TSTP Solution File: MGT020+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT020+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 22:18:53 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of formulae : 105 ( 19 unt; 0 def)
% Number of atoms : 301 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 347 ( 151 ~; 162 |; 20 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ).
fof(mp_earliest_time_point,axiom,
! [E,T] :
( environment(E)
=> ( ( in_environment(E,initial_FM_EP(E))
=> subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
& ( subpopulations(first_movers,efficient_producers,E,T)
=> greater_or_equal(T,initial_FM_EP(E)) ) ) ) ).
fof(mp_positive_function_difference,axiom,
! [E,T,T1,T2] :
( ( environment(E)
& greater_or_equal(T,T1)
& greater_or_equal(T2,T)
& subpopulations(first_movers,efficient_producers,E,T2)
& greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
=> greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ) ).
fof(mp_time_point_occurs,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ) ).
fof(mp_initial_time,axiom,
! [E] :
( environment(E)
=> greater_or_equal(initial_FM_EP(E),start_time(E)) ) ).
fof(mp_times_in_order,axiom,
! [E,T1,T2] :
( ( environment(E)
& greater_or_equal(T1,start_time(E))
& greater(T2,T1)
& in_environment(E,T2) )
=> in_environment(E,T1) ) ).
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
=> ( greater(X,Y)
| X = Y ) ) ).
fof(a8,hypothesis,
! [E] :
( environment(E)
=> greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ) ).
fof(prove_l2,conjecture,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ) ).
fof(subgoal_0,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
inference(strip,[],[prove_l2]) ).
fof(negate_0_0,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E,T] :
( ~ greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))
& environment(E)
& subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))
& environment(skolemFOFtoCNF_E)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E] :
( ~ environment(E)
| greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
inference(canonicalize,[],[a8]) ).
fof(normalize_0_4,plain,
! [E] :
( ~ environment(E)
| greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [E] :
( ~ environment(E)
| ( ( ~ in_environment(E,initial_FM_EP(E))
| subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
& ! [T] :
( ~ subpopulations(first_movers,efficient_producers,E,T)
| greater_or_equal(T,initial_FM_EP(E)) ) ) ),
inference(canonicalize,[],[mp_earliest_time_point]) ).
fof(normalize_0_6,plain,
! [E] :
( ~ environment(E)
| ( ( ~ in_environment(E,initial_FM_EP(E))
| subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
& ! [T] :
( ~ subpopulations(first_movers,efficient_producers,E,T)
| greater_or_equal(T,initial_FM_EP(E)) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [E,T] :
( ( ~ environment(E)
| ~ in_environment(E,initial_FM_EP(E))
| subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
& ( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater_or_equal(T,initial_FM_EP(E)) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [E] :
( ~ environment(E)
| ~ in_environment(E,initial_FM_EP(E))
| subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(canonicalize,[],[mp_greater_or_equal]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater_or_equal(T,initial_FM_EP(E)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_13,plain,
! [E] :
( ~ environment(E)
| greater_or_equal(initial_FM_EP(E),start_time(E)) ),
inference(canonicalize,[],[mp_initial_time]) ).
fof(normalize_0_14,plain,
! [E] :
( ~ environment(E)
| greater_or_equal(initial_FM_EP(E),start_time(E)) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [E,T1,T2] :
( ~ environment(E)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ in_environment(E,T2)
| in_environment(E,T1) ),
inference(canonicalize,[],[mp_times_in_order]) ).
fof(normalize_0_16,plain,
! [E,T1,T2] :
( ~ environment(E)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ in_environment(E,T2)
| in_environment(E,T1) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| in_environment(E,T) ),
inference(canonicalize,[],[mp_time_point_occurs]) ).
fof(normalize_0_18,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| in_environment(E,T) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[l3]) ).
fof(normalize_0_20,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [E,T,T1,T2] :
( ~ environment(E)
| ~ greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
| ~ greater_or_equal(T,T1)
| ~ greater_or_equal(T2,T)
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ),
inference(canonicalize,[],[mp_positive_function_difference]) ).
