TSTP Solution File: MGT058-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT058-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 : 600s
% DateTime : Sun Jul 17 22:19:56 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of clauses : 81 ( 19 unt; 18 nHn; 78 RR)
% Number of literals : 166 ( 59 equ; 76 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_smaller_or_equal_2,axiom,
( ~ smaller(A,B)
| smaller_or_equal(A,B) ) ).
cnf(definition_smaller_or_equal_3,axiom,
( A != B
| smaller_or_equal(A,B) ) ).
cnf(definition_greater_or_equal_4,axiom,
( ~ greater_or_equal(A,B)
| greater(A,B)
| A = B ) ).
cnf(definition_smaller_8,axiom,
( ~ greater(A,B)
| smaller(B,A) ) ).
cnf(definition_3_30,axiom,
( ~ fragile_position(A)
| ~ smaller_or_equal(age(A,B),sigma)
| positional_advantage(A,B) ) ).
cnf(definition_4_36,axiom,
( ~ robust_position(A)
| ~ smaller_or_equal(age(A,B),tau)
| ~ positional_advantage(A,B) ) ).
cnf(lemma_10_43,negated_conjecture,
age(sk3,sk4) = zero ).
cnf(lemma_10_44,negated_conjecture,
greater_or_equal(sigma,zero) ).
cnf(lemma_10_45,negated_conjecture,
greater_or_equal(tau,zero) ).
cnf(lemma_10_46,negated_conjecture,
fragile_position(sk3) ).
cnf(lemma_10_47,negated_conjecture,
robust_position(sk3) ).
cnf(refute_0_0,plain,
( ~ fragile_position(sk3)
| ~ smaller_or_equal(age(sk3,sk4),sigma)
| positional_advantage(sk3,sk4) ),
inference(subst,[],[definition_3_30:[bind(A,$fot(sk3)),bind(B,$fot(sk4))]]) ).
cnf(refute_0_1,plain,
( ~ smaller(zero,tau)
| smaller_or_equal(zero,tau) ),
inference(subst,[],[definition_smaller_or_equal_2:[bind(A,$fot(zero)),bind(B,$fot(tau))]]) ).
cnf(refute_0_2,plain,
( ~ greater(tau,zero)
| smaller(zero,tau) ),
inference(subst,[],[definition_smaller_8:[bind(A,$fot(tau)),bind(B,$fot(zero))]]) ).
cnf(refute_0_3,plain,
( ~ greater_or_equal(tau,zero)
| tau = zero
| greater(tau,zero) ),
inference(subst,[],[definition_greater_or_equal_4:[bind(A,$fot(tau)),bind(B,$fot(zero))]]) ).
cnf(refute_0_4,plain,
( tau = zero
| greater(tau,zero) ),
inference(resolve,[$cnf( greater_or_equal(tau,zero) )],[lemma_10_45,refute_0_3]) ).
cnf(refute_0_5,plain,
( tau = zero
| smaller(zero,tau) ),
inference(resolve,[$cnf( greater(tau,zero) )],[refute_0_4,refute_0_2]) ).
cnf(refute_0_6,plain,
( tau = zero
| smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( smaller(zero,tau) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( ~ positional_advantage(sk3,sk4)
| ~ robust_position(sk3)
| ~ smaller_or_equal(age(sk3,sk4),tau) ),
inference(subst,[],[definition_4_36:[bind(A,$fot(sk3)),bind(B,$fot(sk4))]]) ).
cnf(refute_0_8,plain,
( age(sk3,sk4) != zero
| ~ smaller_or_equal(zero,tau)
| smaller_or_equal(age(sk3,sk4),tau) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(sk3,sk4),tau) ),[0],$fot(zero)]]) ).
cnf(refute_0_9,plain,
( ~ smaller_or_equal(zero,tau)
| smaller_or_equal(age(sk3,sk4),tau) ),
inference(resolve,[$cnf( $equal(age(sk3,sk4),zero) )],[lemma_10_43,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ positional_advantage(sk3,sk4)
| ~ robust_position(sk3)
| ~ smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk3,sk4),tau) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(zero,tau) ),
inference(resolve,[$cnf( robust_position(sk3) )],[lemma_10_47,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ positional_advantage(sk3,sk4)
| tau = zero ),
inference(resolve,[$cnf( smaller_or_equal(zero,tau) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( age(sk3,sk4) != zero
| ~ smaller_or_equal(zero,sigma)
| smaller_or_equal(age(sk3,sk4),sigma) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(sk3,sk4),sigma) ),[0],$fot(zero)]]) ).
