(refute_0_45,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_46,plain,
smaller_or_equal(Y,Y),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
smaller_or_equal(tau,tau),
inference(subst,[],[refute_0_46:[bind(Y,$fot(tau))]]) ).
cnf(refute_0_48,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| sigma = zero ),
inference(resolve,[$cnf( smaller_or_equal(tau,tau) )],[refute_0_47,refute_0_42]) ).
cnf(refute_0_49,plain,
sigma = zero,
inference(resolve,[$cnf( positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) )],[refute_0_25,refute_0_48]) ).
cnf(refute_0_50,plain,
( sigma != zero
| zero = sigma ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(sigma)),bind(Y0,$fot(zero))]]) ).
cnf(refute_0_51,plain,
zero = sigma,
inference(resolve,[$cnf( $equal(sigma,zero) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( zero != sigma
| ~ smaller_or_equal(sigma,tau)
| smaller_or_equal(zero,tau) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(zero,tau) ),[0],$fot(sigma)]]) ).
cnf(refute_0_53,plain,
( ~ smaller_or_equal(sigma,tau)
| smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( $equal(zero,sigma) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| ~ smaller_or_equal(sigma,tau) ),
inference(resolve,[$cnf( smaller_or_equal(zero,tau) )],[refute_0_53,refute_0_7]) ).
cnf(refute_0_55,plain,
( zero != sigma
| ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(zero,sigma) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(zero,sigma) ),[0],$fot(sigma)]]) ).
cnf(refute_0_56,plain,
( ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(zero,sigma) ),
inference(resolve,[$cnf( $equal(zero,sigma) )],[refute_0_51,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ smaller_or_equal(sigma,sigma)
| positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) ),
inference(resolve,[$cnf( smaller_or_equal(zero,sigma) )],[refute_0_56,refute_0_14]) ).
cnf(refute_0_58,plain,
smaller_or_equal(sigma,sigma),
inference(subst,[],[refute_0_46:[bind(Y,$fot(sigma))]]) ).
cnf(refute_0_59,plain,
positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0),
inference(resolve,[$cnf( smaller_or_equal(sigma,sigma) )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
~ smaller_or_equal(sigma,tau),
inference(resolve,[$cnf( positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) )],[refute_0_59,refute_0_54]) ).
cnf(refute_0_61,plain,
( tau != zero
| zero != sigma
| tau = sigma ),
introduced(tautology,[equality,[$cnf( ~ $equal(tau,sigma) ),[0],$fot(zero)]]) ).
cnf(refute_0_62,plain,
( tau != zero
| tau = sigma ),
inference(resolve,[$cnf( $equal(zero,sigma) )],[refute_0_51,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0)
| tau = sigma ),
inference(resolve,[$cnf( $equal(tau,zero) )],[refute_0_33,refute_0_62]) ).
cnf(refute_0_64,plain,
tau = sigma,
inference(resolve,[$cnf( positional_advantage(skolemFOFtoCNF_X,skolemFOFtoCNF_T0) )],[refute_0_59,refute_0_63]) ).
cnf(refute_0_65,plain,
( tau != sigma
| ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(sigma,tau) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(sigma,tau) ),[1],$fot(sigma)]]) ).
cnf(refute_0_66,plain,
( ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(sigma,tau) ),
inference(resolve,[$cnf( $equal(tau,sigma) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
~ smaller_or_equal(sigma,sigma),
inference(resolve,[$cnf( smaller_or_equal(sigma,tau) )],[refute_0_66,refute_0_60]) ).
cnf(refute_0_68,plain,
$false,
inference(resolve,[$cnf( smaller_or_equal(sigma,sigma) )],[refute_0_58,refute_0_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT058+1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 7 13:31:30 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------