fof(normalize_0_22,plain,
! [E,T,T1,T2] :
( ~ environment(E)
| ~ greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
| ~ greater_or_equal(T,T1)
| ~ greater_or_equal(T2,T)
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
~ greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ environment(E)
| greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ environment(skolemFOFtoCNF_E)
| greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_3,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ environment(E)
| ~ in_environment(E,initial_FM_EP(E))
| subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E))
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_4:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_6,plain,
( ~ greater_or_equal(X,Y)
| X = Y
| greater(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E))
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_T)),bind(Y,$fot(initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_8,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| greater_or_equal(T,initial_FM_EP(E)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_9:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_11,plain,
( ~ environment(skolemFOFtoCNF_E)
| greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| greater(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_12,refute_0_7]) ).
cnf(refute_0_14,plain,
( ~ environment(E)
| greater_or_equal(initial_FM_EP(E),start_time(E)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
( ~ environment(skolemFOFtoCNF_E)
| greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),start_time(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_14:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_16,plain,
greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),start_time(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ environment(E)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ in_environment(E,T2)
| in_environment(E,T1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_18,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(X_22,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),start_time(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,X_22)
| in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_17:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T1,$fot(initial_FM_EP(skolemFOFtoCNF_E))),bind(T2,$fot(X_22))]]) ).
cnf(refute_0_19,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(X_22,initial_FM_EP(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,X_22)
| in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),start_time(skolemFOFtoCNF_E)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ greater(X_22,initial_FM_EP(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,X_22)
| in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ greater(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E))
| ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_20:[bind(X_22,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_22,plain,
( ~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( greater(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| in_environment(E,T) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_24,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_23:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_25,plain,
( ~ environment(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_25]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
( ~ environment(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_27,refute_0_5]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_31,plain,
( ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))))
| ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_30:[bind(T,$fot(initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_32,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E))
| greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_9:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_33,plain,
( ~ environment(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),initial_FM_EP(skolemFOFtoCNF_E)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ environment(E)
| ~ greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
| ~ greater_or_equal(T,T1)
| ~ greater_or_equal(T2,T)
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_36,plain,
( ~ environment(X_45)
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))
| ~ greater_or_equal(X_46,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(X_48,X_46)
| ~ subpopulations(first_movers,efficient_producers,X_45,X_48)
| decreases(difference(disbanding_rate(first_movers,X_46),disbanding_rate(efficient_producers,X_46)))
| greater(disbanding_rate(first_movers,X_48),disbanding_rate(efficient_producers,X_48)) ),
inference(subst,[],[refute_0_35:[bind(E,$fot(X_45)),bind(T,$fot(X_46)),bind(T1,$fot(initial_FM_EP(skolemFOFtoCNF_E))),bind(T2,$fot(X_48))]]) ).
cnf(refute_0_37,plain,
( ~ environment(X_45)
| ~ greater_or_equal(X_46,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(X_48,X_46)
| ~ subpopulations(first_movers,efficient_producers,X_45,X_48)
| decreases(difference(disbanding_rate(first_movers,X_46),disbanding_rate(efficient_producers,X_46)))
| greater(disbanding_rate(first_movers,X_48),disbanding_rate(efficient_producers,X_48)) ),
inference(resolve,[$cnf( greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) )],[refute_0_3,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(X_50,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(skolemFOFtoCNF_T,X_50)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| decreases(difference(disbanding_rate(first_movers,X_50),disbanding_rate(efficient_producers,X_50)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(subst,[],[refute_0_37:[bind(X_45,$fot(skolemFOFtoCNF_E)),bind(X_46,$fot(X_50)),bind(X_48,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_39,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater_or_equal(X_50,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(skolemFOFtoCNF_T,X_50)
| decreases(difference(disbanding_rate(first_movers,X_50),disbanding_rate(efficient_producers,X_50)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_8,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ greater_or_equal(X_50,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(skolemFOFtoCNF_T,X_50)
| decreases(difference(disbanding_rate(first_movers,X_50),disbanding_rate(efficient_producers,X_50)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_39]) ).
cnf(refute_0_41,plain,
~ greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_42,plain,
( ~ greater_or_equal(X_50,initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(skolemFOFtoCNF_T,X_50)
| decreases(difference(disbanding_rate(first_movers,X_50),disbanding_rate(efficient_producers,X_50))) ),
inference(resolve,[$cnf( greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),initial_FM_EP(skolemFOFtoCNF_E))
| ~ greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))) ),
inference(subst,[],[refute_0_42:[bind(X_50,$fot(initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_44,plain,
( ~ greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E))
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( greater_or_equal(initial_FM_EP(skolemFOFtoCNF_E),initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_34,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E)
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))) ),
inference(resolve,[$cnf( greater_or_equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_12,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,initial_FM_EP(skolemFOFtoCNF_E))
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))) )],[refute_0_45,refute_0_31]) ).