cnf(refute_0_14,plain,
( ~ smaller_or_equal(zero,sigma)
| smaller_or_equal(age(sk3,sk4),sigma) ),
inference(resolve,[$cnf( $equal(age(sk3,sk4),zero) )],[lemma_10_43,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ fragile_position(sk3)
| ~ smaller_or_equal(zero,sigma)
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk3,sk4),sigma) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
( ~ smaller_or_equal(zero,sigma)
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( fragile_position(sk3) )],[lemma_10_46,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ smaller(zero,sigma)
| smaller_or_equal(zero,sigma) ),
inference(subst,[],[definition_smaller_or_equal_2:[bind(A,$fot(zero)),bind(B,$fot(sigma))]]) ).
cnf(refute_0_18,plain,
( ~ greater(sigma,zero)
| smaller(zero,sigma) ),
inference(subst,[],[definition_smaller_8:[bind(A,$fot(sigma)),bind(B,$fot(zero))]]) ).
cnf(refute_0_19,plain,
( ~ greater_or_equal(sigma,zero)
| sigma = zero
| greater(sigma,zero) ),
inference(subst,[],[definition_greater_or_equal_4:[bind(A,$fot(sigma)),bind(B,$fot(zero))]]) ).
cnf(refute_0_20,plain,
( sigma = zero
| greater(sigma,zero) ),
inference(resolve,[$cnf( greater_or_equal(sigma,zero) )],[lemma_10_44,refute_0_19]) ).
cnf(refute_0_21,plain,
( sigma = zero
| smaller(zero,sigma) ),
inference(resolve,[$cnf( greater(sigma,zero) )],[refute_0_20,refute_0_18]) ).
cnf(refute_0_22,plain,
( sigma = zero
| smaller_or_equal(zero,sigma) ),
inference(resolve,[$cnf( smaller(zero,sigma) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
( sigma = zero
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(zero,sigma) )],[refute_0_22,refute_0_16]) ).
cnf(refute_0_24,plain,
( sigma = zero
| tau = zero ),
inference(resolve,[$cnf( positional_advantage(sk3,sk4) )],[refute_0_23,refute_0_12]) ).
cnf(refute_0_25,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_26,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( sigma != zero
| zero = sigma ),
inference(subst,[],[refute_0_27:[bind(X,$fot(sigma)),bind(Y,$fot(zero))]]) ).
cnf(refute_0_29,plain,
( tau = zero
| zero = sigma ),
inference(resolve,[$cnf( $equal(sigma,zero) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( zero != sigma
| ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(zero,sigma) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(zero,sigma) ),[0],$fot(sigma)]]) ).
cnf(refute_0_31,plain,
( ~ smaller_or_equal(sigma,sigma)
| tau = zero
| smaller_or_equal(zero,sigma) ),
inference(resolve,[$cnf( $equal(zero,sigma) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ smaller_or_equal(sigma,sigma)
| tau = zero
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(zero,sigma) )],[refute_0_31,refute_0_16]) ).
cnf(refute_0_33,plain,
( B != B
| smaller_or_equal(B,B) ),
inference(subst,[],[definition_smaller_or_equal_3:[bind(A,$fot(B))]]) ).
cnf(refute_0_34,plain,
B = B,
introduced(tautology,[refl,[$fot(B)]]) ).
cnf(refute_0_35,plain,
smaller_or_equal(B,B),
inference(resolve,[$cnf( $equal(B,B) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
smaller_or_equal(sigma,sigma),
inference(subst,[],[refute_0_35:[bind(B,$fot(sigma))]]) ).
cnf(refute_0_37,plain,
( tau = zero
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(sigma,sigma) )],[refute_0_36,refute_0_32]) ).
cnf(refute_0_38,plain,
tau = zero,
inference(resolve,[$cnf( positional_advantage(sk3,sk4) )],[refute_0_37,refute_0_12]) ).
cnf(refute_0_39,plain,
( tau != zero
| zero = tau ),
inference(subst,[],[refute_0_27:[bind(X,$fot(tau)),bind(Y,$fot(zero))]]) ).
cnf(refute_0_40,plain,
zero = tau,
inference(resolve,[$cnf( $equal(tau,zero) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( age(sk3,sk4) != zero
| zero != tau
| age(sk3,sk4) = tau ),
introduced(tautology,[equality,[$cnf( ~ $equal(age(sk3,sk4),tau) ),[0],$fot(zero)]]) ).
cnf(refute_0_42,plain,
( age(sk3,sk4) != zero
| age(sk3,sk4) = tau ),
inference(resolve,[$cnf( $equal(zero,tau) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
age(sk3,sk4) = tau,
inference(resolve,[$cnf( $equal(age(sk3,sk4),zero) )],[lemma_10_43,refute_0_42]) ).
cnf(refute_0_44,plain,
( age(sk3,sk4) != tau
| ~ smaller_or_equal(tau,sigma)
| smaller_or_equal(age(sk3,sk4),sigma) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(sk3,sk4),sigma) ),[0],$fot(tau)]]) ).
cnf(refute_0_45,plain,
( ~ smaller_or_equal(tau,sigma)
| smaller_or_equal(age(sk3,sk4),sigma) ),
inference(resolve,[$cnf( $equal(age(sk3,sk4),tau) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ fragile_position(sk3)
| ~ smaller_or_equal(tau,sigma)
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk3,sk4),sigma) )],[refute_0_45,refute_0_0]) ).
cnf(refute_0_47,plain,
( ~ smaller_or_equal(tau,sigma)
| positional_advantage(sk3,sk4) ),
inference(resolve,[$cnf( fragile_position(sk3) )],[lemma_10_46,refute_0_46]) ).
cnf(refute_0_48,plain,
( age(sk3,sk4) != tau
| ~ smaller_or_equal(tau,tau)
| smaller_or_equal(age(sk3,sk4),tau) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(age(sk3,sk4),tau) ),[0],$fot(tau)]]) ).
cnf(refute_0_49,plain,
( ~ smaller_or_equal(tau,tau)
| smaller_or_equal(age(sk3,sk4),tau) ),
inference(resolve,[$cnf( $equal(age(sk3,sk4),tau) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ positional_advantage(sk3,sk4)
| ~ robust_position(sk3)
| ~ smaller_or_equal(tau,tau) ),
inference(resolve,[$cnf( smaller_or_equal(age(sk3,sk4),tau) )],[refute_0_49,refute_0_7]) ).
cnf(refute_0_51,plain,
( ~ positional_advantage(sk3,sk4)
| ~ smaller_or_equal(tau,tau) ),
inference(resolve,[$cnf( robust_position(sk3) )],[lemma_10_47,refute_0_50]) ).
cnf(refute_0_52,plain,
smaller_or_equal(tau,tau),
inference(subst,[],[refute_0_35:[bind(B,$fot(tau))]]) ).
cnf(refute_0_53,plain,
~ positional_advantage(sk3,sk4),
inference(resolve,[$cnf( smaller_or_equal(tau,tau) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
~ smaller_or_equal(tau,sigma),
inference(resolve,[$cnf( positional_advantage(sk3,sk4) )],[refute_0_47,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ smaller(tau,sigma)
| smaller_or_equal(tau,sigma) ),
inference(subst,[],[definition_smaller_or_equal_2:[bind(A,$fot(tau)),bind(B,$fot(sigma))]]) ).
cnf(refute_0_56,plain,
( sigma != zero
| zero != tau
| sigma = tau ),
introduced(tautology,[equality,[$cnf( ~ $equal(sigma,tau) ),[0],$fot(zero)]]) ).
cnf(refute_0_57,plain,
( sigma != zero
| sigma = tau ),
inference(resolve,[$cnf( $equal(zero,tau) )],[refute_0_40,refute_0_56]) ).
cnf(refute_0_58,plain,
( sigma = tau
| smaller(zero,sigma) ),
inference(resolve,[$cnf( $equal(sigma,zero) )],[refute_0_21,refute_0_57]) ).
cnf(refute_0_59,plain,
( zero != tau
| ~ smaller(zero,sigma)
| smaller(tau,sigma) ),
introduced(tautology,[equality,[$cnf( smaller(zero,sigma) ),[0],$fot(tau)]]) ).
cnf(refute_0_60,plain,
( ~ smaller(zero,sigma)
| smaller(tau,sigma) ),
inference(resolve,[$cnf( $equal(zero,tau) )],[refute_0_40,refute_0_59]) ).
cnf(refute_0_61,plain,
( sigma = tau
| smaller(tau,sigma) ),
inference(resolve,[$cnf( smaller(zero,sigma) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
( sigma = tau
| smaller_or_equal(tau,sigma) ),
inference(resolve,[$cnf( smaller(tau,sigma) )],[refute_0_61,refute_0_55]) ).
cnf(refute_0_63,plain,
sigma = tau,
inference(resolve,[$cnf( smaller_or_equal(tau,sigma) )],[refute_0_62,refute_0_54]) ).
cnf(refute_0_64,plain,
( sigma != tau
| tau = sigma ),
inference(subst,[],[refute_0_27:[bind(X,$fot(sigma)),bind(Y,$fot(tau))]]) ).
cnf(refute_0_65,plain,
tau = sigma,
inference(resolve,[$cnf( $equal(sigma,tau) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( tau != sigma
| ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(tau,sigma) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(tau,sigma) ),[0],$fot(sigma)]]) ).
cnf(refute_0_67,plain,
( ~ smaller_or_equal(sigma,sigma)
| smaller_or_equal(tau,sigma) ),
inference(resolve,[$cnf( $equal(tau,sigma) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
~ smaller_or_equal(sigma,sigma),
inference(resolve,[$cnf( smaller_or_equal(tau,sigma) )],[refute_0_67,refute_0_54]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( smaller_or_equal(sigma,sigma) )],[refute_0_36,refute_0_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : MGT058-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:09:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------