cnf(refute_0_47,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E))
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_46:[bind(E,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_48,plain,
( ~ environment(skolemFOFtoCNF_E)
| skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_29,refute_0_47]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_T = initial_FM_EP(skolemFOFtoCNF_E),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_0,refute_0_48]) ).
cnf(refute_0_50,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_51,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_52,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_T != initial_FM_EP(skolemFOFtoCNF_E)
| initial_FM_EP(skolemFOFtoCNF_E) = skolemFOFtoCNF_T ),
inference(subst,[],[refute_0_52:[bind(X0,$fot(skolemFOFtoCNF_T)),bind(Y0,$fot(initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_54,plain,
initial_FM_EP(skolemFOFtoCNF_E) = skolemFOFtoCNF_T,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_T,initial_FM_EP(skolemFOFtoCNF_E)) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),
introduced(tautology,[refl,[$fot(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_56,plain,
( disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)) != disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E))
| initial_FM_EP(skolemFOFtoCNF_E) != skolemFOFtoCNF_T
| disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(first_movers,skolemFOFtoCNF_T) ),
introduced(tautology,[equality,[$cnf( $equal(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E))) ),[1,1],$fot(skolemFOFtoCNF_T)]]) ).
cnf(refute_0_57,plain,
( initial_FM_EP(skolemFOFtoCNF_E) != skolemFOFtoCNF_T
| disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(first_movers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( $equal(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(first_movers,skolemFOFtoCNF_T),
inference(resolve,[$cnf( $equal(initial_FM_EP(skolemFOFtoCNF_E),skolemFOFtoCNF_T) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
( disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)) != disbanding_rate(first_movers,skolemFOFtoCNF_T)
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) ),
introduced(tautology,[equality,[$cnf( greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) ),[0],$fot(disbanding_rate(first_movers,skolemFOFtoCNF_T))]]) ).
cnf(refute_0_60,plain,
( ~ greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) ),
inference(resolve,[$cnf( $equal(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(first_movers,skolemFOFtoCNF_T)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)),
introduced(tautology,[refl,[$fot(disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_62,plain,
( disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)) != disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))
| initial_FM_EP(skolemFOFtoCNF_E) != skolemFOFtoCNF_T
| disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(efficient_producers,skolemFOFtoCNF_T) ),
introduced(tautology,[equality,[$cnf( $equal(disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) ),[1,1],$fot(skolemFOFtoCNF_T)]]) ).
cnf(refute_0_63,plain,
( initial_FM_EP(skolemFOFtoCNF_E) != skolemFOFtoCNF_T
| disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(efficient_producers,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( $equal(disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)) = disbanding_rate(efficient_producers,skolemFOFtoCNF_T),
inference(resolve,[$cnf( $equal(initial_FM_EP(skolemFOFtoCNF_E),skolemFOFtoCNF_T) )],[refute_0_54,refute_0_63]) ).
cnf(refute_0_65,plain,
( disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)) != disbanding_rate(efficient_producers,skolemFOFtoCNF_T)
| ~ greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) ),
introduced(tautology,[equality,[$cnf( greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) ),[1],$fot(disbanding_rate(efficient_producers,skolemFOFtoCNF_T))]]) ).
cnf(refute_0_66,plain,
( ~ greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( $equal(disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E)))
| greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) )],[refute_0_60,refute_0_66]) ).
cnf(refute_0_68,plain,
greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)),
inference(resolve,[$cnf( greater(disbanding_rate(first_movers,initial_FM_EP(skolemFOFtoCNF_E)),disbanding_rate(efficient_producers,initial_FM_EP(skolemFOFtoCNF_E))) )],[refute_0_3,refute_0_67]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( greater(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)) )],[refute_0_68,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT020+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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 12:43:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem 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
% 0.12/0.37
%------------------------------------------------------------------------------